Partial Differential Equations (PDEs) for Engineering
Transcript of Partial Differential Equations (PDEs) for Engineering
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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