MIT OCW 18.03 - Mathematics - Differential Equations
Haynes Miller and Arthur Mattuck

folder MIT OCW - Mathematics -Differential Equations (33 files)
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file33. Relation Between Non-linear Systems and First-order ODEs.mp4 214.74MB
file32. Limit Cycles.mp4 196.69MB
file31. Non-linear Autonomous Systems.mp4 202.39MB
file30. Decoupling Linear Systems with Constant Coefficients.mp4 202.55MB
file29. Matrix Exponentials.mp4 210.05MB
file28. Matrix Methods for Inhomogeneous Systems.mp4 201.47MB
file27. Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients.mp4 216.26MB
file26. Continuation, Repeated Real Eigenvalues.mp4 200.03MB
file25. Homogeneous Linear Systems with Constant Coefficients.mp4 210.65MB
file24. Introduction to First-order Systems of ODEs.mp4 202.36MB
file23. Use with Impulse Inputs.mp4 192.91MB
file22. Using Laplace Transform to Solve ODEs with Discontinuous Inputs.mp4 190.59MB
file21. Convolution Formula.mp4 190.59MB
file20. Derivative Formulas.mp4 219.04MB
file19. Introduction to the Laplace Transform.mp4 204.59MB
file17. Finding Particular Solutions via Fourier Series.mp4 196.42MB
file16. Continuation, More General Periods.mp4 212.44MB
file15. Introduction to Fourier Series.mp4 212.58MB
file14. Interpretation of the Exceptional Case Resonance.mp4 191.00MB
file13. Finding Particular Sto Inhomogeneous ODEs.mp4 205.33MB
file12. Continuation, General Theory for Inhomogeneous ODEs.mp4 199.19MB
file11. Theory of General Second-order Linear Homogeneous ODEs.mp4 111.00MB
file10. Continuation, Complex Characteristic Roots.mp4 199.52MB
file9. Solving Second-order Linear ODE's with Constant Coefficients.mp4 214.87MB
file8. Continuation.mp4 217.25MB
file7. First-order Linear with Constant Coefficients.mp4 176.58MB
file6. Complex Numbers and Complex Exponentials.mp4 176.58MB
file5. First-order Autonomous ODEs.mp4 194.65MB
file4. First-order Substitution Methods.mp4 114.19MB
file3. Solving First-order Linear ODEs.mp4 214.87MB
file2. Euler's Numerical Method.mp4 217.75MB
file1. The Geometrical View of y'=f(x,y).mp4 210.16MB
Type: Course

title= {MIT OCW 18.03 - Mathematics - Differential Equations},
journal= {},
author= {Haynes Miller and Arthur Mattuck},
year= {2010},
url= {},
license= {},
abstract= {##Course 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.

18.03 Differential Equations has 18.01 Single Variable Calculus as a prerequisite. 18.02 Multivariable Calculus is a corequisite, meaning students can take 18.02 and 18.03 simultaneously.

Buy at Amazon Edwards, C., and D. Penney. Elementary Differential Equations with Boundary Value Problems. 6th ed. Upper Saddle River, NJ: Prentice Hall, 2003. ISBN: 9780136006138.

Note: The 5th Edition (Buy at Amazon ISBN: 9780131457744) will serve as well.

Students also need two sets of notes "18.03: Notes and Exercises" by Arthur Mattuck, and "18.03 Supplementary Notes" by Haynes Miller.

This course is a study of Ordinary Differential Equations (ODE's), including modeling physical systems.

##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.


The lecture period is used to help students gain expertise in understanding, constructing, solving, and interpreting differential equations. * Students must come to lecture prepared to participate actively. At the first recitation, students are given a set of flashcards to bring to each lecture. They are used during class sessions to vote on answers to questions posed occasionally in the lecture. In case of divided opinions, a discussion follows. As a further element of active participation in class, students will often be asked to spend a minute responding to a short feedback question at the end of the lecture.

These small groups meet twice a week to discuss and gain experience with the course material. Even more than the lectures, the recitations involve active participation. The recitation leader may begin by asking for questions or hand out problems to work on in small groups. Students are encouraged to ask questions early and often. Recitation leaders also hold office hours.

Another resource of great value to students is the tutoring room. This is staffed by experienced undergraduates. Extra staff is added before hour exams. This is a good place to go to work on homework.

##The Ten Essential Skills
Students should strive for personal mastery over the following skills. These are the skills that are used in other courses at MIT. This list of skills is widely disseminated among the faculty teaching courses listing 18.03 as a prerequisite. At the moment, 140 courses at MIT list 18.03 as a prerequisite or a corequisite.

Model a simple system to obtain a first order ODE. Visualize solutions using direction fields and isoclines, and approximate them using Euler's method.
Solve a first order linear ODE by the method of integrating factors or variation of parameter.
Calculate with complex numbers and exponentials.
Solve a constant coefficient second order linear initial value problem with driving term exponential times polynomial. If the input signal is sinusoidal, compute amplitude gain and phase shift.
Compute Fourier coefficients, and find periodic solutions of linear ODEs by means of Fourier series.
Utilize Delta functions to model abrupt phenomena, compute the unit impulse response, and express the system response to a general signal by means of the convolution integral.
Find the weight function or unit impulse response and solve constant coefficient linear initial value problems using the Laplace transform together with tables of standard values. Relate the pole diagram of the transfer function to damping characteristics and the frequency response curve.
Calculate eigenvalues, eigenvectors, and matrix exponentials, and use them to solve first order linear systems. Relate first order systems with higher-order ODEs.
Recreate the phase portrait of a two-dimensional linear autonomous system from trace and determinant.
Determine the qualitative behavior of an autonomous nonlinear two-dimensional system by means of an analysis of behavior near critical points.
The Ten Essential Skills is also available as a (PDF).

Each homework assignment has two parts: a first part drawn from the book or notes, and a second part consisting of problems which will be handed out. Both parts are keyed closely to the lectures. Students should form the habit of doing the relevant problems between successive lectures and not try to do the whole set the night before they are due.},
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