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These video lectures of Professor Arthur Mattuck teaching 18.03 were recorded live in the Spring 2003 and do not correspond precisely to the lectures taught in the Spring of 2004. Professor Mattuck has inspired and informed generations of MIT students with his engaging lectures.
The videotaping was made possible by The d'Arbeloff Fund for Excellence in MIT Education.
Note: Lecture 18, 34, and 35 are not available
Lecture #1: The geometrical view of y'=f(x,y): direction fields, integral curves.
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Lecture #17: Finding particular solutions via Fourier series; resonant terms;hearing musical sounds.
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Lecture #2: Euler's numerical method for y'=f(x,y) and its generalizations.
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Lecture #19: Introduction to the Laplace transform; basic formulas.
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Lecture #3: Solving first-order linear ODE's; steady-state and transient solutions.
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Lecture #20: Derivative formulas; using the Laplace transform to solve linear ODE's.
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Lecture #4: First-order substitution methods: Bernouilli and homogeneous ODE's.
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Lecture #21: Convolution formula: proof, connection with Laplace transform, application to physical problems.
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Lecture #5: First-order autonomous ODE's: qualitative methods, applications.
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Lecture #22: Using Laplace transform to solve ODE's with discontinuous inputs.
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Lecture #6: Complex numbers and complex exponentials.
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Lecture #23: Use with impulse inputs; Dirac delta function, weight and transfer functions.
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Lecture #7: First-order linear with constant coefficients: behavior of solutions, use of complex methods.
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Lecture #24: Introduction to first-order systems of ODE's; solution by elimination, geometric interpretation of a system.
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Lecture #8: Continuation; applications to temperature, mixing, RC-circuit, decay, and growth models.
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Lecture #25: Homogeneous linear systems with constant coefficients: solution via matrix eigenvalues (real and distinct case).
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Lecture #9: Solving second-order linear ODE's with constant coefficients: the three cases.
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Lecture #26: Continuation: repeated real eigenvalues, complex eigenvalues.
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Lecture #10: Continuation: complex characteristic roots; undamped and damped oscillations.
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Lecture #27: Sketching solutions of 2x2 homogeneous linear system with constant coefficients.
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Lecture #11: Theory of general second-order linear homogeneous ODE's: superposition, uniqueness, Wronskians.
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Lecture #28: Matrix methods for inhomogeneous systems: theory, fundamental matrix, variation of parameters.
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Lecture #12: Continuation: general theory for inhomogeneous ODE's. Stability criteria for the constant-coefficient ODE's.
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Lecture #29: Matrix exponentials; application to solving systems.
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Lecture #13: Finding particular solutions to inhomogeneous ODE's: operator and solution formulas involving exponentials.
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Lecture #30: Decoupling linear systems with constant coefficients.
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Lecture #14: Interpretation of the exceptional case: resonance.
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Lecture #31: Non-linear autonomous systems: finding the critical points and sketching trajectories; the non-linear pendulum.
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Lecture #15: Introduction to Fourier series; basic formulas for period 2(pi).
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Lecture #32: Limit cycles: existence and non-existence criteria.
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Lecture #16: Continuation: more general periods; even and odd functions; periodic extension.
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Lecture #33: Relation between non-linear systems and first-order ODE's; structural stability of a system, borderline sketching cases; illustrations using Volterra's equation and principle.
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