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Video Lectures

Watch video lectures that complement the course material. Visual explanations to deepen your understanding of differential equations.

Course Introduction

Start here to understand what differential equations are all about

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Introduction Video

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Introduction Start Here

The Language of Change

An introductory video that sets the stage for the entire course. Discover why differential equations are the mathematical language used to describe change in nature, engineering, and science — from population growth to electrical circuits to mechanical vibrations.

📚 Course Introduction 🎯 Recommended for all students

Chapter 1: First-Order ODEs

Animated lectures with voiceover narration

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Separable Equations

Definition, separation technique, 6-step method, worked example, equilibrium solutions

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Linear Equations

Integrating factor method, standard form, derivation, two worked examples

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Exact Equations

Exactness test, potential functions, 7-step method, IVP example

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Non-Exact & Integrating Factors

Case 1 μ(x), Case 2 μ(y), 6-step algorithm, two worked examples

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Homogeneous Equations

Homogeneous functions, v = y/x substitution, 5-step method, worked examples

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Bernoulli Equations

Substitution v = y^(1-n), reduction to linear form, three worked examples

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Chapter 1: Exam Review — 12 Problems

Method selection flowchart, 12 exam-style problems with step-by-step solutions, covers all 6 methods

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Chapter 2: Second-Order ODEs

Animated lectures with voiceover narration

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Homogeneous with Constant Coefficients

Characteristic equation, distinct real roots, repeated roots, complex roots, mind map

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Undetermined Coefficients

Guessing table, modification rule, resonance, 6 worked examples, flowchart

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Variation of Parameters

Wronskian, VP formulas, derivation, 5 worked examples including tan and exponential

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Euler (Cauchy–Euler) Equations

Indicial equation, 3 root cases, reduction of order, transformation to constant coefficients

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Chapter 2: Exam Review — 12 Problems

Method selection flowchart, 12 exam-style problems with step-by-step solutions, covers all 4 methods

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Chapter 3: Laplace Transforms

Animated lectures with voiceover narration

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Definition & Properties

Laplace definition, linearity, s-shifting theorem, transform table, derivative transforms

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Inverse Laplace Transform

Partial fractions, cover-up method, completing the square, 8 worked examples

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Solving ODEs with Laplace

6-step method, transfer function, 8 worked IVP examples including RLC circuits

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Step Functions & Convolution

Unit step, second shifting theorem, convolution integral & theorem, impulse response

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Chapter 3: Exam Review — 9 Problem Types

Complete transform table, all 9 exam problem types with solutions, decision flowchart, exam strategies

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Chapter 4: Systems of Differential Equations

Animated lectures with voiceover narration

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Matrices & Eigenvalues

Matrix operations, determinants, eigenvalue definition, characteristic equation, 3 eigenvalue cases

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Homogeneous Systems

Eigenvalue method, 3 solution cases, generalized eigenvectors, converting higher-order ODEs

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Phase Portraits & Stability

8 equilibrium types, trace-determinant classification, stability analysis, worked examples

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Applications: Two-Tank & Engineering

Two-tank mixing, coupled springs, normal modes, RLC circuits, population dynamics

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Chapter 4: Exam Review — Complete Review

Eigenvalues, 3 solution cases, phase portraits, trace-determinant method, two-tank problems, exam strategies

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