By Kenneth Eriksson, Donald Estep, Claes Johnson
Applied arithmetic: physique & Soul is a arithmetic schooling reform undertaking built at Chalmers collage of expertise and encompasses a sequence of volumes and software program. this system is encouraged through the pc revolution beginning new chances of computational mathematical modeling in arithmetic, technology and engineering. It involves 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 innovations and purposes meant for undergraduate courses in engineering and technology. additional volumes current themes comparable to Dynamical platforms, Fluid Dynamics, good Mechanics and Electro-Magnetics on a sophisticated undergraduate/graduate point.
The authors are major researchers in Computational arithmetic who've written quite a few profitable books.
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Extra resources for Applied Mathematics Body and Soul, Volume 2: Integrals and Geometry in Rn
8 Globally Convergent Newton Methods . . 1 Introduction....... 4 Hooke's Law . . . . 6 Fourier's Law for Heat Flow . . 7 Newton and Rocket Propulsion . 9 Einstein's Law of Motion. 1 Introduction............... 2 Curves in IRn . . . . . . . 4 Surfaces in IRn, n ~ 3 . . . . . 5 Lipschitz Continuity . . . . . 7 The Chain Rule . . . . . . . . . 8 The Mean Value Theorem . . . . . . 12 Directional Derivatives . . . 14 Taylor's Theorem. . . . . 15 The Contraction Mapping Theorem.
5 Lipschitz Continuity . . . . . 7 The Chain Rule . . . . . . . . . 8 The Mean Value Theorem . . . . . . 12 Directional Derivatives . . . 14 Taylor's Theorem. . . . . 15 The Contraction Mapping Theorem. 18 The Implicit Function Theorem. 19 Newton's Method. . . . . 20 Differentiation Under the Integral Sign. 6 Curves/Surfaces and the Gradient Level Curves . . . . . . Local Existence of Level Curves . Level Curves and the Gradient . Level Surfaces . . . .
3 Linear Functions Are Analytic. . . . . . 4 The Function J(z) = z2 Is Analytic. . . . . 5 The Function J(z) = zn Is Analytic for n = 1,2,... 6 Rules of Differentiation. . . 7 The Function J(z) = z-n . . . . . . . 8 The Cauchy-Riemann Equations . . . . . 9 The Cauchy-Riemann Equations and the Derivative. 12 Conjugate Harmonic Functions . . . . . . 14 Curves in the Complex Plane . . . . 15 Conformal Mappings . . . . . . . 17 Inversion. . . . . . . . . .
Applied Mathematics Body and Soul, Volume 2: Integrals and Geometry in Rn by Kenneth Eriksson, Donald Estep, Claes Johnson