Calculus and linear algebra in recip...
Karpfinger, Christian.

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  • Calculus and linear algebra in recipes = terms, phrases and numerous examples in short learning units /
  • 紀錄類型: 書目-電子資源 : Monograph/item
    正題名/作者: Calculus and linear algebra in recipes/ by Christian Karpfinger.
    其他題名: terms, phrases and numerous examples in short learning units /
    作者: Karpfinger, Christian.
    出版者: Berlin, Heidelberg :Springer Berlin Heidelberg : : 2022.,
    面頁冊數: xxvi, 1038 p. :ill., digital ;24 cm.
    內容註: 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.
    Contained By: Springer Nature eBook
    標題: Calculus. -
    電子資源: https://doi.org/10.1007/978-3-662-65458-3
    ISBN: 9783662654583
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