| | >>Link: Geometry\Arithmetic |
| | >>Link: Geometry\Functions |
| | >>Link: Geometry\Geometry |
| | >>Link: Geometry\Linear Algebra |
| | >>Link: Geometry\Differentiation |
| | >>Link: Geometry\Infinite Series |
| | >>Link: Geometry\Integral Calculus |
| | >>Link: Geometry\Differential Equations |
| | >>Link: Geometry\Calculus of Variations |
| | Linear Integral Equations |
| | >>Link: Geometry\Linear Integral Equations |
| | Algebra and Discrete Mathematics |
| | >>Link: Geometry\Algebra and Discrete Mathematics |
| | >>Link: Geometry\Functional Analysis |
| | Vector Analysis and Vector Fields |
| | >>Link: Geometry\Vector Analysis and Vector Fields |
| | >>Link: Geometry\Function Theory |
| | >>Link: Geometry\Integral Transformations |
| | Probability Theory and Mathematical Statistics |
| | >>Link: Geometry\Probability Theory and Mathematical Statistics |
| | Dynamical Systems and Chaos |
| | >>Link: Geometry\Dynamical Systems and Chaos |
| | >>Link: Geometry\Optimization |
| | >>Link: Geometry\Numerical Analysis |
| | >>Link: Geometry\Computer Algebra Systems |
| | >>Link: Page-1\Mathematics\Geometry |
| | Calculations in Right-Angled Triangles in the Plane |
| | Calculations in General Triangles in the Plane |
| | Applications in Surveying |
| | >>Link: Plane Geometry\Plane Geometry |
| | Lines and Planes in Space |
| | Solids Bounded by Curved Surfaces |
| | >>Link: Spherical Trigonometry\Spherical Trigonometry |
| | >>Link: Differential Geometry\Differential Geometry |
| | Vector Algebra and Analytical Geometry |
| | >>Link: Vector Algebra and Analytical Geometry\Vector Algebra and Analytical Geometry |
| | >>Link: Page-1\Mathematics\Arithmetic |
| | Elementary Rules for Calculations |
| | >>Link: Elementary Rules for Calculations\Elementary Rules for Calculations |
| | Definition of a Finite Series |
| | Arithmetic Mean or Arithmetic Average |
| | Geometric Mean or Geometric Average |
| | Relations Between the Means of Two Positive Values |
| | >>Link: Algebraic and Transcendental Equations\Complex Numbers |
| | Calculation with Complex Numbers |
| | Imaginary and Complex Numbers |
| | >>Link: Algebraic and Transcendental Equations\Business Mathematics |
| | Calculation of Compound Interest |
| | Calculation of Interest or Percentage |
| | Algebraic and Transcendental Equations |
| | >>Link: Algebraic and Transcendental Equations\Algebraic and Transcendental Equations |
| | Transforming Algebraic Equations to Normal Form |
| | Reducing Transcendental Equations to Algebraic Equations |
| | Equations of Degree at Most Four |
| | >>Link: Algebraic and Transcendental Equations\Inequalities |
| | Solution of Linear and Quadratic Inequalities |
| | >>Link: Page-1\Mathematics\Functions |
| | Polynomials of n-th Degree |
| | >>Link: Area Functions\Area Functions |
| | >>Link: Notion of Functions\Notion of Functions |
| | Square Root of a Linear Binomial |
| | Square Root of a Quadratic Polynomial |
| | >>Link: Trigonometric Functions (Functions of Angles)\Trigonometric Functions |
| | Inverse Trigonometric Functions |
| | >>Link: Inverse Trigonometric Functions\Inverse Trigonometric Functions |
| | Functions of Several Variables |
| | >>Link: Functions of Several Variables\Functions of Several Variables |
| | Exponential Functions and Logarithmic Functions |
| | Generalized Error Function |
| | Product of Power and Exponential Functions |
| | >>Link: Rational Functions\Rational Functions |
| | >>Link: Elementary Functions\Elementary Functions |
| | Curves of Order Three (Cubic Curves) |
| | Cartesian Folium (Folium of Descartes) |
| | Determination of Empirical Curves |
| | >>Link: Determination of Empirical Curves\Determination of Empirical Curves |
| | >>Link: Hyperbolic Functions\Hyperbolic Functions |
| | Curves of Order Four (Quartics) |
| | >>Link: Nomography\Nomography |
| | >>Link: Scales and Graph Paper\Scales and Graph Paper |
| | Common (Standard) Cycloid |
| | Prolate and Curtate Cycloids or Trochoids |
| | Prolate and Curtate Epicycloid and Hypocycloid |
| | >>Link: Page-1\Mathematics\Linear Algebra |
| | Arithmetical Operations with Matrices |
| | Rules of Calculation for Matrices |
| | Rules of Calculation for Determinants |
| | Evaluation of Determinants |
| | Systems of Linear Equations |
| | >>Link: Systems of Linear Equations\Systems of Linear Equations |
| | Eigenvalue Problems for Matrices |
| | Special Eigenvalue Problem |
| | Characteristic Polynomial |
| | Real Symmetric Matrices, Similarity Transformations |
| | Transformation of Principal Axes of Quadratic Forms |
| | Suggestions for the Numerical Calculations of Eigenvalues |
| | Singular Value Decomposition |
| | General Eigenvalue Problem |
| | Algebra and Discrete Mathematics |
| | >>Link: Page-1\Mathematics\Algebra and Discrete Mathematics |
| | Concept of SetSpecial Sets |
| | Equivalence and Order Relations |
| | >>Link: Fuzzy Logic\Fuzzy Logic |
| | Formulas in Predicate Calculus |
| | Boolean Algebras and Switch Algebra |
| | Boolean Algebras as Orderings |
| | Algorithms of Graph Theory |
| | >>Link: Algorithms of Graph Theory\Algorithms of Graph Theory |
| | >>Link: Cryptology\Cryptology |
| | >>Link: Elementary Number Theory\Elementary Number Theory |
| | Classical Algebraic Structures |
| | >>Link: Classical Algebraic Structures\Classical Algebraic Structures |
| | >>Link: Page-1\Mathematics\Differentiation |
| | Differentiation of Functions of One Variable |
| | Rules of Differentiation for Functions of One Variable |
| | Derivatives of the Elementary Functions |
| | Basic Rules of Differentiation |
| | Derivatives of Higher Order |
| | Definition of Derivatives of Higher Order |
| | Derivatives of Higher Order of some Elementary Functions |
| | Higher Derivatives of Functions Given in Parametric Form |
| | Derivatives of Higher Order of the Inverse Function |
| | Fundamental Theorems of Differential Calculus |
| | Mean Value Theorem of Differential Calculus |
| | Taylor's Theorem of Functions of One Variable |
| | Generalized Mean Value Theorem of Differential Calculus |
| | Determination of the Extreme Values and Inflection Points |
| | Necessary Conditions for the Existence of a Relative Extreme Value |
| | Relative Extreme Values of a Differentiable |
| | Determination of Absolute Extrema |
| | Determination of the Extrema of Implicit Functions |
| | Differentiation of Functions of Several Variables |
| | >>Link: Differentiation of Functions of Several Variables\Differentiation of Functions of Several Variables |
| | >>Link: Page-1\Mathematics\Infinite Series |
| | Properties of Sequences of Numbers |
| | Definition of Sequence of Numbers |
| | Monotone Sequences of Numbers |
| | Limits of Sequences of Numbers |
| | >>Link: Number Series\Number Series |
| | >>Link: Fourier Series\Fourier Series |
| | Properties of Uniformly Convergent Series |
| | Calculations with Power Series |
| | Taylor Series Expansion, Maclaurin Series |
| | >>Link: Page-1\Mathematics\Integral Calculus |
| | >>Link: Line Integrals\Line Integrals |
| | Independence of the Line Integral of the Path of Integration |
| | Line Integrals of General Type |
| | Line Integrals of the Second Type |
| | Line Integrals of the First Type |
| | >>Link: Definite Integrals\Definite Integrals |
| | >>Link: Indefinite Integrals\Indefinite Integrals |
| | Notion of the Double Integral |
| | Evaluation of the Double Integral |
| | Applications of the Double Integral |
| | Notion of the Triple Integral |
| | Evaluation of the Triple Integral |
| | Applications of the Triple Integral |
| | >>Link: Surface Integrals\Surface Integrals |
| | Surface Integral of the Second Type |
| | Surface Integral in General Form |
| | Surface Integral of the First Type |
| | >>Link: Page-1\Mathematics\Differential Equations |
| | Ordinary Differential Equations |
| | >>Link: Ordinary Differential Equations\Ordinary Differential Equations |
| | Differential Equations of Higher Order and Systems of Differential Equations |
| | First-Order Differential Equations |
| | Partial Differential Equations |
| | >>Link: Partial Differential Equations\Partial Differential Equations |
| | Non-Linear Partial Differential Equations, Solitons, Periodic Patterns and Chaos |
| | Some further Partial Differential Equations From Natural Sciences and Engineering |
| | Linear Second-Order Partial Differential Equations |
| | First-Order Partial Differential Equations |
| | >>Link: Page-1\Mathematics\Calculus of Variations |
| | Variational Problems of One Variable |
| | Simple Variational Problems and Extremal Curves |
| | Euler Differential Equation of the Variational Calculus |
| | Variational Problems with Side Conditions |
| | Variational Problems with Higher-Order Derivatives |
| | Variational Problem with Several Unknown Functions |
| | Variational Problems using Parametric Representation |
| | Variational Problems with Functions of Several Variables |
| | Simple Variational Problem |
| | More General Variational Problems |
| | Numerical Solution of Variational Problems |
| | First and Second Variation |
| | Linear Integral Equations |
| | >>Link: Page-1\Mathematics\Linear Integral Equations |
| | Introduction and Classification |
| | Fredholm Integral Equations of the Second Kind |
| | >>Link: Fredholm Integral Equations of the Second Kind\Fredholm Integral Equations of the Second Kind |
| | Fredholm Integral Equations of the First Kind |
| | Integral Equations with Degenerate Kernels |
| | Reduction of an Integral Equation into a Linear System of Equations |
| | Solution of the Homogeneous Integral Equation of the First Kind |
| | Construction of Two Special Orthonormal Systems for a Given Kernel |
| | Volterra Integral Equations |
| | Solution by Differentiation |
| | Solution of the Volterra Integral Equation of the Second Kind by Neumann Series |
| | Convolution Type Volterra Integral Equations |
| | Numerical Methods for Volterra Integral Equations of the Second Kind |
| | Singular Integral Equations |
| | Singular Integral Equation with Cauchy Kernel |
| | Formulation of the Problem |
| | Properties of Cauchy Type Integrals |
| | The Hilbert Boundary Value Problem |
| | Solution of the Hilbert Boundary Value Problem |
| | Solution of the Characteristic Integral Equation |
| | >>Link: Page-1\Mathematics\Functional Analysis |
| | Examples of Non-Linear Operators |
| | Differentiability of Non-Linear Operators |
| | Schauder's Fixed-Point Theorem |
| | Positive Non-Linear Operators |
| | Monotone Operators in Banach Spaces |
| | Some Properties of Normed Spaces |
| | Examples of Banach Spaces |
| | >>Link: Hilbert Spaces\Hilbert Spaces |
| | >>Link: Metric Spaces\Metric Spaces |
| | Compact Sets and Compact Operators |
| | >>Link: Compact Sets and Compact Operators\Compact Sets and Compact Operators |
| | Continuous Linear Operators and Functionals |
| | >>Link: Continuous Linear Operators and Functionals\Continuous Linear Operators and Functionals |
| | Measure and Lebesgue Integral |
| | >>Link: Measure and Lebesgue Integral\Measure and Lebesgue Integral |
| | >>Link: Vector Spaces\Vector Spaces |
| | Adjoint Operators in Normed Spaces |
| | Adjoint of a Bounded Operator |
| | Adjoint Operator of an Unbounded Operator |
| | Positive Definite Operators |
| | Projectors in a Hilbert Space |
| | Dynamical Systems and Chaos |
| | >>Link: Page-1\Mathematics\Dynamical Systems and Chaos |
| | Ordinary Differential Equations and Mappings |
| | >>Link: Ordinary Differential Equations and Mappings\Ordinary Differential Equations and Mappings |
| | Discrete Dynamical Systems |
| | Structural Stability (Robustness) |
| | Qualitative Theory of Ordinary Differential Equations |
| | Quantitative Description of Attractors |
| | >>Link: Quantitative Description of Attractors\Quantitative Description of Attractors |
| | Chaos in One-Dimensional Mappings |
| | Strange Attractors and Chaos |
| | Probability Measures on Attractors |
| | Bifurcation Theory and Routes to Chaos |
| | >>Link: Bifurcation Theory and Routes to Chaos\Bifurcation Theory and Routes to Chaos |
| | Bifurcations in Morse Smale Systems |
| | Vector Analysis and Vector Fields |
| | >>Link: Page-1\Mathematics\Vector Analysis and Vector Fields |
| | Basic Notions of the Theory of Vector Fields |
| | >>Link: Basic Notions of the Theory of Vector Fields\Basic Notions of the Theory of Vector Fields |
| | Differential Operators of Space |
| | >>Link: Differential Operators of Space\Differential Operators of Space |
| | Integration in Vector Fields |
| | >>Link: Integration in Vector Fields\Integration in Vector Fields |
| | Pure Rotation Field or Zero-Divergence Field |
| | Vector Fields with Point-Like Sources |
| | Coulomb Field of a Point-Like Charge |
| | Gravitational Field of a Point Mass |
| | Discrete Source Distribution |
| | Continuous Source Distribution |
| | Differential Equations of Vector Field Theory |
| | Laplace Differential Equation |
| | Poisson Differential Equation |
| | Vector Analysis and Vector Fields: |
| | >>Link: Page-1\Mathematics\Function Theory |
| | Functions of Complex Variables |
| | >>Link: Functions of Complex Variables\Functions of Complex Variables |
| | Integration in the Complex Plane |
| | >>Link: Integration in the Complex Plane\Integration in the Complex Plane |
| | Power Series Expansion of Analytic Functions |
| | >>Link: Power Series Expansion of Analytic Functions\Power Series Expansion of Analytic Functions |
| | Evaluation of Real Integrals by Complex Integrals |
| | Application of Cauchy Integral Formulas |
| | Application of the Residue Theorem |
| | Application of the Jordan Lemma |
| | Examples of the Jordan Lemma |
| | Algebraic and Elementary Transcendental Functions |
| | Elementary Transcendental Functions |
| | Description of Curves in Complex Form |
| | Relation to Elliptic Integrals |
| | >>Link: Page-1\Mathematics\Integral Transformations |
| | >>Link: Laplace Transformation\Laplace Transformation |
| | >>Link: Fourier Transformation\Fourier Transformation |
| | >>Link: Z-Transformation\Z-Transformation |
| | Notion of Integral Transformation |
| | General Definition of Integral Transformations |
| | Special Integral Transformations |
| | Linearity of Integral Transformations |
| | Integral Transformations for Functions of Several Variables |
| | Applications of Integral Transformations |
| | Discrete Wavelet Transformation |
| | Fast Wavelet Transformation |
| | Discrete Haar Wavelet Transformation |
| | Probability Theory and Mathematical Statistics |
| | >>Link: Page-1\Mathematics\Probability Theory and Mathematical Statistics |
| | Collection of the Formulas of Combinatorics |
| | >>Link: Probability Theory\Probability Theory |
| | >>Link: Mathematical Statistics\Mathematical Statistics |
| | Measurement Error and its Distribution |
| | Qualitative Characterization of Measurement Errors |
| | Density Function of the Measurement Error |
| | Quantitative Characterization of the Measurement Error |
| | Determining the Result of a Measurement with Bounds on the Error |
| | Error Estimation for Direct Measurements with the Same Accuracy |
| | Error Estimation for Direct Measurements with Different Accuracy |
| | Error Propagation and Error Analysis |
| | Gauss Error Propagation Law |
| | >>Link: Page-1\Mathematics\Optimization |
| | >>Link: Non-linear Optimization\Non-linear Optimization |
| | Penalty Function and Barrier Methods |
| | Gradient Methods for Problems with Inequality Type Constraints |
| | Methods for Unconstrained Problems |
| | Numerical Search Procedures |
| | Solution Methods for Quadratic Optimization Problems |
| | Special Non-linear Optimization Problems |
| | Formulation of the ProblemTheoretical Basis |
| | >>Link: Linear Programming\Linear Programming |
| | Formulation of the Problem and Geometrical Representation |
| | Basic Notions of Linear Programming, Normal Form |
| | Special Linear Programming Problems |
| | Discrete Dynamic Programming |
| | >>Link: Discrete Dynamic Programming\Discrete Dynamic Programming |
| | Bellman Functional Equation Method |
| | Examples of Applications of the Functional Equation Method |
| | Bellman Functional Equations |
| | Bellman Optimality Principle |
| | Examples of Discrete Decision Models |
| | Discrete Dynamic Decision Models |
| | >>Link: Page-1\Mathematics\Numerical Analysis |
| | Approximation, Computation of Adjustment, Harmonic Analysis |
| | >>Link: Approximation, Computation of Adjustment, Harmonic Analysis\Approximation, Computation of Adjustment, Harmonic Analysis |
| | Numerical Solution of Equation Systems |
| | >>Link: Numerical Solution of Equation Systems\Numerical Solution of Equation Systems |
| | Non-Linear Equation Systems |
| | Systems of Linear Equations |
| | Approximate Integration of Ordinary Differential Equations |
| | >>Link: Approximate Integration of Ordinary Differential Equations\Approximate Integration of Ordinary Differential Equations |
| | >>Link: Numerical Integration\Numerical Integration |
| | General Quadrature Formulas |
| | Interpolation Quadratures |
| | Quadrature Formulas of Gauss |
| | Approximate Integration of Partial Differential Equations |
| | Approximation by Given Functions |
| | Finite Element Method (FEM) |
| | Numerical Solution of Non-Linear Equations in a Single Unknown |
| | >>Link: Numerical Solution of Non-Linear Equations in a Single Unknown\Numerical Solution of Non-Linear Equations in a Single Unknown |
| | Solution of Polynomial Equations |
| | Representation of Curves and Surfaces with Splines |
| | >>Link: Representation of Curves and Surfaces with Splines\Representation of Curves and Surfaces with Splines |
| | Bernstein-Bezier Representation of Curves and Surfaces |
| | >>Link: Using the Computer\Using the Computer |
| | Application of Computer Algebra Systems |
| | Libraries of Numerical Methods |
| | Numerical Problems in Calculations with Computers |
| | Internal Symbol Representation |
| | >>Link: Page-1\Mathematics\Computer Algebra Systems |
| | Brief Characterization of Computer Algebra Systems |
| | Examples of Basic Application Fields |
| | Graphical Representations |
| | Programming in Computer Algebra Systems |
| | Structure of Computer Algebra Systems |
| | >>Link: Computer Mathematica\Computer Mathematica |
| | Graphics in Computer Algebra Systems |
| | >>Link: Graphics in Computer Algebra Systems\Graphics in Computer Algebra Systems |
| | Applications of Computer Algebra Systems |
| | Manipulation of Algebraic Expressions |
| | Solution of Equations and Systems of Equations |
| | Elements of Linear Algebra |
| | Differential and Integral Calculus |
| | Elementary Rules for Calculations |
| | >>Link: Geometry\Arithmetic\Elementary Rules for Calculations |
| | Reducing to the Simplest Form |
| | Determination of the Integral Rational Part |
| | Decomposition into Partial Fractions |
| | Transformations of Proportions |
| | Indirect Proof or Proof by Contradiction |
| | Powers Roots and Logarithms |
| | Algebraic Expressions in Detail |
| | Integral Rational Expressions |
| | Representation in Polynomial Form |
| | Determination of the Greatest Common Divisor of Two Polynomials |
| | Natural Integer and Rational Numbers |
| | Irrational and Transcendental Numbers |
| | Algebraic and Transcendental Equations |
| | >>Link: Geometry\Arithmetic\Algebraic and Transcendental Equations |
| | Transforming Algebraic Equations to Normal Form |
| | Systems of n Algebraic Equations |
| | Equations of Degree at Most Four |
| | Equations of Degree One (Linear Equations) |
| | Equations of Degree Two (Quadratic Equations) |
| | Equations of Degree Three (Cubic Equations) |
| | Equations of Higher Degree |
| | General Properties of Algebraic Equations |
| | Equations with Real Coefficients |
| | Reducing Transcendental Equations to Algebraic Equations |
| | Equations with Hyperbolic Functions |
| | >>Link: Geometry\Arithmetic\Business Mathematics |
| | Calculation of Interest or Percentage |
| | Calculation of Compound Interest |
| | Equal Principal Repayments |
| | Future Amount of an Ordinary Annuity |
| | Balance after n Annuity Payments |
| | >>Link: Geometry\Arithmetic\Inequalities |
| | Triangle Inequality for Real Numbers |
| | Triangle Inequality for Complex Numbers |
| | Inequalities for Absolute Values of Differences of Real and Complex Numbers |
| | Inequality for Arithmetic and Geometric Means |
| | Inequality for Arithmetic and Quadratic Means |
| | Inequalities for Different Means of Real Numbers |
| | Cauchy Schwarz Inequality |
| | Generalized Chebyshev Inequality |
| | Properties of Inequalities of Type I and II |
| | Solution of Linear and Quadratic Inequalities |
| | General Case for Inequalities of Second Degree |
| | >>Link: Geometry\Arithmetic\Complex Numbers |
| | Imaginary and Complex Numbers |
| | Equality of Complex Numbers |
| | Trigonometric Form of Complex Numbers |
| | Exponential Form of a Complex Number |
| | Conjugate Complex Numbers |
| | Calculation with Complex Numbers |
| | General Rules for the Basic Operations |
| | Taking Powers of Complex Numbers |
| | Taking of the n-th Root of a Complex Number |
| | >>Link: Geometry\Functions\Notion of Functions |
| | Definition of the Limit of a Function |
| | Definition by Limit of Sequences |
| | Cauchy Condition for Convergence |
| | Infinity as a Limit of a Function |
| | Left-Hand and Right-Hand Limit of a Function |
| | Limit of a Function as x Tends to Infinity |
| | Theorems About Limits of Functions |
| | Order of Magnitude of Functions |
| | >>Note: Order of Magnitude of Functions and Landau Order Symbols |
| | Functions of Several Variables |
| | Certain Types of Functions |
| | Representation with Even and Odd Functions |
| | Methods for Defining a Real Function |
| | Analytic Representation of a Function |
| | Notion of Continuity and Discontinuity |
| | Most Frequent Types of Discontinuities |
| | Continuity and Discontinuity of Elementary Functions |
| | Properties of Continuous Functions |
| | >>Link: Geometry\Functions\Elementary Functions |
| | Inverse Trigonometric Functions |
| | Inverse Hyperbolic Functions |
| | >>Note: Functions of Angles |
| | >>Link: Geometry\Functions\Trigonometric Functions |
| | Definition and Representation |
| | Range and Behavior of the Functions |
| | Important Formulas for Trigonometric Functions |
| | Relations Between the Trigonometric Functions of the Same Angle (Addition Theorems) |
| | Trigonometric Functions of the Sum and Difference of Two Angles |
| | Trigonometric Functions of an Integer Multiple of an Angle |
| | Trigonometric Functions of Half-Angles |
| | Sum and Difference of Two Trigonometric Functions |
| | Products of Trigonometric Functions |
| | Powers of Trigonometric Functions |
| | Description of Oscillations |
| | Formulation of the Problem |
| | Superposition of Oscillations |
| | Vector Diagram for Oscillations |
| | >>Link: Geometry\Functions\Hyperbolic Functions |
| | Definition of Hyperbolic Functions |
| | Graphical Representation of the Hyperbolic Functions |
| | Important Formulas for the Hyperbolic Functions |
| | Hyperbolic Functions of One Variable |
| | Expressing a Hyperbolic Function by Another One with the Same Argument |
| | Formulas for Negative Arguments |
| | Hyperbolic Functions of the Sum and Difference of Two Arguments |
| | Hyperbolic Functions of Double Arguments |
| | De Moivre Formula for Hyperbolic Functions |
| | Hyperbolic Functions of Half-Argument |
| | Sum and Difference of Hyperbolic Functions |
| | Relation Between Hyperbolic and Trigonometric Functions with Complex Arguments z |
| | >>Link: Geometry\Functions\Area Functions |
| | Determination of Area Functions Using Natural Logarithm |
| | Relations Between Different Area Functions |
| | Sum and Difference of Area Functions |
| | Formulas for Negative Arguments |
| | Determination of Empirical Curves |
| | >>Link: Geometry\Functions\Determination of Empirical Curves |
| | Determination of Parameters |
| | Useful Empirical Formulas |
| | Square Root of a Quadratic Polynomial |
| | Curve of Order Three, Type II |
| | Curve of Order Three, Type III |
| | Curve of Order Three, Type I |
| | Product of Power and Exponential Functions |
| | Functions of Several Variables |
| | >>Link: Geometry\Functions\Functions of Several Variables |
| | Definition and Representation |
| | Representation of Functions of Several Variables |
| | Geometric Representation of Functions of Several Variables |
| | Different Domains in the Plane |
| | Three or Multidimensional Domains |
| | Methods to Determine a Function |
| | Various Ways to Define a Function |
| | Properties of Continuous Functions |
| | Theorem on Zeros of Bolzano |
| | Intermediate Value Theorem |
| | Theorem about the Boundedness of a Function |
| | >>Note: About the Existence of Maximum and Minimum |
| | Generalization for Several Variables |
| | >>Link: Geometry\Functions\Nomography |
| | Alignment Charts with Three Straight-Line Scales Through a Point |
| | Alignment Charts with Two Parallel and One Inclined Straight-Line Scales |
| | Alignment Charts with Two Parallel Straight Lines and a Curved Scale |
| | Net Charts for More Than Three Variables |
| | >>Link: Geometry\Functions\Scales and Graph Paper |
| | Graph Paper with a Reciprocal Scale |
| | Inverse Trigonometric Functions |
| | >>Link: Geometry\Functions\Inverse Trigonometric Functions |
| | Definition of the Inverse Trigonometric Functions |
| | Reduction to the Principal Value |
| | Relations Between the Principal Values |
| | Formulas for Negative Arguments |
| | Sum and Difference of arcsin x and arcsin y |
| | Sum and Difference of arccos x and arccos y |
| | Sum and Difference of arctan x and arctan y |
| | Special Relations for arcsin x arccos x, arctan x |
| | >>Link: Geometry\Functions\Rational Functions |
| | Special Fractional Linear Function (Inverse Proportionality) |
| | Linear Fractional Function |
| | >>Link: Geometry\Geometry\Plane Geometry |
| | Angle Between Two Intersecting Lines |
| | Pairs of Angles with Intersecting Parallels |
| | Angles Measured in Degrees and in Radians |
| | Geometrical Definition of Circular and Hyperbolic Functions |
| | Definition of Circular or Trigonometric Functions |
| | Definitions of the Hyperbolic Functions |
| | Statements about Plane Triangles |
| | Circumscribing Quadrangle |
| | Some Regular Convex Polygons |
| | The Circle and Related Shapes |
| | >>Link: Geometry\Geometry\Spherical Trigonometry |
| | Basic Concepts of Geometry on the Sphere |
| | Curve, Arcand Angle on the Sphere |
| | Special Coordinate Systems |
| | Spherical Lune or Biangle |
| | Euler Triangles and Non-Euler Triangles |
| | Basic Properties of Spherical Triangles |
| | Fundamental Formulas and Applications |
| | Calculation of Spherical Triangles |
| | Basic ProblemsAccuracy Observations |
| | Right-Angled Spherical Triangles |
| | Spherical Triangles with Oblique Angles |
| | Vector Algebra and Analytical Geometry |
| | >>Link: Geometry\Geometry\Vector Algebra and Analytical Geometry |
| | Analytical Geometry of the Plane |
| | Coordinate Systems in the Plane |
| | Coordinate Transformations |
| | Special Notation in the Plane |
| | Quadratic Curves (Curves of Second Order or Conic Sections) |
| | Analytical Geometry of Space |
| | Transformation of Orthogonal Coordinates |
| | Special Quantities in Space |
| | Surfaces of Second Order or Quadratic Surfaces, General Theory |
| | Spatial Coordinate Systems |
| | Combination of Vector Products |
| | Covariant and Contravariant Coordinates of a Vector |
| | Geometric Applications of Vector Algebra |
| | Calculation Rules for Vectors |
| | Scalar Product and Vector Product |
| | >>Link: Geometry\Geometry\Differential Geometry |
| | Ways to Define a Plane Curve |
| | Local Elements of a Curve |
| | Special Points of a Curve |
| | General Discussion of a Curve Given by an Equation |
| | Envelope of a Family of Curves |
| | Ways to Define a Space Curve |
| | Tangent Plane and Surface Normal |
| | Line Elements of a Surface |
| | Ruled Surfaces and Developable Surfaces |
| | Geodesic Lines on a Surface |
| | Systems of Linear Equations |
| | >>Link: Geometry\Linear Algebra\Systems of Linear Equations |
| | Calculation of the Inverse of a Matrix |
| | Solution of Systems of Linear Equations |
| | Definition and Solvability |
| | Overdetermined Linear Equation Systems |
| | Overdetermined Linear Systems of Equations and Linear Mean Square Value Problems |
| | Suggestions for Numerical Solutions of Mean Square Value Problems |
| | >>Link: Geometry\Linear Algebra\Tensors |
| | Transformation of Coordinate Systems |
| | Tensors in Cartesian Coordinates |
| | Tensors with Special Properties |
| | Tensors in Curvilinear Coordinate Systems |
| | Covariant and Contravariant Basis Vectors |
| | Covariant and Contravariant Coordinates of Tensors of Rank 1 |
| | Covariant, Contravariant and Mixed Coordinates of Tensors of Rank 2 |
| | Symmetry with Respect to the Origin |
| | Introduction to the Notion of Pseudotensors |
| | Differentiation of Functions of Several Variables |
| | >>Link: Geometry\Differentiation\Differentiation of Functions of Several Variables |
| | Partial Derivative of a Function |
| | Geometrical Meaning for Functions of Two Variables |
| | Differentials of x and f(x) |
| | Basic Properties of the Differential |
| | Total Differential and Differentials of Higher Order |
| | Notion of Total Differential of a Function of Several Variables |
| | >>Note: Complete Differential |
| | Derivatives and Differentials of Higher Order |
| | Taylor's Theorem for Functions of Several Variables |
| | Rules of Differentiation for Functions of Several Variables |
| | Differentiation of Composite Functions |
| | Differentiation of Implicit Functions |
| | Substitution of Variables in Differential Expressions and Coordinate Transformations |
| | Function of Two Variables |
| | Extreme Values of Functions of Several Variables |
| | Determination of Extreme Values of Functions of Two Variables |
| | Determination of the Extreme Values of a Function of n Variables |
| | Solution of Approximation Problems |
| | Extreme Value Problem with Side Conditions |
| | >>Link: Geometry\Infinite Series\Number Series |
| | General Convergence Theorems |
| | Convergence and Divergence of Infinite Series |
| | General Theorems about the Convergence of Series |
| | Convergence Criteria for Series with Positive Terms |
| | Absolute and Conditional Convergence |
| | Properties of Absolutely Convergent Series |
| | The Values of Some Important Number Series |
| | Bernoulli and Euler Numbers |
| | Estimation of the Remainder |
| | Alternating Convergent Series |
| | >>Link: Geometry\Infinite Series\Fourier Series |
| | Trigonometric Sum and Fourier Series |
| | Most Important Properties of the Fourier Series |
| | Determination of Coefficients for Symmetric Functions |
| | Different Kinds of Symmetries |
| | Forms of the Expansion into a Fourier Series |
| | Determination of the Fourier Coefficients with Numerical Methods |
| | Fourier Series and Fourier Integrals |
| | Remarks on the Table of Some Fourier Expansions |
| | >>Link: Geometry\Integral Calculus\Definite Integrals |
| | Basic Notions, Rules and Theorems |
| | Definition and Existence of the Definite Integral |
| | Properties of Definite Integrals |
| | Further Theorems about the Limits of Integration |
| | Evaluation of the Definite Integral |
| | Application of Definite Integrals |
| | General Principles for Application of the Definite Integral |
| | Applications in Mechanics and Physics |
| | Improper Integrals, Stieltjes and Lebesgue Integrals |
| | Generalization of the Notion of the Integral |
| | Integrals with Infinite Integration Limits |
| | Integrals with Unbounded Integrand |
| | Definition of Parametric Integrals |
| | Differentiation Under the Symbol of Integration |
| | Integration Under the Symbol of Integration |
| | Integration by Series Expansion, Special Non-Elementary Functions |
| | >>Link: Geometry\Integral Calculus\Indefinite Integrals |
| | Primitive Function or Antiderivative |
| | Integrals of Elementary Functions |
| | Integration of Rational Functions |
| | Integrals of Integer Rational Functions (Polynomials) |
| | Integrals of Fractional Rational Functions |
| | Four Cases of Partial Fraction Decomposition |
| | Integration of Irrational Functions |
| | Substitution to Reduce to Integration of Rational Functions |
| | Integration of Binomial Integrands |
| | Integration of Trigonometric Functions |
| | Integration of Further Transcendental Functions |
| | Integrals with Exponential Functions |
| | Integrals with Hyperbolic Functions |
| | Application of Integration by Parts |
| | Integrals of Transcendental Functions |
| | >>Link: Geometry\Integral Calculus\Line Integrals |
| | Line Integrals of the First Type |
| | Evaluation of the Line Integral of the First Type |
| | Application of the Line Integral of the First Type |
| | Line Integrals of the Second Type |
| | Calculation of the Line Integral of the Second Type |
| | Line Integrals of General Type |
| | Properties of the Line Integral of General Type |
| | Integral Along a Closed Curve |
| | Independence of the Line Integral of the Path of Integration |
| | Existence of a Primitive Function |
| | Determination of the Primitive Function |
| | Zero-Valued Integral Along a Closed Curve |
| | >>Link: Geometry\Integral Calculus\Surface Integrals |
| | Surface Integral of the First Type |
| | Notion of the Surface Integral of the First Type |
| | Evaluation of the Surface Integral of the First Type |
| | Applications of the Surface Integral of the First Type |
| | Surface Integral of the Second Type |
| | Notion of the Surface Integral of the Second Type |
| | Evaluation of Surface Integrals of the Second Type |
| | Surface Integral in General Form |
| | Notion of the Surface Integral in General Form |
| | Properties of the Surface Integrals |
| | An Application of the Surface Integral |
| | Ordinary Differential Equations |
| | >>Link: Geometry\Differential Equations\Ordinary Differential Equations |
| | First-Order Differential Equations |
| | Important Solution Methods |
| | Implicit Differential Equations |
| | Singular Integrals and Singular Points |
| | Approximation Methods for Solution of First-Order Differential Equations |
| | Differential Equations of Higher Order and Systems of Differential Equations |
| | Linear n-th Order Differential Equations |
| | Solution of Linear Differential Equations with Constant Coefficients |
| | Systems of Linear Differential Equations with Constant Coefficients |
| | Linear Second-Order Differential Equations |
| | Fundamental Properties of Eigenfunctions and Eigenvalues |
| | Expansion in Eigenfunctions |
| | Partial Differential Equations |
| | >>Link: Geometry\Differential Equations\Partial Differential Equations |
| | First-Order Partial Differential Equations |
| | Linear First-Order Partial Differential Equations |
| | Non-Linear First-Order Partial Differential Equations |
| | Linear Second-Order Partial Differential Equations |
| | Classification and Properties of Second-Order Differential Equations with Two Independent Variables |
| | Classification and Properties of Linear Second-Order Differential Equations with more than two Independent Variables |
| | Integration Methods for Linear Second-Order Partial Differential Equations |
| | Some further Partial Differential Equations From Natural Sciences and Engineering |
| | Formulation of the Problem and the Boundary Conditions |
| | Heat Conduction and Diffusion Equation for Homogeneous Media |
| | Non-Linear Partial Differential Equations, Solitons, Periodic Patterns and Chaos |
| | Formulation of the Physical-Mathematical Problem |
| | Korteweg de Vries Equation (KdV) |
| | Non-Linear Schrödinger Equation (NLS) |
| | Sine-Gordon Equation (SG) |
| | Further Non-linear Evolution Equations with Soliton Solutions |
| | Fredholm Integral Equations of the Second Kind |
| | >>Link: Geometry\Linear Integral Equations\Fredholm Integral Equations of the Second Kind |
| | Integral Equations with Degenerate Kernel |
| | Successive Approximation Method, Neumann Series |
| | Fredholm Solution Method, Fredholm Theorems |
| | Numerical Methods for Fredholm Integral Equations of the Second Kind |
| | Approximation of the Integral |
| | Classical Algebraic Structures |
| | >>Link: Geometry\Algebra and Discrete Mathematics\Classical Algebraic Structures |
| | Definition and Basic Properties |
| | Subgroups and Direct Products |
| | Particular Representations |
| | Direct Sum of Representations |
| | Direct Product of Representations |
| | Reducible and Irreducible Representations |
| | Irreducible Representations of the Symmetric Group SM |
| | Symmetry Operations, Symmetry Elements |
| | Symmetry Groups or Point Groups |
| | Symmetry Operations with Molecules |
| | Symmetry Groups in Crystallography |
| | Symmetry Groups in Quantum Mechanics |
| | Further Applications of Group Theory in Physics |
| | Finite Fields and Shift Registers |
| | Subspaces, Dimension Formula |
| | Euclidean Vector Spaces, Euclidean Norm |
| | Linear Operators in Vector Spaces |
| | >>Link: Geometry\Algebra and Discrete Mathematics\Cryptology |
| | Security of Cryptosystems |
| | Methods of Conventional Cryptography |
| | Linear Substitution Ciphers |
| | Methods of Classical Cryptanalysis |
| | Diffie-Hellman Key Exchange |
| | AES Algorithm (Advanced Encryption Standard) |
| | IDEA Algorithm (International Data Encryption Algorithm) |
| | >>Link: Geometry\Algebra and Discrete Mathematics\Fuzzy Logic |
| | Basic Notions of Fuzzy Logic |
| | Interpretation of Fuzzy Sets |
| | Membership Functions on the Real Line |
| | Aggregation of Fuzzy Sets |
| | Concepts for Aggregation of Fuzzy Sets |
| | Practical Aggregator Operations of Fuzzy Sets |
| | Fuzzy Product Relation R 0 S |
| | Fuzzy Inference (Approximate Reasoning) |
| | Knowledge-Based Fuzzy Systems |
| | Knowledge-Based Interpolation Systems |
| | Algorithms of Graph Theory |
| | >>Link: Geometry\Algebra and Discrete Mathematics\Algorithms of Graph Theory |
| | Basic Notions and Notation |
| | Traverse of Undirected Graphs |
| | >>Link: Geometry\Algebra and Discrete Mathematics\Elementary Number Theory |
| | Divisibility and Elementary Divisibility Rules |
| | Criteria for Divisibility |
| | Greatest Common Divisor and Least Common Multiple |
| | Linear Diophantine Equations |
| | Congruences and Residue Classes |
| | >>Link: Geometry\Functional Analysis\Vector Spaces |
| | Linear and Affine Linear Subsets |
| | Linearly Independent Elements |
| | Convex Subsets and the Convex Hull |
| | Linear Operators and Functionals |
| | Homomorphism and Endomorphism |
| | Complexification of Real Vector Spaces |
| | Cone and Partial Ordering |
| | >>Link: Geometry\Functional Analysis\Metric Spaces |
| | Balls, Neighborhoods and Open Sets |
| | Convergence of Sequences in Metric Spaces |
| | Dense Subsets and Separable Metric Spaces |
| | Some Fundamental Theorems in Complete Metric Spaces |
| | Some Applications of the Contraction Mapping Principle |
| | Completion of a Metric Space |
| | Compact Sets and Compact Operators |
| | >>Link: Geometry\Functional Analysis\Compact Sets and Compact Operators |
| | Compact Subsets of a Normed Space |
| | Definition of Compact Operator |
| | Properties of Linear Compact Operators |
| | Weak Convergence of Elements |
| | Compact Operators in Hilbert Space |
| | Compact Self-Adjoint Operators |
| | Continuous Linear Operators and Functionals |
| | >>Link: Geometry\Functional Analysis\Continuous Linear Operators and Functionals |
| | Boundedness, Norm and Continuity of Linear Operators |
| | Boundedness and the Norm of Linear Operators |
| | The Space of Linear Continuous Operators |
| | Convergence of Operator Sequences |
| | Linear Continuous Operators in Banach Spaces |
| | Elements of the Spectral Theory of Linear Operators |
| | Resolvent Set and the Resolvent of an Operator |
| | Continuous Linear Functionals |
| | Continuous Linear Functionals in Hilbert Spaces, Riesz Representation Theorem |
| | Continuous Linear Functionals in Lp |
| | Extension of a Linear Functional |
| | Separation of Convex Sets |
| | Second Adjoint Space and Reflexive Spaces |
| | Measure and Lebesgue Integral |
| | >>Link: Geometry\Functional Analysis\Measure and Lebesgue Integral |
| | Sigma Algebra and Measures |
| | Properties of the Class of Measurable Functions |
| | Definition of the Integral |
| | Some Properties of the Integral |
| | Formula of Partial Integration |
| | Derivative of a Distribution |
| | >>Link: Geometry\Functional Analysis\Hilbert Spaces |
| | Notion of a Hilbert Space |
| | Unitary Spaces and Some of their Properties |
| | Properties of Orthogonality |
| | Fourier Series in Hilbert Spaces |
| | Parseval Equation, Riesz-Fischer Theorem |
| | Existence of a Basis, Isomorphic Hilbert Spaces |
| | Differential Operators of Space |
| | >>Link: Geometry\Vector Analysis and Vector Fields\Differential Operators of Space |
| | Review of Spatial Differential Operations |
| | Fundamental Relations and Results |
| | Rules of Calculation for Spatial Differential Operators |
| | Expressions of Vector Analysis in Cartesian, Cylindrical and Spherical Coordinates |
| | Directional and Space Derivatives |
| | Directional Derivative of a Scalar Field |
| | Directional Derivative of a Vector Field |
| | Gradient of a Scalar Field |
| | Definition of the Gradient |
| | Gradient and Volume Derivative |
| | Gradient and Directional Derivative |
| | Further Properties of the Gradient |
| | Gradient of the Scalar Field in Different Coordinates |
| | Divergence of Vector Fields |
| | Divergence in Different Coordinates |
| | Rules for Evaluation of the Divergence |
| | Divergence of a Central Field |
| | Rotation of Vector Fields |
| | Definitions of the Rotation |
| | Rotation in Different Coordinates |
| | Rules for Evaluating the Rotation |
| | Rotation of a Potential Field |
| | Nabla Operator, Laplace Operator |
| | Nabla Operator Applied Twice |
| | Rules for Calculations with the Nabla Operator |
| | Vector Analysis and Vector Fields: |
| | Integration in Vector Fields |
| | >>Link: Geometry\Vector Analysis and Vector Fields\Integration in Vector Fields |
| | Line Integral and Potential in Vector Fields |
| | Line Integral in Vector Fields |
| | Interpretation of the Line Integral in Mechanics |
| | Properties of the Line Integral |
| | Line Integral in Cartesian Coordinates |
| | Integral Along a Closed Curve in a Vector Field |
| | Conservative or Potential Field |
| | Evaluation of the Surface Integral |
| | Surface Integrals and Flow of Fields |
| | Surface Integrals in Cartesian Coordinates as Surface Integral of Second Type |
| | Integral Theorem and Integral Formula of Gauss |
| | Integral Theorem of Stokes |
| | Integral Theorems of Green |
| | Vector Analysis and Vector Fields: |
| | Basic Notions of the Theory of Vector Fields |
| | >>Link: Geometry\Vector Analysis and Vector Fields\Basic Notions of the Theory of Vector Fields |
| | Vector Functions of a Scalar Variable |
| | Derivative of a Vector Function |
| | Rules of Differentiation for Vectors |
| | Taylor Expansion for Vector Functions |
| | Scalar Field or Scalar Point Function |
| | Important Special Cases of Scalar Fields |
| | Coordinate Definition of a Field |
| | Level Surfaces and Level Lines of a Field |
| | Vector Field or Vector Point Function |
| | Important Cases of Vector Fields |
| | Coordinate Representation of Vector Fields |
| | Transformation of Coordinate Systems |
| | Vector Analysis and Vector Fields: |
| | Functions of Complex Variables |
| | >>Link: Geometry\Function Theory\Functions of Complex Variables |
| | Continuity, Differentiability |
| | Definition of a Complex Function |
| | Limit of a Complex Function |
| | Continuous Complex Functions |
| | Differentiability of a Complex Function |
| | Definition of Analytic Functions |
| | Examples of Analytic Functions |
| | Properties of Analytic Functions |
| | Notion and Properties of Conformal Mappings |
| | Simplest Conformal Mappings |
| | The Schwarz Reflection Principle |
| | Arbitrary Mappings of the Complex Plane |
| | Power Series Expansion of Analytic Functions |
| | >>Link: Geometry\Function Theory\Power Series Expansion of Analytic Functions |
| | Convergence of Series with Complex Terms |
| | Convergence of a Number Sequence with Complex Terms |
| | Convergence of an Infinite Series with Complex Terms |
| | Power Series with Complex Terms |
| | Principle of Analytic Continuation |
| | Isolated Singular Points and the Residue Theorem |
| | Integration in the Complex Plane |
| | >>Link: Geometry\Function Theory\Integration in the Complex Plane |
| | Definite and Indefinite Integral |
| | Definition of the Integral in the Complex Plane |
| | Properties and Evaluation of Complex Integrals |
| | Cauchy Integral Theorem for Simply Connected Domains |
| | Cauchy Integral Theorem for Multiply Connected Domains |
| | Analytic Function on the Interior of a Domain |
| | Analytic Function on the Exterior of a Domain |
| | >>Link: Geometry\Integral Transformations\Laplace Transformation |
| | Properties of the Laplace Transformation |
| | Laplace Transformation, Original and Image Space |
| | Rules for the Evaluation of the Laplace Transformation |
| | Transforms of Special Functions |
| | Dirac Function and Distributions |
| | Inverse Transformation into the Original Space |
| | Inverse Transformation with the Help of Tables |
| | Partial Fraction Decomposition |
| | Solution of Differential Equations using Laplace Transformation |
| | Ordinary Linear Differential Equations with Constant Coefficients |
| | Ordinary Linear Differential Equations with Coefficients Dependingon the Variable |
| | Partial Differential Equations |
| | Integral Transformations: |
| | >>Link: Geometry\Integral Transformations\Fourier Transformation |
| | Properties of the Fourier Transformation |
| | Fourier Transformation and Inverse Transformation |
| | Rules of Calculation with the Fourier Transformation |
| | Transforms of Special Functions |
| | Solution of Differential Equations using the Fourier Transformation |
| | Ordinary Linear Differential Equations |
| | Partial Differential Equations |
| | Integral Transformations: |
| | >>Link: Geometry\Integral Transformations\Z-Transformation |
| | Properties of the Z-Transformation |
| | Definition of the Z-Transformation |
| | Relation to the Laplace Transformation |
| | Inverse of the Z- Transformation |
| | Applications of the Z-Transformation |
| | General Solution of Linear Difference Equations |
| | Second-Order Difference Equations (Initial Value Problem) |
| | Second-Order Difference Equations (Boundary Value Problem) |
| | Integral Transformations: |
| | >>Link: Geometry\Probability Theory and Mathematical Statistics\Mathematical Statistics |
| | Statistic Function or Sample Function |
| | Statistic Function or Sample Function |
| | Statistical Summarization and Analysis of Given Data |
| | Goodness of Fit Test for a Normal Distribution |
| | Distribution of the Sample Mean |
| | Confidence Limits for the Mean |
| | Confidence Interval for the Variance |
| | Structure of Hypothesis Testing |
| | Correlation and Regression |
| | Linear Correlation of two Measurable Characters |
| | Linear Regression for two Measurable Characters |
| | Multidimensional Regression |
| | Example of a Monte Carlo Simulation |
| | Application of the Monte Carlo Method in Numerical Mathematics |
| | Further Applications of the Monte Carlo Method |
| | >>Link: Geometry\Probability Theory and Mathematical Statistics\Probability Theory |
| | Event, Frequency and Probability |
| | Frequencies and Probabilities |
| | Conditional Probability, Bayes Theorem |
| | Random Variables, Distribution Functions |
| | Expected Value and Variance, Chebyshev Inequality |
| | Multidimensional Random Variable |
| | Hypergeometric Distribution |
| | Standard Normal Distribution, Gaussian Error Function |
| | Logarithmic Normal Distribution |
| | c2 (Chi-Square) Distribution |
| | Law of Large Numbers, Limit Theorems |
| | Stochastic Processes and Stochastic Chains |
| | Basic Notions, Markov Chains |
| | Ordinary Differential Equations and Mappings |
| | >>Link: Geometry\Dynamical Systems and Chaos\Ordinary Differential Equations and Mappings |
| | Qualitative Theory of Ordinary Differential Equations |
| | Existence of Flows, Phase Space Structure |
| | Linear Differential Equations |
| | Topological Equivalence of Differential Equations |
| | Discrete Dynamical Systems |
| | Steady States, Periodic Orbits and Limit Sets |
| | Topological Conjugacy of Discrete Systems |
| | Structural Stability (Robustness) |
| | Structurally Stable Differential Equations |
| | Structurally Stable Discrete Systems |
| | Dynamical Systems and Chaos: |
| | Quantitative Description of Attractors |
| | >>Link: Geometry\Dynamical Systems and Chaos\Quantitative Description of Attractors |
| | Probability Measures on Attractors |
| | Elements of Ergodic Theory |
| | Dimensions Defined by Invariant Measures |
| | Local Hausdor, Dimension According to Douady and Oesterle |
| | Strange Attractors and Chaos |
| | Chaos in One-Dimensional Mappings |
| | Dynamical Systems and Chaos: |
| | Bifurcation Theory and Routes to Chaos |
| | >>Link: Geometry\Dynamical Systems and Chaos\Bifurcation Theory and Routes to Chaos |
| | Bifurcations in Morse Smale Systems |
| | Local Bifurcations in Neighborhoods of Steady States |
| | Local Bifurcations in a Neighborhood of a Periodic Orbit |
| | Cascade of Period Doublings |
| | Global Homoclinic Bifurcations |
| | Dynamical Systems and Chaos: |
| | >>Link: Geometry\Optimization\Linear Programming |
| | Formulation of the Problem and Geometrical Representation |
| | The Form of a Linear Programming Problem |
| | Examples and Graphical Solutions |
| | Basic Notions of Linear Programming, Normal Form |
| | Normal Form of the Linear Programming Problem |
| | Transition to the New Simplex Tableau |
| | Determination of an Initial Simplex Tableau |
| | Duality in Linear Programming |
| | Special Linear Programming Problems |
| | Discrete Dynamic Programming |
| | >>Link: Geometry\Optimization\Discrete Dynamic Programming |
| | Discrete Dynamic Decision Models |
| | n-Stage Decision Processes |
| | Dynamic Programming Problem |
| | Examples of Discrete Decision Models |
| | Bellman Functional Equations |
| | Properties of the Cost Function |
| | Formulation of the Functional Equations |
| | Bellman Optimality Principle |
| | Bellman Functional Equation Method |
| | Determination of Minimal Costs |
| | Determination of the Optimal Policy |
| | Examples of Applications of the Functional Equation Method |
| | Optimal Purchasing Policy |
| | >>Link: Geometry\Optimization\Non-linear Optimization |
| | Formulation of the ProblemTheoretical Basis |
| | Formulation of the Problem |
| | Special Non-linear Optimization Problems |
| | Solution Methods for Quadratic Optimization Problems |
| | Numerical Search Procedures |
| | Minimum Search in n-Dimensional Euclidean Vector Space |
| | Methods for Unconstrained Problems |
| | Method of Steepest Descent (Gradient Method) |
| | Application of the Newton Method |
| | Conjugate Gradient Methods |
| | Method of Davidon, Fletcher and Powell (DFP) |
| | Mutation-Selection-Strategy |
| | Gradient Methods for Problems with Inequality Type Constraints |
| | Method of Feasible Directions |
| | Gradient Projection Method |
| | Penalty Function and Barrier Methods |
| | Approximation, Computation of Adjustment, Harmonic Analysis |
| | >>Link: Geometry\Numerical Analysis\Approximat |
| |