Differential Equations A-Z: Solve, Analyze, Apply
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
Requirements
- No prior knowledge of differential equations is required — this course starts from the fundamentals
- A scientific calculator or math software (e.g., Desmos, WolframAlpha, or a CAS tool) may be helpful for solving and visualizing problems
- Uunderstanding of calculus, including derivatives and integrals
- Familiarity with basic algebra and functions (exponential, logarithmic, trigonometric)
- Some experience with graphing and interpreting mathematical models
Description
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.
Who this course is for:
- Undergraduate students enrolled in a first course in differential equations
- STEM majors (engineering, physics, biology, economics) seeking a practical grasp of differential equations
- Learners preparing for advanced coursework involving dynamic systems or mathematical modeling
- Self-learners looking to understand how differential equations apply to real-world scientific problems
- Anyone who wants to strengthen their problem-solving skills with step-by-step mathematical reasoning
Instructors
- 5.0 Instructor Rating
- 10 Reviews
- 640 Students
- 6 Courses
Welcome to Sadat Academy! Here, we are committed to providing high-quality education across a wide range of subjects, ensuring students develop a strong foundation in both theoretical knowledge and practical skills. With years of experience in delivering structured and engaging courses, Sadat Academy offers a curriculum designed to foster student success and a deep understanding of the material.
We provide quality learning materials in Physics, Algebra, Trigonometry, Precalculus, General Chemistry, Organic Chemestry, Physics, Math, and Statistics.
At Sadat Academy, we are dedicated to guiding students toward academic excellence and ensuring they develop the critical thinking skills necessary for success. Whether students are beginners or looking to deepen their knowledge, our carefully designed curriculum fosters a love for learning and provides the support needed to succeed in every subject. Join us at Sadat Academy and embark on an enriching educational journey.
- 5.0 Instructor Rating
- 1 Review
- 359 Students
- 2 Courses
With over a decade of experience teaching mathematics at both the high school and college levels, Tara Sada has helped thousands of students transform their fear of calculus into genuine understanding—and even enjoyment. His teaching philosophy is simple: make complex ideas intuitive, engaging, and relevant to the real world.
But what truly sets Tara Sadat is his teaching style: clear, patient, and always centered on why things work—not just how. He believes anyone can learn calculus with the right explanation and the right mindset, and he brings that belief to every lecture he delivers.