Calculus
1
Review
4 Topics
Algebra
Analytic Geometry
Functions
Trigonometry
2
Chapter 1: Functions and Models
5 Topics
1.1. Four Ways to Represent a Function
1.2. Mathematical Models: A Catalog of Essential Functions
1.3. New Functions from Old Functions
1.4. Exponential Functions
1.5. Inverse Functions and Logarithms
3
Chapter 2: Limits and Derivatives
7 Topics
2.1. The Tangent and Velocity Problems
2.2. The Limit of a Function
2.3. Calculating Limits Using the Limit Laws
2.5. Continuity
2.6. Limits at Infinity; Horizontal Asymptotes
2.7. Derivatives and Rates of Change
2.8. The Derivative as a Function
4
Chapter 3: Differentiation Rules
10 Topics
3.1. Derivatives of Polynomials and Exponential Functions
3.2. The Product and Quotient Rules
3.3. Derivatives of Trigonometric Functions
3.4. The Chain Rule
3.5. Implicit Differentiation
3.6. Derivatives of Logarithmic and Inverse Trigonometric Functions
3.7. Rates of Change
3.9. Related Rates
3.10. Linear Approximations and Differentials
3.11. Hyperbolic Functions
5
Chapter 4: Applications of Differentiation
4 Topics
4.1. Maximum and Minimum Values
4.2. The Mean Value Theorem
4.3. What derivatives Tell Us About the Shape of a Graph
4.4. Intermediate Forms and l’Hopital’s Rule
6
Chapter 5: Integrals
5 Topics
5.1. The Area and Distance Problems
5.2. The Definite Integral
5.3. The Fundamental Theorem of Calculus
5.4. Indefinite Integrals and the Net Change Theorem
5.5. The Substitution Rule
7
Chapter 6: Applications of Integration
4 Topics
6.1. Areas Between Curves
6.2. Volumes
6.3. Volumes by Cylindrical Shells
6.5. Average Value of a Function
8
Chapter 7: Techniques of Integration
6 Topics
7.1. Integration by Parts
7.2. Trigonometric Integrals
7.3. Trigonometric Substitution
7.4. Integration of Rational Functions by Partial Fractions
7.5. Strategy for Integration
7.8. Improper Integrals
9
Chapter 8: Further Applications of Integration
2 Topics
8.1. Arc Length
8.2. Area of Surface of Revolution
10
Chapter 10: Parametric Equations and Polar Coordinates
4 Topics
10.1. Curves Defined by Parametric Equations
10.2. Calculus with Parametric Curves
10.3. Polar Coordinates
10.4. Calculus in Polar Coordinates (Areas & Lengths in Polar Coordinates)
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