Differential Equations (ODEs): First-Order & Second-Order Equations, Systems, Laplace Transforms, and Series Solutions
Differential Equations with Baby Steps is designed to make one of the most challenging math courses feel clear, structured, and easy. Differential equations are often taught in a rushed and intimidating way, this is why many students struggle and lose confidence in themselves. The goal of this course is to change that.
What you’ll learn
- First Order Differential Equations: Linear Differential Equations and Separable Differential Equations.
- Second Order Differential Equations: Linear Homogenous Equations, the Wronskian, Reduction of Order, Undetermined Coefficients and Variation of Parameters.
- Modeling with Differential Equations: Euler’s Method, Modeling, Water Tank Problems, Direction Fields.
- Systems of Differential Equations: Review of Matrices, Linear Algebraic Equations, Eigenvalues, and Eigenvectors, Homogeneous Systems and Complex Eigenvalues.
- Laplace Transforms: Laplace Solution of Initial Value Problems, Step Functions, ODEs with Discontinuous Functions, Impulse Functions and Convolution Integral.
- Series Solutions: Power Series, Series Solutions of Linear ODEs, Singular Points, Fourier Series.
Course Content
- Getting Started –> 1 lecture • 1min.
- Baby Step 1: First order Differential Equations –> 5 lectures • 1hr 28min.
- Baby Step 2: Second Order Differential Equations –> 8 lectures • 2hr 16min.
- Baby Step 3: Modeling With Differential Equations –> 4 lectures • 48min.
- Baby Step 4: Systems of Differential Equations –> 5 lectures • 1hr 21min.
- Baby Step 5: Laplace Transforms –> 5 lectures • 1hr.
- Baby Step 6: Series Solutions –> 4 lectures • 50min.
Requirements
Differential Equations with Baby Steps is designed to make one of the most challenging math courses feel clear, structured, and easy. Differential equations are often taught in a rushed and intimidating way, this is why many students struggle and lose confidence in themselves. The goal of this course is to change that.
Every topic is broken down into small, logical pieces, with clear explanations that focus on why methods/solutions work not just how to apply formulas. We begin with first-order differential equations, then move to second-order equations, real-world modeling, systems of differential equations, Laplace transforms, and finally series solutions. Each section builds naturally on the previous one, so you never feel lost or overwhelmed. After every lecture, I have prepared a quiz designed to reinforce key ideas and strengthen your understanding of the material. In addition, this course includes two full-length practice exams that help you build confidence and improve your test-taking skills.
WHAT MAKES THIS COURSE DIFFERENT?
- Step-by-step teaching with no skipped logic
Every method is explained from scratch. You’ll understand why each technique works not just when to use a formula. - Fast and reliable instructor supportYou can ask questions at any time and receive a clear response within 72 hours.
- Concept-driven quizzes (not memorization-based)Each quiz is carefully designed with high-quality, conceptual questions.
Every answer choice — both correct and incorrect — is fully explained, so you learn why a method works and why common mistakes fail. This trains real understanding instead of formula memorization. - High-quality practice that actually prepares you for exams
Carefully chosen examples, quizzes after every section, and two full-length practice exams help you turn understanding into performance. - Full coverage of a standard university differential equations courseFrom first-order equations to second-order equations, modeling, systems, Laplace transforms, and series solutions — all in one structured path.
- 30-day money back guaranteeIf you don’t like the course, your money is fully guaranteed within the first 30 days.
- Certificate of CompletionEarn a certificate of completion after finishing the course to showcase your achievement and add to your academic or professional profile.
Whether you are seeing differential equations for the first time or reviewing the material, this course is built just for you!