Workbook 32

Chapter 1: u-Substitution

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Objectives

Understand how to integrate functions using u-sub.

Video: How To Integrate Using U-Substitution - YouTube
Video: Understand u-substitution, the idea! - YouTube
Video: Integration Using The Substitution Rule - YouTube
Video: U-substitution with definite integral - YouTube
Video: _-substitution intro | AP Calculus AB | Khan Academy - YouTube
Video: U-substitution and back substitution - YouTube
Video: _-substitution: multiplying by a constant | AP Calculus AB | Khan Academy - YouTube
Video: Another u-subsitution example - YouTube
Reference: Integration by substitution - Wikipedia
Reference: u-substitution – Informal Calculus

Prerequisites

Define a derivative as a slope of a tangent line using limits. Additionally, be able to find if a point is differentiable. from Chapter 1: "Differentiation" in Workbook 19
Understand how to calculate definite integrals and their properties. from Chapter 1: "Definite Integrals" in Workbook 30
Understand how to find general antiderivatives, inverse derivative rules, and find general solutions and specific solutions. Find indefinite integrals from Chapter 3: "Antiderivatives" in Workbook 29

Chapter 2: Calculus with Polar Coordinates

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Objectives

Understand how to find slopes of polar functions.

Understand how to find areas of general polar functions.

Prerequisites

Understand how to plot points, change coordinate systems, and create basic shapes in polar from Chapter 4: "Polar Coordinates" in Workbook 11

Chapter 3: Differential Equations

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Objectives

Be able to solve ordinary differential equations, logistic DE's, and seperable differential equations.

Prerequisites

Calculate exponential growth and understand exponents from Chapter 2: "Compound Interest" in Workbook 10
Understand how to calculate partial derivatves. from Chapter 1: "Partial Derivatives and Gradients" in Workbook 21

Chapter 4: Slope Fields

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Objectives

Be able to work with slope fields, both graphing and identifying.

Prerequisites

Be able to solve ordinary differential equations, logistic DE's, and seperable differential equations. from Chapter 3: "Differential Equations" in Workbook 32

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