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Welcome to Math 151: Differential Calculus |
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| Study Guide page (web) | Content page (PDF) |
| Module 1: Curves and Functions | |
| Lesson 1.1 | Elementary curves |
| Lesson 1.2 | Geometry of graphs |
| Lesson 1.3 | Basics of functions |
| Lesson 1.4 | Algebraic functions |
| Lesson 1.5 | Trigonometric functions |
| Lesson 1.6 | Logarithmic and exponential functions |
| Lesson 1.7 | Polar coordinates |
| Lesson 1.8 | Parametric curves |
| Module 2: Limits | |
| Lesson 2.1 | Limiting processes |
| Lesson 2.2 | Intuitive introduction to limits |
| Lesson 2.3 | Calculation of limits |
| Lesson 2.4 | Trigonometric limits |
| Lesson 2.5 | Asymptotes |
| Lesson 2.6 | Continuity |
| Lesson 2.7 | Epsilon-delta definition of limits |
| Module 3: Derivatives | |
| Lesson 3.1 | Slope of a curve and derivatives |
| Lesson 3.2 | Tangent lines and linear approximations |
| Lesson 3.3 | Velocity and rates of change |
| Lesson 3.4 | Derivatives of functions |
| Lesson 3.5 | Higher order derivatives |
| Lesson 3.6 | Antiderivatives and differential equations |
| Lesson 3.7 | Differentiability |
| Module 4: Differentiation tools | |
| Lesson 4.1 | Elementary rules and derivatives of polynomials |
| Lesson 4.2 | Derivatives of exponential and log functions |
| Lesson 4.3 | Product and quotient rules |
| Lesson 4.4 | Derivatives of the trigonometric functions |
| Lesson 4.5 | Chain rule |
| Lesson 4.6 | Generalizations |
| Module 5: Applications of derivatives | |
| Lesson 5.1 | Basic extrema |
| Lesson 5.2 | Applied extrema |
| Lesson 5.3 | Curve sketching |
| Lesson 5.4 | L'Hopital's rule |
| Lesson 5.5 | Newton's method |
| Lesson 5.6 | Mean value theorem |
| Module 6: Further differentiation tools and applications | |
| Lesson 6.1 | Implicit differentiation |
| Lesson 6.2 | Logarithmic differentiation |
| Lesson 6.3 | Derivatives of inverse functions |
| Lesson 6.4 | Related rates problems |
| Lesson 6.5 | Solving elementary differential equations |
| Lesson 6.6 | Parametric and polar differentiation |
