Differential Equations, Spring 2006
by Instructors: Prof. Arthur Mattuck Prof. Haynes Miller
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Description
Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams.
| Name | Description | Released | Price | ||
|---|---|---|---|---|---|
| 1 | VideoLecture 01: The geometrical view of y'=f(x,y): direction fields, integral curves. | -- | 6/27/07 | Free | View In iTunes |
| 2 | VideoLecture 02: Euler's numerical method for y'=f(x,y) and its generalizations. | -- | 6/27/07 | Free | View In iTunes |
| 3 | VideoLecture 03: Solving first-order linear ODE's; steady-state and transient solutions. | -- | 6/27/07 | Free | View In iTunes |
| 4 | VideoLecture 04: First-order substitution methods: Bernouilli and homogeneous ODE's. | -- | 6/27/07 | Free | View In iTunes |
| 5 | VideoLecture 05: First-order autonomous ODE's: qualitative methods, applications. | -- | 6/27/07 | Free | View In iTunes |
| 6 | VideoLecture 06: Complex numbers and complex exponentials. | -- | 6/27/07 | Free | View In iTunes |
| 7 | VideoLecture 07: First-order linear with constant coefficients: behavior of solutions, use of complex methods. | -- | 6/27/07 | Free | View In iTunes |
| 8 | VideoLecture 08: Continuation; applications to temperature, mixing, RC-circuit, decay, and growth models. | -- | 6/27/07 | Free | View In iTunes |
| 9 | VideoLecture 09: Solving second-order linear ODE's with constant coefficients: the three cases. | -- | 6/27/07 | Free | View In iTunes |
| 10 | VideoLecture 10: Continuation: complex characteristic roots; undamped and damped oscillations. | -- | 6/27/07 | Free | View In iTunes |
| 11 | VideoLecture 11: Theory of general second-order linear homogeneous ODE's: superposition, uniqueness, Wronskians. | -- | 6/27/07 | Free | View In iTunes |
| 12 | VideoLecture 12: Continuation: general theory for inhomogeneous ODE's. Stability criteria for the constant-coefficient ODE's. | -- | 6/27/07 | Free | View In iTunes |
| 13 | VideoLecture 13: Finding particular solutions to inhomogeneous ODE's: operator and solution formulas involving exponentials. | -- | 6/27/07 | Free | View In iTunes |
| 14 | VideoLecture 14: Interpretation of the exceptional case: resonance. | -- | 6/27/07 | Free | View In iTunes |
| 15 | VideoLecture 15: Introduction to Fourier series; basic formulas for period 2(pi). | -- | 6/27/07 | Free | View In iTunes |
| 16 | VideoLecture 16: Continuation: more general periods; even and odd functions; periodic extension. | -- | 6/27/07 | Free | View In iTunes |
| 17 | VideoLecture 17: Finding particular solutions via Fourier series; resonant terms;hearing musical sounds. | -- | 6/27/07 | Free | View In iTunes |
| 18 | VideoLecture 19: Introduction to the Laplace transform; basic formulas. | -- | 6/27/07 | Free | View In iTunes |
| 19 | VideoLecture 20: Derivative formulas; using the Laplace transform to solve linear ODE's. | -- | 6/27/07 | Free | View In iTunes |
| 20 | VideoLecture 21: Convolution formula: proof, connection with Laplace transform, application to physical problems. | -- | 6/27/07 | Free | View In iTunes |
| 21 | VideoLecture 22: Using Laplace transform to solve ODE's with discontinuous inputs. | -- | 6/27/07 | Free | View In iTunes |
| 22 | VideoLecture 23: Use with impulse inputs; Dirac delta function, weight and transfer functions. | -- | 6/27/07 | Free | View In iTunes |
| 23 | VideoLecture 24: Introduction to first-order systems of ODE's; solution by elimination, geometric interpretation of a system. | -- | 6/27/07 | Free | View In iTunes |
| 24 | VideoLecture 25: Homogeneous linear systems with constant coefficients: solution via matrix eigenvalues (real and distinct case). | -- | 6/27/07 | Free | View In iTunes |
| 25 | VideoLecture 26: Continuation: repeated real eigenvalues, complex eigenvalues. | -- | 6/27/07 | Free | View In iTunes |
| 26 | VideoLecture 27: Sketching solutions of 2x2 homogeneous linear system with constant coefficients. | -- | 6/27/07 | Free | View In iTunes |
| 27 | VideoLecture 28: Matrix methods for inhomogeneous systems: theory, fundamental matrix, variation of parameters. | -- | 6/27/07 | Free | View In iTunes |
| 28 | VideoLecture 29: Matrix exponentials; application to solving systems. | -- | 6/27/07 | Free | View In iTunes |
| 29 | VideoLecture 30: Decoupling linear systems with constant coefficients. | -- | 6/27/07 | Free | View In iTunes |
| 30 | VideoLecture 31: Non-linear autonomous systems: finding the critical points and sketching trajectories; the non-linear pendulum. | -- | 6/27/07 | Free | View In iTunes |
| 31 | VideoLecture 32: Limit cycles: existence and non-existence criteria. | -- | 6/27/07 | Free | View In iTunes |
| 32 | VideoLecture 33: Relation between non-linear systems and first-order ODE's; structural stability of a system, borderline sketching c | -- | 6/27/07 | Free | View In iTunes |
| Total: 32 Episodes |
Customer Reviews
Thanks!!
Great lectures!!!!!
But where is chapter 18?
