Learn to Solve and Apply Differential Equations with Confidence – From First Principles to Laplace Transforms
Mastering Differential Equations: A Practical Introduction
What you’ll learn
- Understand what differential equations are and why they’re essential in science and engineering.
- Solve first order differential equations using methods like separation of variables, integrating factors, and exact equations.
- Analyze and sketch slope fields to visualize solutions.
- Apply first order equations to real-life scenarios such as exponential growth, decay, and mixing problems.
- Solve second order linear differential equations with both constant and variable coefficients.
- Model and analyze mechanical systems involving harmonic motion and damping.
- Use differential equations to describe and solve population models, velocity-acceleration relationships, and electric circuits.
- Learn and apply the Laplace Transform to solve initial value problems.
- Use Laplace techniques including step functions and partial fractions for more complex models.
- Understand series solutions of differential equations near ordinary points.
- Build confidence in mathematical modeling and analytical thinking for technical fields.
Course Content
- Solving First Ordered Differential Equations –> 7 lectures • 1hr 49min.
- Second Ordered Differential Equations –> 8 lectures • 3hr 35min.
- Systems of Differential Equations –> 6 lectures • 2hr 5min.
- Applications of Differential Equations –> 2 lectures • 38min.
- Laplace Transforms and Series Solutions –> 6 lectures • 2hr 44min.
Requirements
Mastering Differential Equations: A Practical Introduction
Have you ever wondered how scientists model population growth, predict radioactive decay, or understand the mechanics of a vibrating spring? Differential equations are the powerful tools behind many of these real-world phenomena. In this comprehensive course, you’ll be introduced to the fundamental methods for solving differential equations and see how they apply directly to problems in science and engineering.
Whether you’re a student tackling this subject for the first time, or you’re brushing up for advanced studies, this course offers a solid, approachable foundation rooted in practical applications. Guided by the highly respected textbook Differential Equations and Boundary Value Problems: Computing and Modeling by Edwards, Penney, and Calvis, the course breaks down complex ideas into digestible, logical steps.
We begin with first order differential equations—how they are formed, what they represent, and how to solve them using techniques like separation of variables and integrating factors. You’ll explore real-world applications like modeling chemical mixtures and exponential decay. From there, we dive into second order equations, essential for understanding motion, vibrations, and systems with inertia.
Next, we turn toward real applications. Through population models, stability analysis, and simulations of electrical circuits and mechanical systems, you’ll see how differential equations bring theoretical math to life. Finally, you’ll gain fluency with Laplace transforms and series solutions—powerful tools for solving initial value problems and handling more complex differential systems.
Throughout the course, the focus remains on intuitive understanding, step-by-step problem solving, and meaningful applications. By the end, you’ll not only be confident in your mathematical skills but also prepared to apply them in scientific and engineering contexts.
Join today and start your journey into one of the most useful branches of mathematics—where calculus meets the real world.