Introduction
This unit describes techniques for using differentiation to solve many important problems. Part C of this unit presents the Mean Value Theorem and introduces notation and concepts used in the study of integration, the subject of the next two units.
Part A: Approximation and Curve Sketching
- Session 23: Linear Approximation
- Session 24: Examples of Linear Approximation
- Session 25: Introduction to Quadratic Appoximation
- Session 26: Using Quadratic Approximations
- Session 27: Sketching Graphs I - Polynomials and Rational Functions
- Session 28: Sketching Graphs II - General Strategies
- Problem Set 3
Part B: Optimization, Related Rates and Newton's Method
- Session 29: Optimization Problems
- Session 30: Optimization Problems II
- Session 31: Related Rates
- Session 32: Ring on a String
- Session 33: Newton's Method
- Problem Set 4
Part C: Mean Value Theorem, Antiderivatives and Differential Equations
- Session 34: Introduction to the Mean Value Theorem
- Session 35: Using the Mean Value Theorem
- Session 36: Differentials
- Session 37: Antiderivatives
- Session 38: Integration by Substitution
- Session 39: Introduction to Differential Equations
- Session 40: Separation of Variables
- Problem Set 5