Student's Solution and Survival Manual for Calculus

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Contents
1 Functions and Graphs
	1.1 What Is Calculus?
	1.2 Preliminaries
	1.3 Lines in the Plane; Parametric Equations
	1.4 Functions and Graphs
	1.5 Inverse Functions; Inverse Trigonometric Functions
	Chapter 1 Review
2 Limits and Continuity
	2.1 The Limit of a Function
	2.2 Algebraic Computation of Limits
	2.3 Continuity
	2.4 Exponential and Logarithmic Functions
	Chapter 2 Review
3 Differentiation
	3.1 An Introduction to the Derivative: Tangents
	3.2 Techniques of Differentiation
	3.3 Derivatives of Trigonometric, Exponential, and Logarithmic Functions
	3.4 Rates of Change: Modeling Rectilinear Motion
	3.5 The Chain Rule
	3.6 Implicit Differentiation
	3.7 Related Rates and Applications
	3.8 Linear Approximation and Differentials
	Chapter 3 Review
4 Additional Applications of the Derivative
	4.1 Extreme Values of a Continuous Function
	4.2 The Mean Value Theorem
	4.3 Using Derivatives to Sketch the Graph of a Function
	4.4 Curve Sketching with Asymptotes: Limits Involving Infinity
	4.5 l'Hôpital's Rule
	4.6 Optimization in the Physical Sciences and Engineering
	4.7 Optimization in Business, Economics, and the Life Sciences
	Chapter 4 Review
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
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
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
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
9 Vectors in the Plane and in Space
	9.1 Vectors in R^2
	9.2 Coordinates and Vectors in R^3
	9.3 The Dot Product
	9.4 The Cross Product
	9.5 Lines in R^3
	9.6 Planes in R^3
	9.7 Quadric Surfaces
	Chapter 9 Review
10 Vector-Valued Functions
	10.1 Introduction to Vector Functions
	10.2 Differentiation and Integration of Vector Functions
	10.3 Modeling Ballistics and Planetary Motion
	10.4 Unit Tangent and Principal Unit Normal Vectors; Curvature
	10.5 Tangential and Normal Components of Acceleration
	Chapter 10 Review
Cumulative Review Problems - Chapters 1–10
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
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
13 Vector Analysis
	13.1 Properties of a Vector Field: Divergence and Curl
	13.2 Line Integrals
	13.3 The Fundamental Theorem and Path Independence
	13.4 Green's Theorem
	13.5 Surface Integrals
	13.6 Stokes' Theorem and Applications
	13.7 Divergence Theorem and Applications
	Chapter 13 Review
Cumulative Review Problems - Chapters 11–13
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
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