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E-raamat: Calculus and Linear Algebra in Recipes: Terms, theorems and numerous examples in short learning units

  • Formaat: EPUB+DRM
  • Sari: Mathematics and Statistics
  • Ilmumisaeg: 08-Apr-2026
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783662726235
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Calculus and Linear Algebra in Recipes: Terms, theorems and numerous examples in short learning unitsSuurem pilt
  • Formaat: EPUB+DRM
  • Sari: Mathematics and Statistics
  • Ilmumisaeg: 08-Apr-2026
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783662726235
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This book provides a clear and easy-to-understand introduction to higher mathematics with numerous examples. The author shows how to solve typical problems in a recipe-like manner and divides the material into short, easily digestible learning units.



Have you ever cooked a 3-course meal based on a recipe? That generally works quite well, even if you are not a great cook. What does this have to do with mathematics? Well, you can solve a lot of math problems recipe-wise: Need to solve a Riccati's differential equation or the singular value decomposition of a matrix? Look it up in this book, you'll find a recipe for it here. Recipes are available for problems from the field of:



· Calculus in one and more variables,



· Linear algebra,



· Vector analysis,



· Theory on differential equations, ordinary and partial,



· Theory of integral transformations,



· Function theory.



Other features of this book include:



· The division of Higher Mathematics into approximately 100 chapters of roughly equal length. Each chapter covers approximately the material of a 90-minute lecture.



· Numerous exercises and solutions



· Many problems in higher mathematics can be solved with computers. We always indicate how it works with MATLAB®.



This 2nd English edition has been completely revised and numerous examples, illustrations, explanations and further exercises have been added.
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.
Prof. Dr. Christian Karpfinger teaches at the Technical University of Munich; in 2004 he was awarded the State Teaching Award of the Free State of Bavaria.
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