Workbook 34

Chapter 1: Power Series

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Objectives

Be able to use calculate the radius and intervals of convergence. Use calculus to approximate power series integrals and derivatives.

Prerequisites

Understand how to use sequences to form series. Determine convergence and divergence of series. from Chapter 3: "Series" in Workbook 33
Understand how to apply the series tests, including TFD, Integral Test, Ratio Test, both Comparison Tests, and the Root Test. from Chapter 4: "Convergence Tests for Series" in Workbook 33

Chapter 2: Population Proportion Statistics

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Objectives

Understand how the binomial distribution models sample outcomes when the true population is known. Be able to use the beta distribution.

Video: Comparing population proportions 1 | Probability and Statistics | Khan Academy - YouTube
Video: The Beta distribution explained in 3 minutes - YouTube
Reference: Beta distribution - Wikipedia
Reference: Population proportion - Wikipedia
Reference: Beta distribution | Properties, proofs, exercises

Prerequisites

Understand how to calculate conditional probability. Be able to use the chain rule for probability from Chapter 1: "Conditional Probability" in Workbook 29
Understand how to complete combinatorics problems. Understand the binomial distribution. from Chapter 3: "Beginning Combinatorics" in Workbook 28
Understand Bayes' theorem and be able to apply it to new information from Chapter 2: "Bayes' Theorem" in Workbook 29

Chapter 3: The Normal Distribution

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Objectives

Understand how to find the PDF of a normal distribution, and why it is important.

Prerequisites

Define Bell Curve from Chapter 1: "Basic Statistics" in Workbook 03
Understand how to interpret continus uniform distributions, cumulative probability functions, and probability density functions. from Chapter 4: "Continuous Probability Distributions" in Workbook 30

Chapter 4: Change of Variables

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Objectives

Understand how changing variables effects a PDF and CDF

Prerequisites

Define Bell Curve from Chapter 1: "Basic Statistics" in Workbook 03
Understand how to interpret continus uniform distributions, cumulative probability functions, and probability density functions. from Chapter 4: "Continuous Probability Distributions" in Workbook 30

Chapter 5: Volumes with Integrals

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Objectives

Understand how to find volumes using single integrals and solids of revolution around x, y, and other axis.

Video: Calculating the Volume of a Solid of Revolution by Integration - YouTube
Video: Disk & Washer Method - Calculus - YouTube
Video: Solid of Revolution (part 1) - YouTube
Video: Volume of the Solid of Revolution, the Disc Method! - YouTube
Video: Surface Area of Solid of Revolution (about x-axis, formula explained) - YouTube
Video: Solid of revolution between two functions (leading up to the washer method) | Khan Academy - YouTube
Video: Solid of Revolution (part 6) - YouTube
Video: Generalizing the washer method | Applications of definite integrals | AP Calculus AB | Khan Academy - YouTube
Video: Solid of Revolution (part 5) - YouTube
Video: Volume of Solids: Washer Method Playlist - YouTube
Reference: A solids of revolution graphing calculator
Reference: solids of revolution - Brave Search
Reference: Solid of revolution - Wikipedia
Reference: Solid of Revolution -- from Wolfram MathWorld
Reference: 6.3: Volumes of Revolution: The Shell Method - Mathematics LibreTexts

Prerequisites

Calculate the volume of different solids, including pyramids, cylinders, spheres, and unique shapes from Chapter 3: "Volumes of Common Solids" in Workbook 06
Understand how to calculate definite integrals and their properties. from Chapter 1: "Definite Integrals" in Workbook 30

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