Professor Leonard Courses

How to Evaluate Functions - Precalculus - College Algebra 3

Evaluate functions, navigate domain restrictions, compose functions, and apply the difference quotient in this focused college algebra lesson.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Introduction to Population Models and Logistic Equation

Explore how differential equations model population change through the logistic equation, including mathematical analyses of population explosion and extinction.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Integrating Factor for Exact Differential Equations

Learn how to use an integrating factor to solve exact differential equations.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

Solving Exact Differential Equations

Practice solving exact differential equations by testing exactness, using mixed partials, and working through examples.

• YouTube
• 52 minutes
• Self-Paced
• Free Video

Reducible Second Order Differential Equations, Missing X

Learn to reduce second-order differential equations missing the independent variable through substitution, integration, and solving for the resulting first-order equation.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video

Reducible Second Order Differential Equations, Missing Y

Learn to solve reducible second-order differential equations by substituting when the y variable is missing.

• YouTube
• 47 minutes
• Self-Paced
• Free Video

Special Integration in a Linear Differential Equation Problem

A long, intricate example of solving a first-order linear differential equation with substitutions, product rules, and an integrating factor.

• YouTube
• 39 minutes
• Self-Paced
• Free Video

Existence and Uniqueness of Solutions - Differential Equations

Learn how continuity near an initial point determines whether a differential equation has a solution and whether that solution is unique.

• YouTube
• 46 minutes
• Self-Paced
• Free Video

Introduction to Slope Fields

Explore how slope fields visualize solutions to differential equations through a constructive example and optional computer graphing.

• YouTube
• 36 minutes
• Self-Paced
• Free Video

Problem Solving with Velocity and Acceleration - Differential Equations 8

Solves velocity and acceleration word problems using differential equations and integrals to find position, initial conditions, and maximum height.

• YouTube
• 1 hour 26 minutes
• Self-Paced
• Free Video

Differential Equations with Velocity and Acceleration

Apply differential equations to velocity, acceleration, deceleration, and initial-value problems.

• YouTube
• 44 minutes
• Self-Paced
• Free Video

Graphing Systems of Linear Inequalities

Learn to graph two linear inequalities on one coordinate plane and identify the half-plane representing their shared solution.

• YouTube
• 34 minutes
• Self-Paced
• Free Video

Elimination Method with More Advanced Problems

Practice the elimination method for systems of equations, including fractions, opposite signs, incorrect forms, and other challenging cases.

• YouTube
• 27 minutes
• Self-Paced
• Free Video

Graphing Lines Using a Point and the Slope

Learn how to graph a line from one point by using its slope to find additional points.

• YouTube
• 34 minutes
• Self-Paced
• Free Video

Discovering the Slope Formula

Explore where the slope formula comes from, how to find slope, and how vertical change supports its mathematical use.

• YouTube
• 29 minutes
• Self-Paced
• Free Video