Math 18.03, Concourse - MIT
CC.1803
Lectures by: Robert Winters
email: robert@math.rwinters.com
Recitations by: Robert Winters
Calendar of topics and Notes and Supplements Solutions |
Concourse Stellar site
Concourse 18.03 Stellar site
(former) Concourse 18.01A-02A site
Though there is no required text for the course, two texts that have been used for the course in the past may serve as useful references. They are:
Differential Equations & Linear Algebra by Farlow, Hall, McDill, West. This text was used for the Spring 2014 semester and is published by Pearson and has ISBN #9780131860612.
[Click on the image below for online prices.]
Table of Contents:
1. First-Order Differential Equations
2. Linearity and Nonlinearity
3. Linear Algebra
4. Higher-Order Linear Differential Equations
5. Linear Transformations
6. Linear Systems of Differential Equations
7. Nonlinear Systems of Differential Equations
8. Laplace Transforms
9. Discrete Dynamical Systems
10. Control Theory and the Appendices
Elementary Differential Equations with Boundary Value Problems, 6th Edition by Edwards & Penney (ISBN 0130339679 for 2008 hardcover edition) or an earlier edition. This text was used for the Spring 2013 and earlier semesters.
Table of Contents:
• Ch. 1 - First-Order Differential Equations
• Ch. 2 - Linear Equations of Higher Order
• Ch. 3 - Power Series methods
• Ch. 4 - Laplace Transform Methods
• Ch. 5 - Linear Systems of Differential Equations
• Ch. 6 - Numerical Methods
• Ch. 7 - Nonlinear Systems and Phenomena
• Ch. 8 - Fourier Series Methods
• Ch. 9 - Eigenvalues and Boundary Value Problems
Earlier editions of the Edwards & Penney text would also be good reference texts.
This was the site of the Concourse 18.03 course (a.k.a. CC.1803) that ran for 9 years from Spring 2012 through Spring 2020. I imagine that some version of the course will continue within the remnants of the Concourse Program, a program that billed itself as “integrating science and the humanities” but which made no effort to actually do so for at least the last 8 years. Concourse has sold that false bill of goods simply to justify its continued existence as an MIT Freshman Learning Community. The students of Concourse are much the same as virtually all MIT students - curious, smart, and a pleasure to know. The Concourse Program, in contrast, is built on a foundation of hypocrisy. Themes like justice and truth and knowledge are presented to its students, but what has come to define Concourse are the need for control and enforcing obedience and taking care of the selfish needs of the administrators of the program. Those of us who were simply very good at teaching our courses (and greatly appreciated by our students) and who did our best to actually integrate science and the humanities or, in my case, civic responsibility, have never been valued by the directors of the program. Those who teach in Concourse actually have very little say in how the program operates, and the program has largely been on auto-pilot for some time. That said, you could probably randomly pick 50 MIT freshmen and make it work as long as good teachers were in the program who actively engaged students. I treasure all of my relationships with students built up over 9 years working in Concourse as well as the absolute joy of sharing an office for most of my time there with a truly wonderful teacher of Chemistry and mentor of students. I miss the students more than I can put into words. However, I don’t at all miss working in an oppressive environment with an incompetent and vengeful Assistant Director and a Director who values only blind obedience and who would gladly throw under the bus anyone whose independence in any way threatened her personal insecurities. Any academic program, including any MIT Freshman Learning Community, should aspire to greater things. - Robert Winters |
Announcements:
A variant of this course is now offered at the Harvard University Extension School (Fall 2020).
email: robert@math.rwinters.com
| There's a huge difference between Knowing and Understanding. You can actually know a lot about something and not really understand it. – Richard Feynman |
Syllabus for Concourse Math 18.03 (Spring 2020)
Printable syllabus (PDF, Spring 2020)
Less Bronx-Whitestone Bridge Yielded More Stability During Hurricane Sandy (NY Times; Jan 4, 2013)
A success story of the sister bridge of the Tacoma Narrows Bridge
How do you re-engineer a suspension bridge to prevent collapse due to resonance? There’s a way... and there’s also a better way.
Whitestone Bridge with trusses (1946-2004)
Whitestone Bridge with trusses removed (2004-present)
References:
ODE Manipulatives (“Mathlets”)
This course employs a series of specially written Java™ applets, or Mathlets, developed by the Mathematics Department. Each problem set typically contains a problem based around one or another of them. [Full catalog of Mathlets from Math Dept.]
18.03 Supplementary Notes by Prof. Haynes Miller (used in the mainstream version of this course)
18.03: Notes and Exercises by Prof. Arthur Mattuck
Additional Notes
Subspaces, Span, Linear Independence, Basis of a Subspace; Images and Kernel of a Matrix (RW)
General Linear Spaces (Vector Spaces) and Solutions of ODEs (RW)
Laplace Transform Facts
Notes on Convolution (RW)
Matrix Methods for Solving Systems of 1st Order Linear Differential Equations (new)
Phase portraits for the linear ODE examples
Supplement on Evolution Matrices
Supplement on Linear Coordinates, Alternate Bases, and Evolution Matrices
Sampler of Phase Plane diagrams for uncoupled, coupled, period, and stable sink linear systems and a nonlinear system.
For your viewing pleasure: Arthur Mattuck explains numerical methods for solving ordinary differential equations (Euler's Method)
Numerical Methods: Euler's Method (OCW Video); Example of Euler's Method (OCW Video)
Prerequisites/Corequisites:
18.01 (Single Variable Calculus) is a prerequisite; 18.02 (Multivariable Calculus) is a corequisite, meaning students may take 18.02 and 18.03 simultaneously.
Texts: None required, but two good optional textx are:
(1) Differential Equations & Linear Algebra by Farlow, Hall, McDill, West. This text is published by Pearson and has ISBN #9780131860612.
(2) Elementary Differential Equations with Boundary Value Problems. 6th ed. by Edwards, C., and D. Penney. Upper Saddle River, NJ: Prentice Hall, 2008. ISBN: 9780136006138. [Note: The 5th Edition (ISBN: 9780131457744) or the 4th Edition will serve as well.]
Students will also need two sets of notes “18.03: Notes and Exercises” by Arthur Mattuck, and “18.03 Supplementary Notes” by Haynes Miller (both available online at no cost). We will primarily use these notes and our own Lecture Notes which may be revised as the course proceeds. Additional supplements may also be provided.
Description:
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 Concourse version of the 18.03 course will closely parallel the mainstream 18.03 course. As has been the case for the last few semesters, there will be additional emphasis on Linear Algebra throughout the course, and some topics listed above may be less emphasized than in previous years.
Lectures
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. Students may sometimes be asked to spend a minute responding to a short feedback question at the end of the lecture.
Recitations
These 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.
Office Hours
Regular office hours at times to be determined. You are encouraged to drop by for any matters that cannot adequately be addressed in class.
Tutoring
Tutors/graders are available within Concourse. Another resource of great value to students is the Mathematics Department tutoring room. This is staffed by experienced undergraduates. This is a good place to go to work on homework (as is the Concourse Lounge).
Videos
You may find the 18.03 lecture videos of Arthur Mattuck helpful. They are available on the Open Courseware site and were recorded in Spring 2003.
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).
Homework:
Homework assignments typically will have 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.
Exams:
There are 3 one-hour exams held during lecture session and a three-hour comprehensive final examination.
Grading:
The final grade will be based on the following scheme (subject to minor modification):
25% homework, 35% hour exams, 40% Final Exam
ODE Manipulatives (“Mathlets”):
This course employs a series of specially written Java™ applets, or Mathlets, developed by the Mathematics Department. They may be used in lecture occasionally, and each problem set typically contains a problem based around one or another of them.
Topics and Assignments are posted in the Course Calendar.
If ever you need to get in touch, you can contact me at either robert@math.rwinters.com or Robert@rwinters.com.
Here's something: http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/index.html
Please send comments to Robert Winters.
URL: http://math.rwinters.com/1803
Last modified:
Tuesday, January 3, 2023 10:29 AM