Multivariable and Vector Calculus: An Introduction

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