Calculus and Linear Algebra in Recipes Terms, phrases and numerous examples in short learning units
Have you ever cooked a 3-course meal from a recipe? That generally works out pretty well, even if you're not much of a cook. What does this have to do with mathematics? Well, you can solve a lot of math problems recipe-wise, too: Need to solve a Riccati's differential equation or the singu...
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| Otros Autores: | |
| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
2022.
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| Edición: | 1st ed |
| Colección: | Springer eBooks.
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| Acceso en línea: | Conectar con la versión electrónica |
| Ver en Universidad de Navarra: | https://innopac.unav.es/record=b47244215*spi |
Tabla de Contenidos:
- Preface
- 1 Ways of speaking, symbols and quantities
- 2 The natural, whole 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 Systems of linear equations
- 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 balancing problem
- 14 The linear balancing problem. 14 Generating systems and linear (in)dependence
- 15 Bases of vector spaces
- 16 Orthogonality I
- 17 Orthogonality II
- 18 The linear compensation problem
- 19 The QR-decomposition of a matrix
- 20 Sequences
- 21 Computation of limit values of sequences
- 22 Series
- 23 Illustrations
- 24 Power series
- 25 Limit values and continuity
- 26 Differentiation
- 27 Applications of differential calculus I
- 28 Applications of differential calculus I
- 28 Applications of differential calculus II
- 28 Applications of differential calculus I
- 28 Applications of differential calculus II. 28 Applications of differential calculus II
- 29 Polynomial and spline interpolation
- 30 Integration I
- 31 Integration II
- 32 Improper integrals
- 33 Separable and linear differential equations of the 1st order
- 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 computation of eigenvalues and eigenvectors
- 41 Quadrics
- 42 Schurz decomposition and singular value decomposition
- 43 Jordan normal form I
- 44 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 Domain integrals
- 59 The transformation formula
- 60 Areas and area integrals
- 61 Integral theorems I
- 62 Integral theorems II
- 63 General about differential equations
- 64 The exact differential equation
- 65 Systems of linear differential equations I
- 66 Systems of linear differential equations II
- 67 Systems of linear differential equations II
- 68 Boundary value problems
- 69 Basic concepts of numerics
- 70 Fixed point iteration
- 71 Iterative methods for systems of linear equations
- 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 transform I
- 77 Fourier transform II
- 78 Discrete Fourier transform
- 79 The Laplacian transform
- 80 Holomorphic functions
- 81 Complex integration
- 82 Laurent series
- 83 The residue calculus
- 84 Conformal mappings
- 85 Harmonic functions and Dirichlet's boundary value problem
- 86 Partial differential equations 1st order
- 87 Partial differential equations 2nd order - General
- 88 The Laplace or Poisson equation
- 89 The heat conduction equation
- 90 The wave equation
- 91 Solving pDGLs with Fourier and Laplace transforms
- Index.
