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 commencing new chances of computational mathematical modeling in arithmetic, technological know-how and engineering. It includes 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 thoughts and purposes meant for undergraduate courses in engineering and technology. extra volumes current subject matters comparable to Dynamical platforms, Fluid Dynamics, reliable Mechanics and Electro-Magnetics on a complicated undergraduate/graduate point.

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

**Read or Download Applied Mathematics: Body and Soul: Volume 2: Integrals and Geometry in IRn PDF**

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**Extra resources for Applied Mathematics: Body and Soul: Volume 2: Integrals and Geometry in IRn**

**Sample text**

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 . . .

We begin our study with the simplest kind of differential equation, which is of fundamental importance: Given the function f : I ~ lR. defined on the interval I = [a, bj, find a function u(x) on I, such that the derivative u'(x) of u(x) is equal to f(x) for x E I. K. , Applied Mathematics: Body and Soul © Springer-Verlag Berlin Heidelberg 2004 430 27. 1) for all x E I. We call the solution u(x) of the differential equation u'(x) = f (x) for x E I, a primitive function of f (x), or an integral of f (x).

1 Introduction............... 3 Warm Up II: Series . . . . . . 4 Complex Fourier Series. . . . . 6 Truncated Fourier Series and Best L 2-Approximation . 7 Real Fourier Series . . . . . . 8 Basic Properties of Fourier Coefficients . 9 The Inversion Formula. . . . 12 Different Periods . . . . . . 13 Weierstrass Functions . . . . 16 The Discrete Fourier Transform. . . . . 1 Basic Properties of the Fourier Transform . . . 3 Convolution...... 4 The Inversion Formula . .