Workbook 20

Chapter 1: Optimization

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Objectives

Optimizing a best possible solution given a problem with many variables.

Video: Intro to Linear Programming - YouTube
Video: The Art of Linear Programming - YouTube
Reference: Optimization problem - Wikipedia

Chapter 2: Implicit Differentiation

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Objectives

Understand how to use implicit differentiation to find derivatives with respect to x, vertical and horizontal tangents, and other rates of change.

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
Apply the chain rule to a function to find its derivative. from Chapter 3: "Rules for Finding Derivatives" in Workbook 19
Apply the product rule to a function to find its derivative. from Chapter 3: "Rules for Finding Derivatives" in Workbook 19

Chapter 3: Related Rates

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Objectives

Understand how to solve related rates problems using differentiation

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 use implicit differentiation to find derivatives with respect to x, vertical and horizontal tangents, and other rates of change. from Chapter 2: "Implicit Differentiation" in Workbook 20

Chapter 4: Parametric Functions

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Chapter 5: Multivariate Functions and Partial Derivatives

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Objectives

Understand how to evaluate functions of serveral variables, and be able to take their limits to determine continuity and differentiablity

Prerequisites

Understand the concept of a derivative and how to find it from Chapter 1: "Differentiating Polynomials" in Workbook 17
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

Chapter 6: Partial Derivatives and Gradients

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Objectives

Understand how to calculate partial derivatves.

Understand how to use the chain rule for partial derivatives

Video: Chain Rule With Partial Derivatives - Multivariable Calculus - YouTube
Video: The Multi-Variable Chain Rule: Derivatives of Compositions - YouTube
Video: Multivariable chain rule - YouTube
Reference: Chain rule - Wikipedia

Understand gradient vectors and directional derivatives and their relation

Prerequisites

Understand how to evaluate functions of serveral variables, and be able to take their limits to determine continuity and differentiablity from Chapter 5: "Multivariate Functions and Partial Derivatives" in Workbook 20
Apply the chain rule to a function to find its derivative. from Chapter 3: "Rules for Finding Derivatives" in Workbook 19
Understand and multiply vectors using the dot product from Chapter 2: "The Dot Product" in Workbook 11

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