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=**Calculus Outline of Chapters**=

Chapters 1-4 are covered in the first semester and 5-8 in the second semester. Textbook is Calculus 3rd ed. by Hughes-Hallet.

A Library of Functions
1.1 Functions and Changes 1.2 Exponential Functions 1.3 New Functions From Old 1.4 Logarithmic Functions 1.5 Trigonometric Functions 1.6 Powers, Polynomials, and Rational Functions 1.7 Introduction to Continuity

The Derivative
2.1 How Do We Measure Speed? 2.2 Limits 2.3 The Derivative at a Point 2.4 The Derivative Function 2.5 Interpretations of the Derivative 2.6 The Second Derivative 2.7 Continuity and Differentiability

Short-Cuts to Differentiation
3.1 Powers and Polynomials 3.2 The Exponential Function 3.3 The Product and Quotient Rules 3.4 The Chain Rule 3.5 The Trigonometric Functions 3.6 Applications of the Chain Rule 3.7 Implicit Functions 3.8 Parametric Equations 3.9 Linear Approximation and the Derivative 3.10 Using Local Linearity to Find Limits

Using the Derivative
4.1 Using First and Second Derivatives 4.2 Families of Curves 4.3 Optimization 4.5 Optimization and Modeling 4.6 Hyperbolic Functions 4.7 Theorems About Continuous and Differentiable Functions

The Definite Integral
5.1 How Do We Measure Distance Traveled? 5.2 The Definite Integral 5.3 Interpretations of the Definite Integral 5.4 Theorems About Definite Integrals

Constructing Antiderivatives
6.1 Antiderivatives Graphically and Numerically 6.2 Constructing Antiderivatives Analytically 6.3 Differential Equations 6.4 Second Fundamental Theorem of Calculus 6.5 The Equations of Motion

Integration
7.1 Integration By Substitution 7.2 Integration By Parts 7.3 Tables of Integrals 7.4 Algebraic Identities and Trigonometric Substitutions 7.5 Approximating Definite integrals 7.6 Approximation Errors and Simpson’s Rule 7.7 Improper Integrals 7.8 Comparison of Improper Integrals

Using The Definite Integral
8.1 Areas and Volumes 8.2 Applications to Geometry

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