Course
Course contents
Nine chapters, from first-order equations to the Laplace transform. Each section explains the ideas in small steps, works through original examples, and ends with exercises. Interactive solvers let you enter your own numbers and see every step. Each chapter ends with a quiz that generates new problems every time.
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Systems of Linear Differential Equations
- 7.1 Differential Operators and the Operator Method
- 7.2 Applications of Linear Systems
- 7.3 Basic Theory of Linear Systems in Normal Form (2×2)
- 7.4 Homogeneous Constant-Coefficient Systems (2×2)
- 7.5 Matrices and Vectors
- 7.6 The Matrix Method: Two Equations
- 7.7 The Matrix Method: n Equations
- 7.8 Basic Theorems on Homogeneous Linear Systems
- Chapter quiz
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Approximate Methods for First-Order Equations
- 8.1 Graphical Methods
- 8.2 Power Series Methods
- 8.3 The Method of Successive Approximations
- 8.4 Numerical Methods I: Euler's Method
- 8.5 Numerical Methods II: The Improved Euler Method
- 8.6 Numerical Methods III: Runge–Kutta
- 8.7 Numerical Methods IV: Adams–Bashforth/Adams–Moulton
- 8.8 Numerical Methods V: Higher-Order Equations and Systems
- Chapter quiz
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