| Section | Topic | Learning Activities | Section Concept Guide
(Extra Practice – Not Collected or Graded) |
|---|---|---|---|
| Review | Applications of Logarithms | ||
| 2.1 | The Tangent and Velocity Problems | Overview of Calculus
|
section2_1 |
| 2.2 | The Limit of a Function | Applications of Limits | section2_2 |
| 2.3 | Calculating Limits Using the Limit Laws | Week 2 Worksheet | section2_3 |
| 2.4 | The Precise Definition of a Limit | section2_4 | |
| 2.5 | Continuity | Applications of Continuity | section2_5 |
| 2.6 | Limits at Infinity; Horizontal Asymptotes | section2_6 | |
| 2.7 | Derivatives and Rates of Change | Applications of Derivatives
|
section2_7 |
| 2.8 | The Derivative as a Function | section2_8 | |
| 3.1 | Derivatives of Polynomials and Exponential Functions | Application: Curve Fitting
|
section3_1 |
| 3.2 | The Product and Quotient Rules | section3_2 | |
| 3.3 | Derivatives of Trigonometric Functions | Application: Small-Angle Approximation
|
section3_3 |
| 3.4 | The Chain Rule | section3_4 | |
| 3.5 | Implicit Differentiation | Application: Implicit Differentiation | section3_5 |
| 3.6 | Derivatives of Logarithmic Functions | Week 6 Worksheet | section3_6 |
| 3.8 | Exponential Growth and Decay | Application: Exponential Growth and Decay | section3_8 |
| 3.9 | Related Rates | Week 7 Worksheet | section3_9 |
| 3.10 | Linear Approximations and Differentials | section3_10 | |
| 4.1 | Maximum and Minimum Values | Week 8 Worksheet | section4_1 |
| 4.2 | Mean Value Theorem | section4_2 | |
| 4.3 | How Derivatives Affect the Shape of a Graph | Notes and Examples: Extrema and Graphs
|
section4_3 |
| 4.4 | Indeterminate Forms and l’Hospital’s Rule | section4_4 | |
| 4.7 | Optimization Problems | Application: Optimization (part 1) Application: Optimization (part 2)
|
section4_7 |
| 4.8 | Newton’s Method | Application: Newton’s Method | section4_8 |
| 4.9 | Antiderivatives | Week 11 Worksheet | section4_9 |
| 5.1 | Areas and Distances | Riemann Sums Interactive Tool | section5_1 |
| 5.2 | The Definite Integral | Application: Definite Integrals | section5_2 |
| 5.3 | The Fundamental Theorem of Calculus | Week 12 Worksheet | section5_3 |
| 5.5 | The Substitution Rule | section5_5 | |
| 5.4 | Indefinite Integrals and the Net Change Theorem | Week 13 Worksheet | section5_4 |
| 6.1 | Areas Between Curves | section6_1 | |
| 6.2 | Volumes | Week 14 Worksheet | section6_2 |