Embark on an extensive exploration of differential equations and their real-world applications in this comprehensive video series. Delve into the fundamentals, starting with an introduction to differential equations and progressing through various problem-solving techniques. Master concepts such as initial value problems, slope fields, existence and uniqueness of solutions, and separable equations. Learn to solve linear differential equations using integrating factors, tackle homogeneous first-order equations, and apply substitution methods. Explore advanced topics including Bernoulli equations, embedded derivatives, and reducible second-order differential equations. Gain practical knowledge through population models, logistic equations, and stability analysis. Develop problem-solving skills with velocity and acceleration applications, mixture problems, and harvesting population scenarios.
Overview
Syllabus
The Plan for Differential Equations (Differential Equations 1).
Introduction to Differential Equations (Differential Equations 2).
Checking Solutions in Differential Equations (Differential Equations 3).
Introduction to Initial Value Problems (Differential Equations 4).
Introduction to Time Rate of Change (Differential Equations 5).
Solving Basic Differential Equations with Integration (Differential Equations 6).
Differential Equations with Velocity and Acceleration (Differential Equations 7).
Problem Solving with Velocity and Acceleration (Differential Equations 8).
Introduction to Slope Fields (Differential Equations 9).
Applications of Slope Fields (Differential Equations 10).
Watch Before Diff Eq 11.
Existence and Uniqueness of Solutions (Differential Equations 11).
Separable Differential Equations (Differential Equations 12).
Separable Equations with Initial Values (Differential Equations 13).
Applications with Separable Equations (Differential Equations 14).
Introduction to Linear Differential Equations and Integrating Factors (Differential Equations 15).
Solving Linear Differential Equations with an Integrating Factor (Differential Equations 16).
Domain Restrictions In Differential Equations and Integrating Factors (Differential Equations 17).
Special Integration in a Linear Differential Equation Problem (Differential Equations 18).
Mixture Problems in Linear Differential Equations (Differential Equations 19).
Substitutions for Homogeneous First Order Differential Equations (Differential Equations 20).
Solving Homogeneous First Order Differential Equations (Differential Equations 21).
Solving Differential Equations with a Composition (Obvious) Substitution (Differential Equations 22).
How to Solve Bernoulli Differential Equations (Differential Equations 23).
Solving Differential Equations with Embedded Derivative Substitutions (Differential Equations 24).
How Embedded Derivatives Can Make Differential Equations Easier (Differential Equations 25).
Reducible Second Order Differential Equations, Missing Y (Differential Equations 26).
Reducible Second Order Differential Equations, Missing X (Differential Equations 27).
What are Exact Differential Equations (Differential Equations 28).
Solving Exact Differential Equations (Differential Equations 29).
Integrating Factor for Exact Differential Equations (Differential Equations 30).
Introduction to Population Models and Logistic Equation (Differential Equations 31).
Basic Population Models in Differential Equations (Differential Equations 32).
Birth Rates and Death Rates in Differential Equations (Differential Equations 33).
Using Partial Fractions in Differential Equations (Differential Equations 34).
Population Growth and Decline (Differential Equations 35).
Equilibrium Solutions and Stability of Differential Equations (Differential Equations 36).
Stability of Critical Points (Differential Equations 37).
Harvesting Populations in Differential Equations (Differential Equations 38).
Taught by
Professor Leonard
