Course Calendar
Course 3150-4 meets Mon-Wed in WEB 1250 at 11:50am
Date | Week | Section | Topic |
---|---|---|---|
Jan 7,9 | 1 | 1.1 to 2.2 | Introduction, Periodic functions, Fourier series |
Jan 14,16 | 2 | 2.3, 2.4 | More on Fourier Series |
Jan 21,23 | 3 | 3.1, 3.2 | Examples, Wave equation |
Jan 28,30 | 4 | 3.2, 3.3, 3.4 | Wave Equation, Separation, D'Alembert |
Feb 4,6 | 5 | 3.4, 3.5 | D'Alembert's method, 1-Dim'l Heat Equation |
Feb 11,13 | 6 | 3.6, 3.7 | Boundary conditions, 2-Dim'l Equations |
Feb 20 | 7 | 3.8 | Laplace's Equation, Sample Exam 1 |
Feb 25,27 | 8 | 3.9 | Poisson's equation, Exam 1 Wed Feb 27 Exam 1 Problems and answers |
Mar 4,6 | 9 | 4.1, 4.7, 4.2 | Coordinates, Bessel functions, Drumhead |
Mar 9-17 | 10 | Spring Break | Sat 9 March to Sun 17 March |
Mar 18,20 | 11 | 4.3, 4.4 | Non-symmetric Drumhead, Steady-state heat disk |
Mar 25,27 | 12 | 4.5, 4.6 | Steady-state heat cylinder, Poisson's Equation |
Apr 1,3 | 13 | 7.1, 7.2 | Fourier Integral and Transform |
Apr 8,10 | 14 | 7.3, 7.4, 7.5 | Fourier Transform method, Heat kernel, Fourier sine and cosine transforms |
Apr 15,17 | 15 | 7.6, 7.7, 7.8, 7.9 | Generalized function, Welding torch example, Sample Exam 2 |
Apr 22,24 | 16 | Exam 2 | Exam 2 Mon April 22, Final Exam Review Exam 2 Problems, answers and solutions Final Exam outline, problem types Eight Blackboards Tuesday 30Apr2013: Final Exam Sample 1,2,3 Final Exam problems with student solutions |
Syllabus
Math 3150-4 Partial Differential Equations
Instructor.
Professor Grant B. Gustafson
Email: See the online door card: Here.
Office: JWB 113
- Gustafson's 3150 syllabus S2013.
syllabus ([an error occurred while processing this directive] pdf) - The textbook for the course is Nakhle Asmar, second edition. See the syllabus for details.
- The student solution manual for Asmar's second edition can be found here:
Student Solutions - 3150 format suggestions for reports
How to improve your written work. Writing reports. ([an error occurred while processing this directive] pdf)
Maple and Matlab
Sample maple code for 3150, Spring 2013
The text directory contains copy-and-paste maple sources.
Click Here for directory access
Click Here for a guide to the text files
Maplesoft Quick Reference Cards Click Here
Douglas Meade's Quick Reference Card for Maple 12 to 15 Click Here
A one-page pdf Matlab cheat sheet from Strang's linear algebra course at MIT Click Here
Details for maple 12 to 15 under unix, windows, OS/X
How to use maple 15 (2k text)
Utah Maple tutorial 2013 in html format.
Maple Tutorial Used in LCB115 maple intro lectures.
A rookie maple tutorial for the impatient from Indiana University Click Here
How to do maple graphics using slow internet
Low speed internet and maple graphics ([an error occurred while processing this directive] txt)
Peter Stone's Maple Resource page for a wide range mathematical topics Click Here
Due Dates, Homework Problems, Reading
Final Exam problems with student solutions- Updated due dates 3150 Changes in due dates for submitted work
- Reading (2k text)
- Problems, problem notes, some answers
- 3150 Problems for Asmar Chapter 1: Week 1 Click Here
- 3150 Problems for Asmar Chapter 2: Weeks 1 to 3 Click Here
- 3150 Problems for Asmar Chapter 3: Weeks 4 to 8 Click Here
- 3150 Problems for Asmar Chapter 4: Weeks 9 to 13 Click Here
- 3150 Problems for Asmar Chapter 7: Weeks 14 to 16 Click Here
References in the PDF problems are to Edwards-Penney DE and BVP and Asmar PDE and BVP, editions 1 and 2. The textbooks are available in the math library next to the LCB Math Center. Asmar's book will be available 2013 for 40 dollars paperback, from a new publisher (Pearson dropped the title). The paperback is printed from the same PDF used by Pearson Publishing company, but Asmar has edited errors and reports that
I won't make any money on the new edition. The new edition supports courses that used my book.
Exams
Gustafson's 3150 Midterm and Final Exams Spring 2013
- Midterm Exam 1, Wed Feb 27, 11:45am in WEB 1250
Problems and answers to Exam 1 - Midterm Exam 2, Mon April 22, 11:45am in WEB 1250
Exam 2 Problems, answers and solutions - Final Exam, Thu May 2, 10:25am in WEB 1250
Final Exam problems with student solutions
Gustafson's 3150 Midterm and Final Exam Samples Spring 2013
- Sample exam 1, Gustafson's 3150 course S2013.
Problems only
- Sample exam 1, Gustafson's 3150 course S2013.
Problems and answers - Sample exam 2 and sample final exam, Gustafson's 3150 course S2013.
Problems only
Sample exam 2 solutions
Sample final exam solutions
Gustafson's 3150 Midterm and Final Exams from Fall 2009
- Exam 1, Gustafson's 3150 course F2009. No solutions.
Gustafson's Exam 1, F2009 - Sample exam 2, Gustafson's 3150 course F2009. No solutions.
Gustafson's Exam 2 sample, F2009 - Exam 2 with Solutions, Gustafson's 3150 course F2009
Josh Bailey's Exam 2 solutions F2009 - Sample Final Exam, Gustafson's 3150 course F2009. No solutions.
Gustafson's Final Exam sample F2009
Same pdf file as the exam 2 sample. The final exam sample is appended to the exam 2 sample. - Final Exam with Solutions, Gustafson's 3150 course F2009
Final exam F2009 with solutions
Lecture links
Below appear links to slides or documents projected in class.
Lecture links Weeks 1 to 4
- Week 1
Conveyor belt problem, advection equation
Periodic functions and orthogonal systems
Summary of Ch1 topics - Week 2
Fourier series
Wronskians, filmstrips, method of characteristics, d'Alembert's method, Ch1
Gibbs maple text (.mpl) and Gibbs maple worksheet (.mw)
Summary of Ch2 topics - Week 3
Summary of Ch3 topics in 3.1, 3.2 - Week 4
Interval of dependence graphic, characteristic triangles, maple text (.mpl)
Summary of Ch3 topics in 3.3, 3.4
Lecture links Weeks 5 to 8
- Week 5
Summary of Ch3 topics in 3.5, 3.6 - Week 6
Explanation of convection, conduction, radiation (physics.stackexchange.com, 10Jan2013)
Summary of Ch3 topics in 3.5, 3.6
Summary of Ch3 topics in 3.7, 3.8
Problem 3.7-5 animation and filmstrip - Week 7
Summary of Ch3 topics in 3.7, 3.8
Sample exam 1, problems and answers (17Feb2013) - Week 8
Summary of Ch3 topics in 3.9
Sample exam 1, problem types (25Feb2013)
Trig identities, blackboard (Friday, 22Feb2013)
Arrows --> and boxes mark memorized identities, the rest are derived when needed.
Six blackboards, four maple programs (Friday, 1Mar2013)
Problems 3.4-15, 3.5-13, 3.6-3, 4.0-1
Lecture links Weeks 9 to 12
- Week 9
Summary of Ch3 topics in 3.9
Summary of Ch4 topics in 4.1
Exam 1 problems and answers from Wed, 27 Feb 2013
Frobenius method, Edwards-Penney section 11.3
Series solutions manuscript, Frobenius method (see Example 2), author GBG
Maple assist for the Frobenius method, Problem 4.0-4
Five blackboards (Friday, 8Mar2013)
Problems 4.3-3, 4.1-5, 4.2-1, 4.0-3. Maple assist 4.0-4 (text, pdf).
Plot advice for 4.3-3
Brian Martin's email (9Mar2013) about plotting 4.3-3. - Week 10 (after the Break)
Summary of Ch4 topics in Section 4.2
Summary of Ch4 topics in Section 4.3
Summary of Ch4 topics in Section 4.4
Asmar 2004 Ch4 topics, 4.1 to 4.8 (all PDF)
Four Blackboards Friday 22Mar2013: 4.6-5, 4.4-15c, Xc4.2-12b, Xc4.3-13 - Week 11
Summary of Ch4 topics in Section 4.4
Summary of Ch4 topics in Section 4.5
Summary of Ch4 topics in Section 4.6
Asmar 2004 Ch4 topics, 4.1 to 4.8 (all PDF)
Two Blackboards Friday 29Mar2013: Eigenfunction expansion 4.6, explain coefficient formulas page 233 - Week 12
Summary of Ch7 topics in Section 7.1
Summary of Ch7 topics in Section 7.2
Gibbs overshoot for the unit pulse: Maple TEXT and PDF
Lecture Projections: IKCD cat, Klingon Alphabet, Letters transformed. HTML link
Sample Fourier transforms of simple signals Maple TEXT and PDF
Three Blackboards Friday 5Apr2013: 7.1-18a (one), 7.2-31a (two)
Lecture links Weeks 13 to 15
- Week 13
Summary of Ch7 topics in 7.2
Summary of Ch7 topics in 7.3
Summary of Ch7 topics in 7.4
Example: Plot of an impulse train PDF and Maple text (MPL)
Fourier transform: Definition, properties Slides: PDF
Four Blackboards Friday 12Apr2013: 7.2-18, 7.2-31, Sample exam 2, problem 1 - Week 14
Summary of Ch7 topics in 7.4
Summary of Ch7 topics in 7.5
Summary of Ch7 topics in 7.6
Summary of Ch7 topics in 7.7
Sample exam 2 (April 22) and sample final exam (May 2).
Problems only
Sample exam 2 solutions
Sample final exam solutions
Welding Torch Example and the Nyquist-Shannon Sampling Theorem PDF slides
Six Blackboards Friday 19Apr2013: Sample exam 2, problems 4,3,2
Eight Blackboards Tuesday 30Apr2013: Final Exam Sample 1,2,3
Other 3150 Courses
Below appear archived files from the semesters indicated, for homework,
maple and matlab code, exams and exam solutions, syllabi, problem notes