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Exam Scores Visualizer

Letter Grade Range Histogram with a KDE

Finding All Solutions

Finding all solutions

Exploring with Slope Fields

Matching Curves and Understanding Connections to Initial Conditions

Using Product Rule

Using just product rule to solve.

Integrating Factor

Finding and using an integrating factor.

Distinct Real Roots

Constant Coefficients with Distinct Real Roots

Complex Conjugate Roots

Constant Coefficients with Complex Conjugate Roots

Repeated Roots

Constant Coefficients with Repeated Roots

Reduction of Order

Recovering the full solution set given one homogeneous solution

Cauchy-Euler Equations

The Monomial Analogue of the Constant Coefficients Equations

Exponential Functions

Finding the right constant multiple

Polynomial Functions

Using either Iterative Refinement or Undetermined Coefficients

Sine and Cosine Functions

Using either Iterative Refinement or Undetermined Coefficients

Exponential Functions with Conflicting Roots

The desired exonential is alredy a homogeneous solution

Variation of Parameters

A Determinant and Integration Heavy Method for finding Particular Solutions

Extra Variation of Parameters Problems (external reference)

Warning: These problems can be very tedious. Practice these sparingly if at all.

Damped Motion

Over, Under, and Critically Damped Harmonic Motion

Laplace Transform (external reference)

Use the 6.1 problems that practice transforming back and forth

What Are Eigenvectors?

Getting a better understanding

How Do We Use Eigenvectors?

Using eigen-axes to model matrices

Computing Eigen-coordinates

A very short guide

Computing Eigenvectors

How to Compute Eigenvalues and Eigenvectors of a Matrix

DE Connection

Using eigenvectors in differential equations

Review Worksheet

A comprehensive pdf with the definition through diagonalization and applications

Homogeneous System with Distinct Real Roots

More Precisely: Method works for any 2x2 matrix that is diagonalizable

Inner Products and Approximations

Approximating e^x with quadratic functions.

Sine and Cosine Properties

The Special Properties of Sine and Cosine following from the previous section

Computing Fourier Coefficients

Computations and Visual Examples

Computing Sine Coefficients

Find the sine coefficients to best approximate each function

Multi-variable Limits

Considering more approaches than just left and right

Partial Derivatives

Why do we hold y constant?

Lagrange Multipliers

Level sets and gradient alignment

Gradient Descent and Area

How to Improve Riemann Sum Estimates

Fundamental Principles of Area and Volume

Building shapes with prisms and cones

Volume of a Pyramid

Slices, Riemann Sums, and 3D Objects

Double Integrals

How can we integrate surfaces with slices?

Line Integrals

How should we think about integrating curves?

Understanding Surface and Flux Integrals

Building intuition for how both are computed with a (sometimes signed) scaling factor

Dot Products and Approximations

Connecting dot products to approximation methods

Sine and Cosine Properties

Geometric Properties of Sine and Cosine following from the previous section

Computing Fourier Coefficients

Geometric Properties of Sine and Cosine following from the previous section

Wave Equation Example

Seeing what a solution does and how it connects to the initial conditions

Topology Introduction

Open Balls are Open

Triangle Axiom

Constructing an Isometry given two congruent triangles

3F - Duality

Revised Notes on Duality to Supplement Chapters 6 and 7

SVD Example

An example of how Singular Value Decomposition works

7A - Self-adjoint and Normal Operators

Notes for Section 7A

7B - Spectral Theorem

Notes for Section 7B

7C - Positive Operators

Notes for Section 7C

7D - Isometries, Unitary Operators, and QR Factorization

Notes for Section 7D

Roots of Complex Numbers

Visualizing the Regular Polygon of Roots and Principal Roots

Limits that Do Not Exist

Figures that help demonstrate an argument from board in class

Express In Terms of

What does it mean? How is it used?

Log-a-button

Logarithms with multiplicative thinking

Times Tables

Multiplying 2 through 9

Warmup

Single digit and double digit problems to master before multi-digit

Introduction

Borrowing and 100-pairs

Multi-digit Subtraction

Multi-digit subtraction with borrowing

Multi-digit Subtraction

A stand-alone problem

Old Subtraction Game

Old Javascript Version -- Subtraction Practice with Points

Addition

Adding Practice with Points

Regular Game

Game with Prime Buttons.

Game with Colors

Experimental Color-mixing Version

GCF

Greatest Common Factor with Prime Buttons

GCF with Subtraction

Find the GCF the Ancient Greek Way