| 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
1.8 Continuity |
| Week 3 |
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; Horizontal Asymptotes
3.5 Summary of Curve Sketching
3.6 Graphing with Calculus and Calculators |
| Week 8 |
Midterm Exam |
| Week 9 |
3.7 Optimization Problems
3.8 Newton’s Method
3.9 Antiderivatives |
| Week 10 |
4.1 Areas and Distances
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 Volumes
5.3 Volumes by Cylindrical Shells
5.5 Average Value of a Function |
| Week 13 |
6.1 Inverse Functions
6.2 Exponential Functions and Their Derivatives
6.3 Logarithmic Functions |
| Week 14 |
6.4 Derivatives of Logarithmic
6.5 Exponential Growth and Decay
6.6 Inverse Trigonometric Functions |
| Week 15 |
6.7 Hyperbolic Functions
6.8 Indeterminate Forms and l’Hospital’s Rule |
| Week 16 |
Final Exam |
self-directed
learning |
02.Viewing multimedia materials related to industry and academia.
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