Download Applied Mathematics Body and Soul, Volume 3: Calculus in by Kenneth Eriksson, Donald Estep, Claes Johnson PDF

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 encouraged via the pc revolution commencing new possibilitites of computational mathematical modeling in arithmetic, technological know-how and engineering. It contains a synthesis of Mathematical research (Soul), Numerical Computation (Body) and alertness. Volumes I-III current a contemporary model of Calculus and Linear Algebra, together with constructive/numerical recommendations and functions meant for undergraduate courses in engineering and technological know-how. extra volumes current subject matters reminiscent of Dynamical platforms, Fluid Dynamics, stable Mechanics and Electro-Magnetics on a sophisticated undergraduate/graduate point.

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

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Extra resources for Applied Mathematics Body and Soul, Volume 3: Calculus in Several Dimensions

Sample text

26 The Area of a Parallelogram Spanned by Two Vectors . . . . . 27 Straight Lines . . . . . . 29 When Are Two Lines Parallel? 30 A System of Two Linear Equations in Two U nknowns . . . . . . . . 31 Linear Independence and Basis . . . . 32 The Connection to Calculus in One Variable. 33 Linear Mappings f : ~2 ----* ~. • . 34 Linear Mappings f : ~2 ----* ~2 . . . . . 36 A First Encounter with Matrices . . 37 First Applications of Matrix Notation . . . . 48 Addition of Matrices .

7 One-Sided Derivatives . . . . . . . 12 xxxv Quadratie Approximation . . . . The Derivative of an Inverse Function Implieit Differentiation. Partial Derivatives A Sum Up So Far . 1 Introduetion. 3 Newton's Method . . . . . . 4 Newton's Method Converges Quadratieally . 6 What Is the Error of an Approximate Root? 7 Stopping Criterion . . . . . . 8 Globally Convergent Newton Methods . .. 1 Introduction . . . . 4 Hooke's Law . . . . 6 Fourier's Law for Heat Flow . .

4 The Constructivists. . . 6 Real Numbers . . . . . . . . . . 7 Cantor Versus Kronecker . . . . . . . 8 Deciding Whether a Number is Rational or Irrational. 9 The Set of All Possible Books . . . . 10 Recipes and Good Food . . . . . . 12 The Search for Rigor in Mathematics . 14 Summary . . 1 The Function Vx . . . . . . 2 Computing with the Function Vx . 3 Is Vx Lipschitz Continuous on ~+? q . 7 Turbulent Flow is Hölder (Lipschitz) Continuous with Exponent ~ . . .

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