Applied Mathematics Body and Soul, Volume 1: Derivatives and by Kenneth Eriksson, Donald Estep, Claes Johnson

By Kenneth Eriksson, Donald Estep, Claes Johnson

Applied arithmetic: physique & Soul is a arithmetic schooling reform undertaking constructed at Chalmers college of know-how and features a sequence of volumes and software program. this system is influenced through the pc revolution starting new possibilitites of computational mathematical modeling in arithmetic, technology and engineering. It contains a synthesis of Mathematical research (Soul), Numerical Computation (Body) and alertness. Volumes I-III current a latest model of Calculus and Linear Algebra, together with constructive/numerical strategies and purposes meant for undergraduate courses in engineering and technology. extra volumes current issues reminiscent of Dynamical platforms, Fluid Dynamics, strong Mechanics and Electro-Magnetics on a complicated undergraduate/graduate point.

The authors are best researchers in Computational arithmetic who've written numerous profitable books.

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8 The Sampling Theorem . . 9 The Laplace Transform. . 1 Differentiability and analyticity . . . . . . . 2 The Cauchy-Riemann Equations . . . . . . 4 Conjugate Harmonic Functions . . . . . . 5 Curves in the Complex Plane . . . . . . . 7 Complex Integrals . . . . . 8 Cauchy's Theorem . . . . . 9 Cauchy's Representation Formula . 10 Taylor's Formula . . 11 The Residue Theorem . . . . 2 Convolution . . . . . 4 Parseval's Formula . . . 5 Discrete Fourier Transforms .

2 Definition of exp(z) . . . 4 de Moivres Formula . 5 Definition of log(z) .. 1 Introduction . . . 3 Rational Functions: Partial Fractions . 4 Products of Polynomial and Trigonometric or Exponential Functions . . . . . . . . 5 Combinations of Trigonometric and Root Functions . 7 Products of Polynomials and Logarithm Functions . 1 Introduction . . . . . . . . . A(x)u(x) + j(x) . . 3 The Differential Equation u"(x)- u(x) = 0 . 5 The Differential Equation I:~=O akDku(x) = f(x) .

1 Introduction . . 3 Differentiability . . 4 The Chain Rule . . 7 Taylor's Theorem . . . . 9 Inverse Function Theorem . 10 Implicit Function Theorem . 11 Newton's Method . . 13 Curve Integrals . 14 Multiple Integrals .. 15 Surface Integrals .. 17 Stokes' Theorem . . . . 4 7805 7806 Introduction 0 0 0 0 An Inverse Problem An Inverse Problem An Inverse Problem An Inverse Problem The Backward Heat Introduction 0 0 0 0 0 0 0 0 0 0 0 0 0 0 The Connection Between ~~ and ~; 80 Differential Equations Tool Bag 8001 8002 8003 1037 1038 1041 1042 1044 1047 1048 1051 1051 1052 1053 1053 1059 1060 1061 1062 1063 1065 1067 1068 1068 1070 1072 1073 1074 1074 1079 0000000000000000000 for One-Dimensional Convection for One-Dimensional Diffusion for Poisson's Equation for Laplace's Equation Equation 0 0 0 0 0 0 0 0 79 Optimal Control 7901 7902 1037 Introduction 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 The Equation u'(x) = ,\(x)u(x) 0 0 0 0 The Equation u'(x) = ,\(x)u(x) + f(x) 1079 1081 1083 1085 1088 1089 1093 1093 1095 1097 1097 1098 1098 Contents Volume 3 XLI The Differential Equation I:~=O akDku(x) = 0 The Damped Linear Oscillator .

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