1. An Introduction to Limits

2. Properties of Limits

3. Techniques for Evaluating Limits

4. Continuity and One-Sided Limits

5. Infinite Limits

Differentiation

1. The Derivative and the Tangent Line Problem

2. Basic Differentiation Rules and Rates of Change

3. The Product and Quotient Rules

4. The Chain Rule

5. Implicit Differentiation

6. Related Rates

 

Applications of Differentiation

1. Extrema on an Interval

2. Rolle's Theorem and the Mean Value Theorem

3. Increasing and Decreasing Functions and the First Derivative Test

4. Concavity and the Second Derivative Test

 

Second Semester

Applications of Differentiation (cont'd)

5.Limits at Infinity

6. A Summary of Curve Sketching

7. Optimization Problems

8. Newton's Method

9. Differntials

10. Business and Economics Applications

 

Integration

1. Antiderivatives and Indefinite Integration

2. Area

3. Riemann Sums and Definite Integrals

4. The Fundamental Theorem of Calculus

5. Integration by Substitution

6. Numerical Integration

 

Logarithmic, Exponential, and Other Transcendental Functions

1. The Natural Logarithmic Function and Differentiation

2. The Natural Logarithmic Function and Integration

3. Inverse Functions

4. Exponential Functions:  Differation and Integration

5. Bases Other Than e and Applications

6. Differential Equations:  Growth and Decay

7. Inverse Trigonometirc Functions and Differentiation

8. Inverse Trigonometric Functions:  Integration and Completing the Square

9. Hyperbolic Functions

 

Applications of Integration

1. Area of a Region Between Two Curves

2. Volume:  The Disc Method

3. Volume:  The Shell Method

4. Arc Length and Surfaces of Revolution

5. Work

6. Fluid Pressure and Fluid Force

7. Moments, Centers of Mass, and Centroids