Week |
Course Content |
Week 1 |
1.1 Four ways to represent a function, 1.2 Mathematical models: a catalog of essential functions, 1.3 New functions from old functions, 1.4 The tangent and velocity problems |
Week 2 |
1.5 The limit of a function, 1.6 Calculating limits using the limit laws, 1.7 The precise definition of a limit |
Week 3 |
1.8 Continuity, 2.1 Derivatives and rates of change, 2.2 The derivative as a function, 2.3 Differentiation formulas |
Week 4 |
2.4 Derivatives of Trigonometric functions, 2.5 The chain rule, 2.6 Implicit differentiation |
Week 5 |
2.7 Rates of change in the Natural and social sciences, 2.8 Related rates, 2.9 Linear approximations, and differentials |
Week 6 |
3.1 Maximum and Minimum values, 3.2 The mean value theorem, 3.3 How derivatives affect the shape of a graph |
Week 7 |
3.4 Limits at infinity and horizontal asymptotes, 3.5 Summary of curve sketching, 3.6 Graphing with calculus and technology |
Week 8 |
3.7 Optimization problems, 3.8 Newton’s method, 3.9 Antiderivatives |
Week 9 |
Midterm |
Week 10 |
4.1 The area and distance problems, 4.2 The definite integral, 4.3 The fundamental theorem of calculus |
Week 11 |
4.4 Indefinite integrals and the net change theorem, 4.5 The substitution rule, 5.1 Areas between curves |
Week 12 |
5.2 Volume, 5.3 Volumes by cylindrical shells, 5.4 Work, 5.5 Average value of a function |
Week 13 |
6.1 Inverse functions and their derivatives, 6.2 Exponential functions and their derivatives, 6.3 Logarithmic functions, 6.4 Derivatives of logarithmic functions |
Week 14 |
6.5 Exponential Growth and decay, 6.6 Inverse Trigonometric functions, 6.7 Hyperbolic functions, 6.8 Indeterminate forms and L’Hospital’s rule |
Week 15 |
7.1 Integration by parts, 7.2 Trigonometric integrals, 7.3 Trigonometric substitution |
Week 16 |
7.4 Integration of rational functions by partial fractions, 7.5 Strategy for Integration, 7.6 Integration using tables and technology |
Week 17 |
7.7 Approximate integration, 7.8 Improper integrals |
Week 18 |
Final |