Here's the course review for Math 1A03:
http://www.macinsiders.com/showthread.php?t=1837 5
Here's what we covered in first term last year (Not in chronological order):
Chapter 1: Functions and Models
1.2: Mathematical Models: A Catalog of Essential Functions
1.3: New Functions from Old Functions
1.5: Exponential Functions
1.6: Inverse Functions and Logarithms
Chapter 2: Limits and Derivatives
2.2: The Limit of a Function
2.5: Continuity
2.6: Limits at Infinity; Horizontal Asymptotes
2.7: Derivatives and Rates of Change
2.8: The Derivative as a Function
Chapter 3: Differentiation Rules
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
3.6: Derivatives of Logarithmic Functions
3.10: Linear Approximations and Differentials
Chapter 4: Applications of Differentiation
4.1: Maximum and Minimum Values
4.3: How Derivatives Affect the Shape of a Graph
4.4: Indeterminate Forms and L'Hospital's Rule
4.5: Summary of Curve Sketching
4.7: Optimization Problems
4.8: Newton's Method
Chapter 5: Integrals
5.1: Areas and Distances
5.2: The Definite Integrals
5.3: The Fundamental Theorem of Calculus
5.4: Indefinite Integrals and the Net Change Theorem
5.5: The Substitution Rule
Chapter 6: Integrals
6.1: Areas Between Curves
6.2: Volumes
6.3: Volumes by Cylindrical Shells
6.4: Work
6.5: Average Value of a Function
Chapter 7: Techniques of Integration
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
7.7: Approximate Integration
That's it! If you know your formulas and theorems, you'll do great.
