Course 18.085: Mathematical Methods for Engineers I
(Fall 2008)

Department of Mathematics
Massachusetts Institute of Technology

[info] [resources] [assignments] [old exams]

General Information

Lecturer: Gilbert Strang (gs@math.mit.edu), room 2-240

Lectures: Room 4-370, MWF 11-12
Weekly homework review WED 4-5 in 4-370

Teaching Assistants: Salman Abolfathe (salman@math.mit.edu, Room 2-489 OFFICE HR FRI 4-5) and Peter Buchak (pmb@math.mit.edu, Room 2-331)

Main Topics:

Applied Linear Algebra (so important!)
Applied Differential Equations (for engineering and science)
Fourier Methods
Algorithms (lu, qr, eig, svd, finite differences, finite elements, FFT)

My Goals for the Course: I hope you will feel that this is the most useful math course you have ever taken. I will do everything I can to make it so. This will not be like a calculus class where a method is explained and you just repeat it on homework and a test. The goals are to see the underlying pattern in so many important applications—and fast ways to compute solutions.

Textbook: Computational Science and Engineering (Wellesley-Cambridge, 2007). I do think you will need to have this textbook. I did everything I could to control the cost and believe that you will use it for a long time.

Grades: Let me try to say this clearly: my life is in teaching, to help you learn. Grades have come out properly for 20 years (almost all A-B). I will NOT spend the semester thinking about grades. I hope you don't either. The homeworks will be important and I plan 2-3 evening exams and NO FINAL. Those exams are open book and a chance for you to bring key ideas together.

Videos: The special event for Fall 2008 is that the lectures will be recorded for OpenCourseWare You will already find a partial earlier set on the website but the course has since evolved. The videos of 18.06 Linear Algebra have been successful on OCW (please use them for help!!). The Lord Foundation gave a new grant for 18.085.

Normally the lead TA runs a weekly review session. This time I plan to do that (and announce the time). It is a good chance for informal questions, which are great in class too (I will repeat them for the recording).

Homework: I will collect homework once a week. I want to ask your help in preparing solutions to go on math.mit.edu/cse . We will choose the clearest (and NEATEST) solutions to scan or to upload (if they are electronic and especially if they are in LaTeX). For that reason we can try two approaches:

Use a number like *78* (assigned from the class list) instead of your name
Put problems on separate pages, each with your number (paper-clipped, not stapled)

I will use MATLAB notation to describe algorithms---that is a good choice for homework (Mathematica and Maple both OK, Octave/Python/Sage are growing).

For a class of this size it's impossible to grade every problem in detail. You may discuss them with others before writing the solution yourself. This class is for learning!! I hope very much that you will enjoy it.

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Assignments

HOMEWORK 1 FOR MONDAY, SEPTEMBER 8: Any 3 problems from section 1.1 and from 1.2. Please PRINT your name so that we can make a class list. Not graded in detail—you may always discuss with others!

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