| >>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 |
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