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Partial Differential Equations (PDEs) for Engineering

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Partial Differential Equations (PDEs) for Engineering MATH 312 Mohammad Motamed [email protected] Spring 2015 WWW: http://www.math.unm.edu/~motamed/Teaching/S15/312/math312S15.html 1 Text: Applied PDEs by Richard Haberman 5th edition Ch 1. Heat Equation Ch 2. Method of separation of variables Ch 3. Fourier series Ch 4 & 12. Wave equation and method of characteristics Ch 7. Higher dimensional PDEs Ch 8. Non-homogeneous problems Ch. 9 & 11. Green’s functions for PDEs (if time allows) http://faculty.smu.edu/rhaberma/ You can find MATLAB m-files for generating figures in the textbook on Prof. Haberman’s homepage: 2
Transcript

Partial Differential Equations (PDEs) for EngineeringMATH 312

Mohammad [email protected]

Spring 2015

WWW: http://www.math.unm.edu/~motamed/Teaching/S15/312/math312S15.html

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Text:

Applied PDEs by Richard Haberman

5th edition

Ch 1. Heat Equation

Ch 2. Method of separation of variables

Ch 3. Fourier series

Ch 4 & 12. Wave equation and method of characteristics

Ch 7. Higher dimensional PDEs

Ch 8. Non-homogeneous problems

Ch. 9 & 11. Green’s functions for PDEs (if time allows)

http://faculty.smu.edu/rhaberma/• You can find MATLAB m-files for generating figures in the textbook on Prof. Haberman’s homepage:

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• M 08:30 - 10:00

• Th 13:30 - 15:00

• by appointment (E-mail)

Office hours @ SLMC 216:

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Grading

Letter Points

A 90-100B 80-89C 70-79F 0-69

Note: the above table is not exact and is subject to change!

๏ Homework & Quizzes 40%

๏ Exams• Midterm 1 15% • Midterm 2 15%• Final 30%

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Homework & Quizzes (40%)

• You are encouraged to work with each other but hand in your own report.

• Late HW will not be accepted. If you are going to miss a deadline, talk to me!

• You need to hand in a hard copy of your report in class on due date. - Do not send me your HW report by email. - Do not slide your HW report under my office door.

• In total 10 homework sets (HW) will be assigned.

• Each HW will consist of a number of questions mainly from textbook.

• Quizzes will be close to HW problems.

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HW Reports• First page of your report must be a cover page, which should look like this:

HW 1(MATH 312)

Student’s full name

DATE

• Organize your report according to the order of questions (2nd page must start with question # 1 in HW and continue with questions #2, #3, ...).

• Do not put any appendix in your report.

• Try to use an editing program/document processor (Microsoft Word, Latex, etc.). If you write by hand, make sure it is readable.

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Exams (60%)

• Exam questions will be very similar to HW problems and practice problems.

• No book/note/etc. are allowed on exam.

• We will have one review lecture before each exam.

• You will get a set of practice problems a few weeks before each exam.

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Why need to study PDEs?

earthquake engineering

Applications

• radar technology (electromagnetic radio waves)

• wireless communication (electromagnetic waves)

• seismic imaging (sound waves)

• ground motion simulation (seismic body waves)

• medical imaging

- sonography (ultrasound waves)

- MRI (radio waves)

- CT (X-rays)

Saturday, October 8, 2011

Applications

• radar technology (electromagnetic radio waves)

• wireless communication (electromagnetic waves)

• seismic imaging (sound waves)

• ground motion simulation (seismic body waves)

• medical imaging

- sonography (ultrasound waves)

- MRI (radio waves)

- CT (X-rays)

Saturday, October 8, 2011

radar technology astronomy

fluid flowheat transfer

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Applied science & engineering

• To model/solve/design systems in science & engineering fields

Mathematical Model (PDEs)

Solution of Mathematical Model

Use the solution:• to design • to make decisions

•Numerical Analysis•Numerical Methods•Computer Algorithms•Computer Simulation

Computational Mathematics

• Example: Earth science / Earthquake engineering

Analytical methods

• Separation of variables• Fourier series and transform• Method of characteristics• etc.

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