Introduction to Ordinary Differential Equations
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Study of ordinary differential equations (e.g., solutions to separable and linear first-order equations and to higher-order linear equations with constant coefficients, systems of linear differential equations, the properties of solutions to differential equations) and linear algebra (e.g., vector spaces and solutions to algebraic linear equations, dimension, eigenvalues, and eigenvectors of a matrix), as well as the application of linear algebra to first-order systems of differential equations and the qualitative theory of nonlinear systems and phase portraits.
More resources on Ordinary Differential Equations
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
Introduction to Ordinary Differential Equations
This introductory courses on (Ordinary) Differential Equations are mainly for the people, who need differential equations mostly for the practical use in their own fields. So we try to provide basic terminologies, concepts, and methods of solving various types of differential equations as well as a rudimentary but indispensable knowledge of the underlying theory and some related applications. The prerequisites of the courses is one- or two- semester calculus course and some exposure to the elementary theory of matrices like determinants, Cramer’s Rule for solving linear systems of equations, eigenvalues and eigenvectors.
Single Variable Calculus (MIT 18.01SC)
MIT's self-paced 18.01SC covers differentiation, applications of derivatives, integration, techniques of integration, and infinite series, with problem sets, recitation videos, and exams with solutions. Completing it gives the standard first-semester calculus foundation.
Introduction to Differential Equations
Learn differential equations: explore methods for solving, modeling, and analyzing them. Taught by the Khan Academy Team.
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Learn differential equations with Paul Dawkins' comprehensive online course! Covers techniques for solving various DE types.
Elementary Differential Equations with Boundary Value Problems (free open edition)
Trench's full undergraduate ODE text, released free by the author under Creative Commons. Later chapters cover two-point boundary value problems, Sturm-Liouville eigenvalue problems, Fourier series, and separation of variables for the heat, wave and Laplace equations.