| LECTURE | SECTIONS | DESCRIPTION |
|---|
| 1 |
1.2, 1.3 |
Precalculus Review: Real line, coordinate plane, distance, circles, straight lines. |
| 2 |
1.4 |
Precalculus Review: Functions, graphs. Trig review: Radians, definition of trig functions, graphs of sin, cos, tan, sec. |
| 3 |
2.1, 2.2 |
Limits: Definition and discussion of intuitive meaning. Rules for limits, computing limits of algebraic functions. One sided limits, squeeze theorem, limits for trig functions, infinite limits. |
| 4 |
2.2 |
Topics of lecture 3, continued. |
| 5 |
2.3 |
Continuity, intermediate value theorem, finding roots. |
| 6 |
2.4 |
Exponentials and logarithms: Definition of e, properties and inverse relation of exp and ln. Compound interest, future value, exponential population growth. |
| 7 |
3.1 |
Definition of the derivative: Direct calculation of derivatives. Relation between the graph of f and the graph of f'. Continuity and differentiability. |
| 8 |
3.2, 3.3 |
Calculation: Sum, product and quotient rules. Higher order derivatives. Differentiation of exponential and trig functions. |
| 9 |
3.4 |
The derivative as a rate of change. Velocity and acceleration. |
| 10 |
3.5 |
Chain rule. |
| 11 |
|
Catch up and review. |
| 12 |
|
FIRST IN-CLASS 80-MINUTE EXAM. |
| 13 |
3.6 |
Implicit differentiation. Derivatives of log and exp to other bases. Derivative of log(|u|). Logarithmic differentiaion |
| 14 |
3.7 |
Related rates. |
| 15 |
3.8 |
Linear approximation. Differentials. Error and relative error of measurement. Marginal analysis. |
| 16 |
4.1, 4.2 |
Optimization of a continuous function on a bounded interval. Statement of mean value theorem and examples 1 & 2. |
| 17 |
4.3 |
First and second derivative analysis and curve sketching. |
| 18 |
4.4 |
Curve sketching with asymptotes. Limits as x approaches plus or minus infinity. |
| 19 |
4.5 |
L'Hopitals's rule. |
| 20 |
4.6 |
Optimization applications: Physical problems. |
| 21 |
|
Catch up and review. |
| 22 |
|
SECOND IN-CLASS 80-MINUTE EXAM. |
| 23 |
4.7 |
Optimization applications: Marginal analysis and profit maximization, inventory problems, physiology problems. |
| 24 |
5.1 |
Antiderivatives. |
| 25 |
5.2, 5.3 |
Riemann sums and the definition of definite integrals. |
| 26 |
5.4 |
Fundamental theorems of calculus. |
| 27 |
5.5 |
Substitution method for both indefinite and definite integrals. |
| 28 |
|
Catch up and review. |
