Topic; Textbook Sections |
Hrs |
Topics |
1. Limits and Continuity 2.1-2.4 (Appendix M,
1.1-1.5 for background) |
5 |
- Tangent lines
- Limits
- Limit laws
- One sided limits, infinite limits, limits at infinity
- Continuity, Intermediate Value Property
|
2. Derivatives 3.1-3.4, 3.7 |
4 |
- Definition of derivative
- Basic differentiation rules
- Differentiability implies continuity
- Vertical tangents
- Basic trigonometric limit
- Derivatives of trigonometric functions
- Chain Rule
- Simple harmonic motion
- Particle in a box
|
3. Exponential, Logarithmic and Inverse Functions, and
Applications 3.8, 6.8, part of 8.1, part of 8.3 |
6 |
- Exponential functions
- Natural logarithm function
- Inverse functions
- Logarithmic differentiation
- Exponential growth and decay (population growth, radioactivity,
chemical kinetics)
- Linear (nonhomogeneous) equations (heating and cooling, damped
motion)
- Inverse trigonometric functions
|
4. Some Applications of the Derivative 3.5-3.6,
3.9, 4.3-4.7 |
14 |
- Maxima and minima of functions on closed intervals
- Applied maximum-minimum problems
- Implicit differentiation
- Related rates
- Increasing and decreasing functions
- Mean Value Theorem and consequences
- First derivative test
- Curve sketching I
- Concavity, second derivative
- Asymptotes
- Curve sketching II
|
5. Linear Approximations, Taylor Series and Newton's
Method 4.2, 10.4, part of 3.10 |
4 |
- Linear approximation
- Taylor polynomials
- Taylor series
- Taylor's formula
- Error in linear approximation
- Newton's method
|