Calculus and Linear Algebra in Recipes
portes grátis
Calculus and Linear Algebra in Recipes
Terms, theorems and numerous examples in short learning units
Karpfinger, Christian
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
04/2026
1049
Mole
Inglês
9783662726228
Pré-lançamento - envio 15 a 20 dias após a sua edição
Descrição não disponível.
Preface.- 1 Terminology, Symbols and Sets.- 2 The Natural Numbers, Integers and Rational Numbers.- 3 The Real Numbers.- 4 Machine Numbers.- 5 Polynomials.- 6 Trigonometric Functions.- 7 Complex Numbers - Cartesian Coordinates.- 8 Complex Numbers - Polar Coordinates.- 9 Linear Equation Systems.- 10 Calculating with Matrices.- 11 LR-Decomposition of a Matrix.- 12 The Determinant.- 13 Vector Spaces.- 14 Generating Systems and Linear (In-)Dependence.- 15 Bases of Vector Spaces.- 16 Orthogonality I.- 17 Orthogonality II.- 18 The Linear Least Squares Problem.- 19 The QR-Decomposition of a Matrix.- 20 Sequences.- 21 Calculation of Limits of Sequences.- 22 Series.- 23 Mappings.- 24 Power Series.- 25 Limits and Continuity.- 26 Differentiation.- 27 Applications of Differential Calculus I.-28 Applications of Differential Calculus II.- 29 Polynomial and Spline Interpolation.- 30 Integration I.- 31 Integration II.- 32 Improper Integrals.- 33 Separable and Linear First Order Differential Equations.- 34 Linear Differential Equations with Constant Coefficients.- 35 Some Special Types of Differential Equations.- 36 Numerics of Ordinary Differential Equations I.- 37 Linear Mappings and Representation Matrices.- 38 Basic Transformation.- 39 Diagonalization - Eigenvalues and Eigenvectors.- 40 Numerical Calculation of Eigenvalues and Eigenvectors.- 41 Quadrics.- 42 Schur Decomposition and Singular Value Decomposition.- 43 The Jordan Normal Form I.- 44 The Jordan Normal Form II.- 45 Definiteness and Matrix Norms.- 46 Functions of Several Variables.- 47 Partial Differentiation - Gradient, Hessian Matrix, Jacobian Matrix.- 48 Applications of Partial Derivatives.- 49 Determination of Extreme Values.- 50 Determination of Extreme Values under Constraints.- 51 Total Differentiation, Differential Operators.- 52 Implicit Functions.- 53 Coordinate Transformations.- 54 Curves I.- 55 Curves II.- 56 Curve Integrals.- 57 Gradient Fields.- 58 Area Integrals.- 59 The Transformation Formula.- 60 Surfaces and Surface Integrals.- 61 Integral Theorems I.- 62 Integral Theorems II.- 63 Generalities on Differential Equations.- 64 The Exact Differential Equation.- 65 Linear Differential Equations Systems I.- 66 Linear Differential Equations Systems II.- 67 Linear Differential Equations Systems III.- 68 Boundary Value Problems.- 69 Basic Concepts of Numerics.- 70 Fixed Point Iteration.- 71 Iterative Methods for Linear Equation Systems.- 72 Optimization.- 73 Numerics of Ordinary Differential Equations II.- 74 Fourier Series - Calculation of Fourier Coefficients.- 75 Fourier Series - Background, Theorems and Application.- 76 Fourier Transformation I.- 77 Fourier Transformation II.- 78 Discrete Fourier Transformation.- 79 The Laplace Transformation.- 80 Holomorphic Functions.- 81 Complex Integration.- 82 Laurent Series.- 83 The Residue Calculus.- 84 Conformal Mappings.- 85 Harmonic Functions and the Dirichlet Boundary Value Problem.- 86 First Order Partial Differential Equations.- 87 Second Order Partial Differential Equations - General.- 88 The Laplace or Poisson Equation.- 89 The Heat Conduction Equation.- 90 The Wave Equation.- 91 Solving pDEs with Fourier- and Laplace Transformations.- Index.
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Analysis;Differential equations;Engineering Mathematics;MATLAB;Mathematics for user;Numerics;Exam preparation;linear algebra
Preface.- 1 Terminology, Symbols and Sets.- 2 The Natural Numbers, Integers and Rational Numbers.- 3 The Real Numbers.- 4 Machine Numbers.- 5 Polynomials.- 6 Trigonometric Functions.- 7 Complex Numbers - Cartesian Coordinates.- 8 Complex Numbers - Polar Coordinates.- 9 Linear Equation Systems.- 10 Calculating with Matrices.- 11 LR-Decomposition of a Matrix.- 12 The Determinant.- 13 Vector Spaces.- 14 Generating Systems and Linear (In-)Dependence.- 15 Bases of Vector Spaces.- 16 Orthogonality I.- 17 Orthogonality II.- 18 The Linear Least Squares Problem.- 19 The QR-Decomposition of a Matrix.- 20 Sequences.- 21 Calculation of Limits of Sequences.- 22 Series.- 23 Mappings.- 24 Power Series.- 25 Limits and Continuity.- 26 Differentiation.- 27 Applications of Differential Calculus I.-28 Applications of Differential Calculus II.- 29 Polynomial and Spline Interpolation.- 30 Integration I.- 31 Integration II.- 32 Improper Integrals.- 33 Separable and Linear First Order Differential Equations.- 34 Linear Differential Equations with Constant Coefficients.- 35 Some Special Types of Differential Equations.- 36 Numerics of Ordinary Differential Equations I.- 37 Linear Mappings and Representation Matrices.- 38 Basic Transformation.- 39 Diagonalization - Eigenvalues and Eigenvectors.- 40 Numerical Calculation of Eigenvalues and Eigenvectors.- 41 Quadrics.- 42 Schur Decomposition and Singular Value Decomposition.- 43 The Jordan Normal Form I.- 44 The Jordan Normal Form II.- 45 Definiteness and Matrix Norms.- 46 Functions of Several Variables.- 47 Partial Differentiation - Gradient, Hessian Matrix, Jacobian Matrix.- 48 Applications of Partial Derivatives.- 49 Determination of Extreme Values.- 50 Determination of Extreme Values under Constraints.- 51 Total Differentiation, Differential Operators.- 52 Implicit Functions.- 53 Coordinate Transformations.- 54 Curves I.- 55 Curves II.- 56 Curve Integrals.- 57 Gradient Fields.- 58 Area Integrals.- 59 The Transformation Formula.- 60 Surfaces and Surface Integrals.- 61 Integral Theorems I.- 62 Integral Theorems II.- 63 Generalities on Differential Equations.- 64 The Exact Differential Equation.- 65 Linear Differential Equations Systems I.- 66 Linear Differential Equations Systems II.- 67 Linear Differential Equations Systems III.- 68 Boundary Value Problems.- 69 Basic Concepts of Numerics.- 70 Fixed Point Iteration.- 71 Iterative Methods for Linear Equation Systems.- 72 Optimization.- 73 Numerics of Ordinary Differential Equations II.- 74 Fourier Series - Calculation of Fourier Coefficients.- 75 Fourier Series - Background, Theorems and Application.- 76 Fourier Transformation I.- 77 Fourier Transformation II.- 78 Discrete Fourier Transformation.- 79 The Laplace Transformation.- 80 Holomorphic Functions.- 81 Complex Integration.- 82 Laurent Series.- 83 The Residue Calculus.- 84 Conformal Mappings.- 85 Harmonic Functions and the Dirichlet Boundary Value Problem.- 86 First Order Partial Differential Equations.- 87 Second Order Partial Differential Equations - General.- 88 The Laplace or Poisson Equation.- 89 The Heat Conduction Equation.- 90 The Wave Equation.- 91 Solving pDEs with Fourier- and Laplace Transformations.- Index.
Este título pertence ao(s) assunto(s) indicados(s). Para ver outros títulos clique no assunto desejado.
