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Table of Contents
Preface
Chapter 1: Limits
Chapter 1 - Overview
Section 1.1
Naive Limits
Section 1.2
Precise Definition of a Limit
Section 1.3
Limit Laws
Section 1.4
Limits for Trig Functions
Section 1.5
Limits at Infinity and Infinite Limits
Section 1.6
Continuity
Section 1.7
Intermediate Value Theorem
Chapter 2: Differentiation
Chapter 2 - Overview
Section 2.1
What is a Derivative?
Section 2.2
Precise Definition of the Derivative
Section 2.3
Differentiation Rules
Section 2.4
The Chain Rule
Section 2.5
Implicit Differentiation
Section 2.6
Derivatives of the Exponential and Logarithmic Functions
Section 2.7
Derivatives of the Trig Functions
Section 2.8
The Inverse Trig Functions and Their Derivatives
Section 2.9
The Hyperbolic Functions and Their Derivatives
Section 2.10
The Inverse Hyperbolic Functions and Their Derivatives
Chapter 3: Applications of Differentiation
Chapter 3 - Overview
Section 3.1
Tangent and Normal Lines
Section 3.2
Newton's Method
Section 3.3
Taylor Polynomials
Section 3.4
Differentials and the Linear Approximation
Section 3.5
Curvature of a Plane Curve
Section 3.6
Related Rates
Section 3.7
What Derivatives Reveal about Graphs
Section 3.8
Optimization
Section 3.9
Indeterminate Forms and L'Hôpital's Rule
Section 3.10
Antiderivatives
Chapter 4: Integration
Chapter 4 - Overview
Section 4.1
Area by Riemann Sums
Section 4.2
The Definite Integral
Section 4.3
Fundamental Theorem of Calculus and the Indefinite Integral
Section 4.4
Integration by Substitution
Section 4.5
Improper Integrals
Section 4.6
Average Value and the Mean Value Theorem
Chapter 5: Applications of Integration
Chapter 5 - Overview
Section 5.1
Area of a Plane Region
Section 5.2
Volume of a Solid of Revolution
Section 5.3
Volume by Slicing
Section 5.4
Arc Length
Section 5.5
Surface Area of a Surface of Revolution
Section 5.6
Differential Equations
Section 5.7
Centroids
Section 5.8
Work
Section 5.9
Hydrostatic Force
Chapter 6: Techniques of Integration
Chapter 6 - Overview
Section 6.1
Integration by Parts
Section 6.2
Trigonometric Integrals
Section 6.3
Trig Substitution
Section 6.4
The Algebra of Partial Fractions
Section 6.5
Integrating the Fractions in a Partial-Fraction Decomposition
Section 6.6
Rationalizing Substitutions
Section 6.7
Numeric Methods
Chapter 7: Additional Applications of Integration
Chapter 7 - Overview
Section 7.1
Polar Coordinates
Section 7.2
Integration in Polar Coordinates
Section 7.3
The Theorems of Pappus
Chapter 8: Infinite Sequences and Series
Chapter 8 - Overview
Section 8.1
Sequences
Section 8.2
Series
Section 8.3
Convergence Tests
Section 8.4
Power Series
Section 8.5
Taylor Series
Appendix: All about Maple
Appendix - Overview
Section A-1
The Working Environment
Section A-2
Arithmetic Calculations
Section A-3
Referencing
Section A-4
Algebraic Expressions and Operations
Section A-5
Evaluation
Section A-6
Coordinate Geometry
Section A-7
Trigonometry
Section A-8
Functions
Section A-9
Graphing
Section A-10
Solving Equations
Section A-11
Factoring and Collecting Terms
Section A-12
Additional Resources
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