Download Applied Mathematics: Body and Soul: Calculus in Several 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 college of know-how and features a sequence of volumes and software program. this system is influenced 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 contemporary model of Calculus and Linear Algebra, together with constructive/numerical ideas and functions meant for undergraduate courses in engineering and technological know-how. extra volumes current themes reminiscent of Dynamical structures, Fluid Dynamics, strong Mechanics and Electro-Magnetics on a complicated undergraduate/graduate point.

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

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1 Introduction..................... 2 Reversing the Order of Upper and Lower Limits. 3 The Whole Is Equal to the Sum of the Parts. . 17 Contents Volume 2 Integrating Piecewise Lipschitz Continuous Functions Linearity............. Monotonicity . . . . . The Triangle Inequality for Integrals Differentiation and Integration are Inverse Operations . . . . Change of Variables or Substitution. Integration by Parts . . . . . The Mean Value Theorem. . . Monotone Functions and the Sign of the Derivative A Function with Zero Derivative is Constant.

3 Real Numbers. 6 Derivatives . . . . . . 7 Differentiation Rules . . . . 9 Integrals . . . 10 The Logarithm . . . . 11 The Exponential . . . . 13 List of Primitive Functions. 14 Series . . . . . . . 1 Introduction and Survey of Basic Objectives . 2 Body /Soul and Artificial Intelligence . 3 The Vector Space Structure of]Rn . . 5 Cauchy's Inequality. . . . . . 7 The Standard Basis. . . . . . . 8 Linear Independence . . . . . . . 9 Reducing a Set of Vectors to Get a Basis .

4 Open Domains . . . . 5 Polar Representation of Complex Numbers . 6 Geometrical Interpretation of Multiplication . 7 Complex Conjugation . . . . . 8 Division................. 10 Roots . . . . . . . . . 11 Solving a Quadratic Equation w 2 + 2bw + c = 0 . 12 Gösta Mittag-LefRer . . . . . . . . 2 Paying Taxes . 3 Hiking...... 6 The Derivative of x 2 Is 2x . . . 7 The Derivative of x n Is nx n - 1 . . 9 The Derivative as a Function . . 11 Denoting the Derivative of f(x) by 1,; ..

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