Cover -- Half-Title -- Title -- Copyright -- Dedication -- Contents -- Preface -- Acknowledgments -- Chapter 1: Vectors and Parametric Curves -- 1.1 Points and Vectors on the Plane -- Exercises 1.1 -- 1.2 Scalar Product on the Plane -- Exercises 1.2 -- 1.3 Linear Independence -- Exercises 1.3 -- 1.4 Geometric Transformations in Two Dimensions -- Exercises 1.4 -- 1.5 Determinants in Two Dimensions -- Exercises 1.5 -- 1.6 Parametric Curves on the Plane -- Exercises 1.6 -- 1.7 Vectors in Space -- Exercises 1.7 -- 1.8 Cross Product -- Exercises 1.8 -- 1.9 Matrices in Three Dimensions -- Exercises 1.9 -- 1.10 Determinants in Three Dimensions -- Exercises 1.10 -- 1.11 Some Solid Geometry -- Exercises 1.11 -- 1.12 Cavalieri and the Pappus-Guldin Rules -- Exercises 1.12 -- 1.13 Dihedral Angles and Platonic Solids -- Exercises 1.13 -- 1.14 Spherical Trigonometry -- Exercises 1.14 -- 1.15 Canonical Surfaces -- Exercises 1.15 -- 1.16 Parametric Curves in Space -- Exercises 1.16 -- 1.17 Multidimensional Vectors -- Exercises 1.17 -- Chapter 2: Differentiation -- 2.1 Some Topology -- Exercises 2.1 -- 2.2 Multivariable Functions -- Exercises 2.2 -- 2.3 Limits and Continuity -- Exercises 2.3 -- 2.4 Definition of the Derivative -- Exercises 2.4 -- 2.5 The Jacobi Matrix -- Exercises 2.5 -- 2.6 Gradients and Directional Derivatives -- Exercises 2.6 -- 2.7 Levi-Civitta and Einste -- Exercises 2.7 -- 2.8 Extrema -- Exercises 2.8 -- 2.9 Lagrange Multipliers -- Exercises 2.9 -- Chapter 3: Integration -- 3.1 Differential Forms -- Exercises 3.1 -- 3.2 Zero-Manifolds -- Exercises 3.2 -- 3.3 One Manifold -- Exercises 3.3 -- 3.4 Closed and Exact Forms -- Exercises 3.4 -- 3.5 Two-Manifolds -- Exercises 3.5 -- 3.6 Change of Variables in Double Integrals -- Exercises 3.6 -- 3.7 Change to Polar Coordinates -- Exercises 3.7 -- 3.8 Three-Manifolds -- Exercises 3.8.

3.9 Change of Variables in Triple Integrals -- Exercises 3.9 -- 3.10 Surface Integrals -- Exercises 3.10 -- 3.11 Green's, Stokes', and Gauss' Theorems -- Exercises 3.11 -- Appendix A: Maple -- A.1 Getting Started and Windows of Maple -- A.2 Arithmetic -- A.3 Symbolic Computation -- A.4 Assignments -- A.5 Working with Output -- A.6 Solving Equations -- A.7 Plots with Maple -- A.8 Limits and Derivatives -- A.9 Integration -- A.10 Matrix -- Appendix B: Matlab -- B.1 Getting Started and Windows of MATLAB -- B.1.1 Using MATLAB in Calculations -- B.2 Plotting -- B.2.1 Two-dimensional Plotting -- B.2.2 Three-Dimensional Plotting -- B.3 Programming in MATLAB -- B.3.1 For Loops -- B.3.2 While Loops -- B.3.3 If, Else, and Elseif -- 3.3.4 Switch -- B.4 Symbolic Computation -- B.4.1 Simplifying Symbolic Expressions -- B.4.2 Differentiating Symbolic Expressions -- B.4.3 Integrating Symbolic Expressions -- B.4.4 Limits Symbolic Expressions -- B.4.5 Taylor Series Symbolic Expressions -- B.4.6 Sums Symbolic Expressions -- B.4.7 Solving Equations as Symbolic Expressions -- Appendix C: Answers to Odd-Numbered Exercises -- Chapter 1 -- Chapter 2 -- Chapter 3 -- Appendix D: Formulas -- D.1 Trigonometric Identities -- D.2 Hyperbolic Functions -- D.3 Table of Derivatives -- D.4 Table of Integrals -- D.5 Summations (Series) -- D.5.1 Finite Element of Terms -- D.5.2 Infinite Element of Terms -- D.6 Logarithmic Identities -- D.7 Exponential Identities -- D.8 Approximations for Small Quantities -- D.9 Vectors -- D.9.1 Vector Derivatives -- D.9.2 Vector Identity -- D.9.3 Fundamental Theorems -- Bibliography -- Index.