Mathematics 1a

Tentative Week-by-Week Syllabus (September 2003)

The Derivative and Limits

September 22-26

• Rates of Change

• The Tangent Line and Velocity Problems (2.1)

• Tangents, Velocity, and Other Rates of Change (2.6 and part of 2.2)

September 29 - October 3

• Derivatives (2.7 and part of 2.2)

• The Derivative as a Function (begin 2.8 and finish 2.2)

• Limits and Continuity (2.3 and part of 2.4)

October 6 - 10

• Implications of Continuity and Limits Involving Infinity (finish 2.4, 2.5)

• Differentiability and Continuity; Higher Order Derivatives (finish 2.8)

• What do f' and f'' say about f? (2.10)

The Mechanics of Differentiation

Columbus Day: No class on Monday, October 13

October 14 - 17

• Linear Approximations, Begin Derivatives of Polynomials (2.9, part of 3.1)

• Derivatives of Polynomials and Exponential Functions (3.1)

October 20 - 24

• The Product and Quotient Rules (3.2)

• Rates of Change in the Natural and Social Sciences (3.3)

• Derivatives of Trigonometric Functions (3.4)

October 27 - 31

• The Chain Rule (3.5)

• Implicit Differentiation (3.6)

• Derivatives of Logarithmic Functions (3.7)

November 3-7

• Linear Approximations and Differentials (3.8)

Applications of Differentiation

• Related Rates (4.1)

• Maximum and Minimum Values (4.2)

Veteran's Day: No class on Tuesday, November 11

November 10-14

• Derivatives and Shapes of Curves (4.3)

• Indeterminate Forms and L'Hopital's Rule (4.5)

• Optimization Problems (4.6)

November 17-21

• More Optimization Problems

• Applications to Economics (4.7)

• Newton's Method (4.8)

Integration

November 24 - 26

• Antiderivatives (4.9)

• Areas and Distances (5.1)

December 1 - 5

• Areas and Distances (5.1)

• The Definite Integral (5.2)

• The Area Function and the Fundamental Theorem of Calculus

December 8 - 12

• Evaluating Definite Integrals (5.3)

• The Fundamental Theorem of Calculus (5.4)

• Substitutions (5.5)

December 15-16

• Area Between Curves; Review of Integration