Author(s): Karl J. Smith, Monty J. Strauss, Magdalena D. Toda
Edition: 6
Publisher: Kendall Hunt Publishing Company
Year: 2013
Language: English
Pages: 1275
City: Dubuque, Iowa
Front Cover
Title Page
Copyright Page
Contents
Preface
5 Integration
5.1 Antidifferentiation
5.2 Area as the Limit of a Sum
5.3 Riemann Sums and the Definite Integral
5.4 The Fundamental Theorems of Calculus
5.5 Integration by Substitution
5.6 Introduction to Differential Equations
5.7 The Mean Value Theorem for Integrals; Average Value
5.8 Numerical Integration: The Trapezoidal Rule and Simpson's Rule
5.9 An Alternative Approach: The Logarithm as an Integral
Chapter 5 Review
Chapter 5 Group Research Project
Cumulative Review Problems - Chapters 1-5
6 Additional Applications of the Integral
6.1 Area Between Two Curves
6.2 Volume
6.3 Polar Forms and Area
6.4 Arc Length and Surface Area
6.5 Physical Applications: Work, Liquid Force, and Centroids
6.6 Applications to Business, Economics, and Life Sciences
Chapter 6 Review
Book Report: To Infinity and Beyond, A Cultural History of the Infinite, by Eli Maor
Chapter 6 Group Research Project
7 Methods of Integration
7.1 Review of Substitution and Integration by Table
7.2 Integration By Parts
7.3 Trigonometric Methods
7.4 Method of Partial Fractions
7.5 Summary of Integration Techniques
7.6 First-Order Differential Equations
7.7 Improper Integrals
7.8 Hyperbolic and Inverse Hyperbolic Functions
Chapter 7 Review
Chapter 7 Group Research Project
8 Infinite Series
8.1 Sequences and Their Limits
8.2 Introduction to Infinite Series; Geometric Series
8.3 The Integral Test; p-series
8.4 Comparison Tests
8.5 The Ratio Test and the Root Test
8.6 Alternating Series; Absolute and Conditional Convergence
8.7 Power Series
8.8 Taylor and Maclaurin Series
Chapter 8 Review
Chapter 8 Group Research Project
Cumulative Review Problems - Chapters 6-8
11 Partial Differentiation
11.1 Functions of Several Variables
11.2 Limits and Continuity
11.3 Partial Derivatives
11.4 Tangent Planes, Approximations, and Differentiability
11.5 Chain Rules
11.6 Directional Derivatives and the Gradient
11.7 Extrema of Functions of Two Variables
11.8 Lagrange Multipliers
Chapter 11 Review
Book Report: Hypatia's Heritage by Margaret Alic
Chapter 11 Group Research Project
12 Multiple Integration
12.1 Double Integration over Rectangular Regions
12.2 Double Integration over Nonrectangular Regions
12.3 Double Integrals in Polar Coordinates
12.4 Surface Area
12.5 Triple Integrals
12.6 Mass, Moments, and Probability Density Functions
12.7 Cylindrical and Spherical Coordinates
12.8 Jacobians: Change of Variables
Chapter 12 Review
Chapter 12 Group Research Project
14 Introduction to Differential Equations
14.1 First-Order Differential Equations
14.2 Second-Order Homogeneous Linear Differential Equations
14.3 Second-Order Nonhomogeneous Linear Differential Equations
Chapter 14 Review
Book Report: Mathematical Experience by Philip J. Davis and Reuben Hersh
Chapter 14 Group Research Project
Appendices
A: Introduction to the Theory of Limits
B: Selected Proofs
C: Significant Digits
D: Short Table of Integrals
E: Trigonometry
F: Determinants
G: Answers to Selected Problems
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Index
Back Cover
