Day

Sections covered and topics

1

1.1 Four ways to represent a function,  the vertical line test, piecewise funs,

     Symmetry, increasing and decreasing functions

1.2 Mathematical Models: Linear, polynomial, power , Rational , algebraic,

     Trigonometric, exponential, and transcendental functions

 2

1.3 Transformation, combination, and composition of functions

1.4 Graphing calculators

1.5 Exponential functions, applications, the number “e”

 3

1.6 Inverse Functions and Logarithms, one-to-one functions, Natural

      Logarithms, inverse trigonometric functions

2.1 The tangent problem, the velocity problem

 4

2.2 The limit of a function, one-sided limits, infinite limits,

      Vertical asymptotes

2.3 Calculating limits using the limit laws

2.5 Continuity, The Intermediate Value Theorem

 5

2.6 Limits at Infinity, horizontal asymptotes 

2.7 Tangents, velocities, and other rates of change

2.8 Derivatives (as the slope of the tangent and as the rate of change)

6 

2.9 The derivative as a function, The derivative notations

3.1 Derivatives of polynomials and exponential functions

7 

3.2 The product and quotient rules  Exam 1 on 5/16

8 

3.3 Rates of change in the natural and social sciences 

3.4 Derivatives of Trigonometric functions  

9 

3.5 The Chain Rule

3.6 Implicit Differentiation, orthogonal trajectories

10

3.7 Higher Derivatives

3.8 Derivatives of Logarithmic functions  

11

3.10 Related rates

3.11 Linear approximations and differentials

 12

4.1 Maximum and minimum values, The Extreme Value Theorem, Fermat’s

     Theorem, critical number

4.2 Rolle’s Theorem, The Mean Value Theorem

13

4.3 Increasing/Decreasing Test, The First Derivative Test, Concavity Test,

      The Second Derivative Test, Graph of functions

4.4 Intermediate forms and L’Hospital’s Rule

14

4.5 Summary of curve sketching

4.6 Graphing with calculus and calculators

15 

4.7 Optimization problems Exam 2 on 5/25

 16

4.10 Anti-derivatives         

5.1 The area problem

 17

5.2 The definite integral, evaluating integrals, properties of the

      Definite integral, comparison properties of the integral

5.3 The fundamental Theorem of calculus

18

5.4 Indefinite Integrals

5.5 The substitution rule, Definite Integrals

19

Review for final, Final on June 1, Friday at 9:00 AM in  SH 509