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Open CosmologyPhysics & cosmology: four years, plus a graduate year
Mathematics · Year II

18.03 Differential Equations

Ordinary differential equations: first-order equations, linear equations with constant coefficients, oscillations and resonance, Fourier series, Laplace transforms, linear systems and non-linear systems.

Based on MIT OpenCourseWare, Spring 2010 · Prof. Arthur Mattuck, Prof. Haynes Miller · Course on OCW

Lectures (0 of 32 with pages so far)

  1. Lecture 1The Geometrical View of y'= f(x,y)MIT ↗
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  2. Lecture 2Euler's Numerical Method for y'=f(x,y)MIT ↗
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  3. Lecture 3Solving First-order Linear ODEsMIT ↗
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  4. Lecture 4First-order Substitution MethodsMIT ↗
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  5. Lecture 5First-order Autonomous ODEsMIT ↗
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  6. Lecture 6Complex Numbers and Complex ExponentialsMIT ↗
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  7. Lecture 7First-order Linear with Constant CoefficientsMIT ↗
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  8. Lecture 8ContinuationMIT ↗
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  9. Lecture 9Solving Second-order Linear ODE's with Constant CoefficientsMIT ↗
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  10. Lecture 10Continuation: Complex Characteristic RootsMIT ↗
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  11. Lecture 11Theory of General Second-order Linear Homogeneous ODEsMIT ↗
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  12. Lecture 12Continuation: General Theory for Inhomogeneous ODEsMIT ↗
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  13. Lecture 13Finding Particular Solutions to Inhomogeneous ODEsMIT ↗
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  14. Lecture 14Interpretation of the Exceptional Case: ResonanceMIT ↗
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  15. Lecture 15Introduction to Fourier SeriesMIT ↗
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  16. Lecture 16Continuation: More General PeriodsMIT ↗
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  17. Lecture 17Finding Particular Solutions via Fourier SeriesMIT ↗
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  18. Lecture 19Introduction to the Laplace TransformMIT ↗
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  19. Lecture 20Derivative FormulasMIT ↗
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  20. Lecture 21Convolution FormulaMIT ↗
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  21. Lecture 22Using Laplace Transform to Solve ODEs with Discontinuous InputsMIT ↗
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  22. Lecture 23Use with Impulse InputsMIT ↗
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  23. Lecture 24Introduction to First-order Systems of ODEsMIT ↗
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  24. Lecture 25Homogeneous Linear Systems with Constant CoefficientsMIT ↗
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  25. Lecture 26Continuation: Repeated Real EigenvaluesMIT ↗
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  26. Lecture 27Sketching Solutions of 2x2 Homogeneous Linear System with Constant CoefficientsMIT ↗
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  27. Lecture 28Matrix Methods for Inhomogeneous SystemsMIT ↗
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  28. Lecture 29Matrix ExponentialsMIT ↗
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  29. Lecture 30Decoupling Linear Systems with Constant CoefficientsMIT ↗
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  30. Lecture 31Non-linear Autonomous SystemsMIT ↗
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  31. Lecture 32Limit CyclesMIT ↗
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  32. Lecture 33Relation Between Non-linear Systems and First-order ODEsMIT ↗
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Note: Lecture 18 was an exam and has no lecture video.