Workbook 21

Chapter 1: Partial Derivatives and Gradients

PDF

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 4: "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

Chapter 2: Introduction to Linear Algebra

PDF

Downloads

A python program transforming a a 10x10 pixel bitmap into an rgb image.

Objectives

Understand the concept of linear algebra, matrices, multiplying vector quantities, etc

Video: Bitmap Images - YouTube
Video: Essence of linear algebra preview - YouTube
Video: Linear transformations and matrices | Chapter 3, Essence of linear algebra - YouTube
Video: How to compress an image with (basic) linear algebra - YouTube
Video: Introduction to Linear Algebra: Systems of Linear Equations - YouTube
Video: What's the big idea of Linear Algebra? **Course Intro** - YouTube
Video: Linear Algebra: Introduction to Vectors - YouTube
Video: Linear Algebra 11 | Matrices - YouTube
Reference: Linear algebra - Wikipedia

Prerequisites

Understand and multiply vectors using the dot product from Chapter 2: "The Dot Product" in Workbook 11
Understand basic python image processing from Chapter 3: "Images in Python" in Workbook 15
Able to do vector addition and subtraction from Chapter 5: "Vectors" in Workbook 07
Understand how to calculate vector valued functions from Chapter 5: "Vector-valued Functions" in Workbook 12
Understand a vector and its properties in depth from Chapter 5: "Vectors" in Workbook 07
Understand the orgin of RGB values and what they represent from Chapter 1: "How Cameras Work" in Workbook 15

Chapter 3: Vectors and Matrices

PDF

Objectives

Understand matrices, vector representations of matrices, dimensions of matrices, matrix multiplication

Video: Linear Algebra 11 | Matrices - YouTube
Video: Intro to Matrices - YouTube
Video: Matrices Top 10 Must Knows (ultimate study guide) - YouTube
Video: Multiplying Matrices - YouTube
Video: Understanding Matrices and Matrix Notation - YouTube
Video: The Applications of Matrices | What I wish my teachers told me way earlier - YouTube
Reference: Matrix (mathematics) - Wikipedia

Understand how to add, subtract, and multiplication matrices

Video: Linear Algebra - Matrix Operations - YouTube
Video: Adding and Subtracting Matrices - YouTube
Video: Matrix addition and subtraction | Matrices | Precalculus | Khan Academy - YouTube
Video: How To Multiply Matrices - Quick & Easy! - YouTube
Reference: Matrix multiplication - Wikipedia

Prerequisites

Able to do vector addition and subtraction from Chapter 5: "Vectors" in Workbook 07
Understand a vector and its properties in depth from Chapter 5: "Vectors" in Workbook 07
Understand the concept of linear algebra, matrices, multiplying vector quantities, etc from Chapter 2: "Introduction to Linear Algebra" in Workbook 21
Understand and multiply vectors using the dot product from Chapter 2: "The Dot Product" in Workbook 11

Chapter 4: Linear Combinations of Vectors

PDF

Objectives

Understand linear combinations of vectors.

Prerequisites

Understand the concept of linear algebra, matrices, multiplying vector quantities, etc from Chapter 2: "Introduction to Linear Algebra" in Workbook 21

Generated 2025-09-05T18:44.