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IR. 17 Graphing Functions f : ~ ---7 ~ • • • • • • • Extending a Lipschitz Continuous Function Intervals of Real Numbers . . . . What Is f(x) if x Is Irrational? . . Continuity Versus Lipschitz Continuity . 1 Bisection . . . . 2 An Example . . 1 Introduction . . . . . 2 The Formalists . . . . 4 The Constructivists. . . 6 Real Numbers . . . . . .

14 Planes . . . . . . . . 18 Distanee from a Point to a Plane . . . 19 Rotation Around a Given Veetor . . . 21 Systems of 3 Linear Equations in 3 Unknowns . 26 The Inverse of a Matrix . . . . 27 Different Bases . . . . . . 29 Orthogonal Matriees . . . . . 1 Introduction......... 3 The Triangle Inequality .. 4 Open Domains . . . . 5 Polar Representation of Complex Numbers . 6 Geometrical Interpretation of Multiplication . 7 Complex Conjugation . . . . . 8 Division.................

14 Uniform Differentiability on an Interval . . . 16 A Slightly Different Viewpoint . 17 Swedenborg . . . . . . 1 Introduction . . . . . 4 The Chain Rule . . . . 5 The Quotient Rule . . . . . . . 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 .

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


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