Video Lecture 1
(56k)
This lecture covers the geometrical view of y'=f(x,y): direction fields, integral curves.
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Video Lecture 2
(56k)
This lecture covers Euler's numerical method for y'=f(x,y) and its generalizations.
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Video Lecture 3
(56k)
This lecture covers solving first-order linear Ordinary Differential Equations; steady-state and transient solutions.
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Video Lecture 4
(56k)
This lecture covers first-order substitution methods: Bernoulli and homogeneous Ordinary Differential Equations.
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Video Lecture 5
(56k)
This lecture covers first-order autonomous Ordinary Differential Equations: qualitative methods, applications.
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Video Lecture 6
(56k)
This lecture covers complex numbers and complex exponentials.
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Video Lecture 7
(56k)
This lecture covers first-order linear with constant coefficients: behavior of solutions, use of complex methods.
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Video Lecture 8
(56k)
This lecture covers applications to temperature, mixing, RC-circuit, decay, and growth models.
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Video Lecture 9
(56k)
This lecture covers solving second-order linear Ordinary Differential Equations with constant coefficients: the three cases.
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Video Lecture 10
(56k)
This lecture covers complex characteristic roots; undamped and damped oscillations.
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Video Lecture 11
(56k)
This lecture covers the theory of general second-order linear homogeneous Ordinary Differential Equations: superposition, uniqueness, Wronskians.
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Video Lecture 12
(56k)
This lecture covers general theory for inhomogeneous Ordinary Differential Equations. Stability criteria for the constant-coefficient Ordinary Differential Equations.
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Video Lecture 13
(56k)
This lecture covers finding particular solutions to inhomogeneous Ordinary Differential Equations: operator and solution formulas involving exponentials.
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Video Lecture 14
(56k)
This lecture covers interpretation of the exceptional case: resonance.
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Video Lecture 15
(56k)
This lecture covers introduction to Fourier series; basic formulas for period 2(pi).
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Video Lecture 16
(56k)
This lecture covers more general periods; even and odd functions; periodic extension.
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Video Lecture 17
(56k)
This lecture covers finding particular solutions via Fourier series; resonant terms; hearing musical sounds.
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Video Lecture 18
(56k)
This lecture covers introduction to the Laplace transform; basic formulas.
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Video Lecture 19
(56k)
This lecture covers derivative formulas; using the Laplace transform to solve linear Ordinary Differential Equations.
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Video Lecture 20
(56k)
This lecture covers convolution formula: proof, connection with Laplace transform, application to physical problems.
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Video Lecture 21
(56k)
This lecture covers using Laplace transform to solve Ordinary Differential Equations with discontinuous inputs.
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Video Lecture 22
(56k)
This lecture covers use with impulse inputs; Dirac delta function, weight and transfer functions.
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Video Lecture 23
(56k)
This lecture covers introduction to first-order systems of Ordinary Differential Equations; solution by elimination, geometric interpretation of a system.
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Video Lecture 24
(56k)
This lecture covers homogeneous linear systems with constant coefficients: solution via matrix
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Video Lecture 25
(56k)
This lecture covers repeated real eigenvalues, complex eigenvalues.
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Video Lecture 26
(56k)
This lecture covers sketching solutions of 2x2 homogeneous linear system with constant coefficients.
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Video Lecture 27
(56k)
This lecture covers matrix methods for inhomogeneous systems: theory, fundamental matrix, variation of parameters.
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Video Lecture 28
(56k)
This lecture covers matrix exponentials; application to solving systems.
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Video Lecture 29
(56k)
This lecture covers decoupling linear systems with constant coefficients.
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Video Lecture 30
(56k)
This lecture covers non-linear autonomous systems: finding the critical points and sketching trajectories; the non-linear pendulum.
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Video Lecture 31
(56k)
This lecture covers limit cycles: existence and non-existence criteria.
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Video Lecture 32
(56k)
This lecture covers relation between non-linear systems and first-order Ordinary Differential Equations; structural stability of a system, borderline sketching cases; illustrations using Volterra's equation and principle.
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