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Differential Equations Syllabus
Solve ordinary and partial differential equations and model dynamic systems across analytical, numerical, and qualitative methods. The full Differential Equations syllabus: 7 subjects, 32 chapters and 100 topics, with 373 flashcards written against it.
Differential Equations subjects
Differential Equations has 7 subjects. Each one is listed below with its chapters in syllabus order; open a subject for every topic and sub-topic inside them.
First-Order Ordinary Differential Equations
- Introduction to Differential Equations · 4 topics
- Separable and Exact Equations · 3 topics
- Linear and Special First-Order Equations · 4 topics
- Qualitative Methods for First-Order Equations · 3 topics
- Modeling with First-Order Equations · 5 topics
Higher-Order Linear Differential Equations
- Theory of Linear Equations · 4 topics
- Homogeneous Equations with Constant Coefficients · 2 topics
- Nonhomogeneous Equations · 2 topics
- Cauchy-Euler and Special Equations · 2 topics
- Applications: Mechanical and Electrical Vibrations · 4 topics
Laplace Transforms and Operational Methods
- The Laplace Transform · 3 topics
- Inverse Transforms and Operational Properties · 4 topics
- Solving Initial-Value Problems · 2 topics
- Special Functions and Convolution · 3 topics
Series Solutions and Special Functions
- Power Series Solutions · 3 topics
- Solutions About Singular Points · 2 topics
- Special Functions · 3 topics
Systems of Differential Equations and Dynamical Systems
- Linear Systems Theory · 2 topics
- Eigenvalue Methods · 4 topics
- Nonhomogeneous Systems · 2 topics
- Phase Plane and Stability Analysis · 4 topics
- Nonlinear Dynamics · 4 topics
Numerical Methods for Differential Equations
- Single-Step Methods · 3 topics
- Multistep and Adaptive Methods · 3 topics
- Numerical Analysis Considerations · 3 topics
- Boundary-Value Problem Methods · 2 topics
Partial Differential Equations and Boundary-Value Problems
- Fourier Series · 4 topics
- Sturm-Liouville Theory · 3 topics
- Classification and Separation of Variables · 3 topics
- The Heat Equation · 3 topics
- The Wave Equation · 3 topics
- Laplace's Equation and Other Methods · 4 topics
Differential Equations flashcards
373 question-and-answer cards across 7 subject decks, each shown in full on its subject page.
- First-Order Ordinary Differential Equations — 59 cards
- Higher-Order Linear Differential Equations — 55 cards
- Laplace Transforms and Operational Methods — 50 cards
- Series Solutions and Special Functions — 50 cards
- Systems of Differential Equations and Dynamical Systems — 50 cards
- Numerical Methods for Differential Equations — 59 cards
- Partial Differential Equations and Boundary-Value Problems — 50 cards
Differential Equations syllabus FAQ
What subjects are in the Differential Equations syllabus?
Differential Equations covers 7 subjects: First-Order Ordinary Differential Equations, Higher-Order Linear Differential Equations, Laplace Transforms and Operational Methods, Series Solutions and Special Functions, Systems of Differential Equations and Dynamical Systems, Numerical Methods for Differential Equations and Partial Differential Equations and Boundary-Value Problems.
How many chapters and topics are in the Differential Equations syllabus?
32 chapters and 100 topics, across 7 subjects. Partial Differential Equations and Boundary-Value Problems is the largest subject, with 20 topics in 6 chapters.
Are there Differential Equations flashcards?
Yes — 373 question-and-answer flashcards in 7 subject decks. Each deck is printed in full on its subject page here, and the same cards are in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.
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