By Kenneth Eriksson, Donald Estep, Claes Johnson
Applied arithmetic: physique & Soul is a arithmetic schooling reform undertaking built at Chalmers collage of know-how and features a sequence of volumes and software program. this system is stimulated by means of the pc revolution establishing new possibilitites of computational mathematical modeling in arithmetic, technology 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 options and functions meant for undergraduate courses in engineering and technology. extra volumes current issues resembling Dynamical structures, 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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Extra info for Applied Mathematics Body and Soul, Volume 3: Calculus in Several Dimensions
1 Introduction . . . . . The Natural Numbers . . 3 Is There a Largest Natural Number? 4 The Set N of All Natural Numbers . 5 Integers................ 6 Absolute Value and the Distance Between Numbers . 7 Division with Remainder . . . . 8 Factorization into Prime Factors .. 1 Induction . . . . . . . 1 Introduction .. 2 How to Construct the Rational Numbers . 3 On the Need for Rational Numbers . . 6 Set Notation . . . . . . . . . The Set Ql of All Rational Numbers . . 8 The Rational Number Line and Intervals .
1 Introduction..................... 4 The Exponential Function exp(x) for x E IR . . 5 An Important Property of exp(x) . . . . . 6 The Inverse of the Exponential is the Logarithm 31. 7 The Function a X with a > 0 and x E IR . . . 1 The Defining Differential Equation . 2 Trigonometrie Identities . . . . 4 Inverses of Trigonometrie Functions . 5 The Functions sinh(x) and eosh(x) . 6 The Hanging Chain. . . . . 7 Comparing u" + k 2 u(x) = 0 and u" - 505 505 509 510 511 513 514 515 .
1 Introduction........... 2 Contraction Mappings . . . 4 Card Sales Model . . . . 5 Private Economy Model . . 6 Fixed Point Iteration in the Card Sales Model . 7 A Contraction Mapping Has a Unique Fixed Point 245 245 246 247 248 249 250 254 XXXII Contents Volume 1 Generalization to 9 : [a, b] ----* [a, b] . . . Linear Convergence in Fixed Point Iteration Quicker Convergence . Quadratic Convergence . 1 Introduction . . . 3 Descartes: Dualism of Body and Soul. 4 The Euclidean Plane ~2 .
Applied Mathematics Body and Soul, Volume 3: Calculus in Several Dimensions by Kenneth Eriksson, Donald Estep, Claes Johnson