Differential equations

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Course overview

Differential equations are equations that relate a function to its derivatives. They describe how quantities change, modeling dynamic systems like motion, growth, or decay. Solutions reveal the behavior of systems over time, forming the backbone of physics, engineering, and economics.

What will i learn?

A student who completes the Mdee Academy Differential Equations course will gain mastery in solving, verifying, and applying both first‑order and second‑order differential equations to real‑world problems. They’ll be equipped not only for exams but also for practical modeling in physics, engineering, and applied sciences

Requirements

solid foundation in calculus
solid foundation in algebra
solid foundation in basic mathematical reasoning.

Curriculum for this course

44 Lessons 10:29:24 Hours

Introduction to differential equations

5 Lessons 00:59:31 Hours

Introduction to differential equations
00:20:04
Formulating a differential equation
00:14:51
Verifying a solution to a differential equation
00:07:53
Solving simple differential equations by direct integration
00:11:19
Differential equations in standard differential form
00:05:24

First‑Order Differential Equations

20 Lessons 04:17:54 Hours

First order differential equations with separable variables
00:13:58
First order homogeneous differential equations
00:19:39
Non homogeneous first order differential equations
00:13:56
Non homogeneous first order differential equations 2
00:14:20
Partial integration
00:09:54
Exact differential equation
00:17:16
Exact differential equation (examples)
00:18:07
Exact differential equation (more examples)
00:06:19
Determining the integrating factor
00:17:05
Solving differential equations using the product rule, no integrating factor needed
00:07:29
Prove that the integrating factor for the differential equation is ...
00:13:17
Solving non exact differential equations using the integrating factor
00:12:39
Bernoulli's first order differential equation
00:18:58
Application of first order differential equations in exponential growth and decay
00:09:50
Application of first order differential equations in exponential growth and decay (examples)
00:11:04
Application of first order differential equations in cooling of substances
00:13:34
Application of first order differential equations in cooling of substances (examples)
00:10:19
Application of first order differential equations in dilution
00:15:52
Application of first order differential equations in dilution (more examples)
00:09:38
Application of first order differential equations in rate of change
00:04:40

Second‑Order Differential Equations

18 Lessons 04:48:44 Hours

Second order differential equations of the simple form
00:17:06
Second order differential equations reduced to first order differential equations
00:24:21
Second order homogeneous differential equations
00:04:22
General solution of AQE with two distinct roots - second order homogeneous differential equation
00:21:39
General solution of AQE with two distinct roots - second order homogeneous DE (more examples)
00:08:10
General solution of AQE with two equal roots - second order homogeneous differential equation
00:11:20
General solution of AQE with two equal roots - second order homogenous DE (more examples)
00:03:52
General solution of AQE with two complex roots - second order homogeneous differential equation
00:12:24
General solution of AQE with two complex roots - second order homogeneous DE (more examples)
00:06:39
Solving a second order differential equation (one cool example)
00:05:49
Non homogeneous second order differential equation
00:12:26
Non homogeneous second order differential equation (examples)
00:30:07
Non homogeneous second order differential equation (more examples)
00:19:04
Superposition differential equations
00:22:53
Simple harmonic motion differential equation
00:26:30
Applying second order differential equations in vibrating springs
00:13:04
Applying second order differential equations in damped vibration
00:20:11
Applying second order differential equations in electric circuits
00:28:47