Single Variable Calculus

2. Applications of Differentiation

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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

Exam 2

• Session 41: Review for Exam 2
• Session 42: Materials for Exam 2

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