Topic; Textbook Sections 
Hrs 
Topics 
1. Limits and Continuity 2.12.4 (Appendix M,
1.11.5 for background) 
5 
 Tangent lines
 Limits
 Limit laws
 One sided limits, infinite limits, limits at infinity
 Continuity, Intermediate Value Property

2. Derivatives 3.13.4, 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 3.53.6,
3.9, 4.34.7 
14 
 Maxima and minima of functions on closed intervals
 Applied maximumminimum 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
