Course Calendar
Date | Section | Topic |
---|---|---|
Week 1: Jan 6, 8 | EPH 12.1 to 12.4 H1.1 to H1.4 | Introduction, Derivation Heat Equation, Boundary Conditions, Equilibrium Temperature |
Week 2: Jan 13, 15 | EPH 12.5,12.6,13.3 EP 4.6,4.10 H1.5,H1.6,H2.3 | Derivation of the Heat Equation in Two or Three Dimensions, Review of Gradient and a Derivation of Fourier's Law of Heat Conduction, Independent reading assignment |
Week 3: Jan 20, 22 | EPH 13.1,13.2,13.3 H2.1,H2.2,H2.3 | Monday Holiday, Martin Luther King. No classes. Introduction, Linearity, Separation of variables (part 1) |
Week 4: Jan 27, 29 | EPH 13.3,13.4 H2.3,H2.4 | Heat Equation with Zero Temperatures at Finite Ends, Worked Examples with the Heat Equation (Other BVP) |
Week 5: Feb 3, 5 | EPH 13.5, Exam Review H2.5 | Laplace's Equation: Solutions and Qualitative Properties, Exam Review, for weeks 1-4 |
Week 6: Feb 10, 12 | EPH 14.1,14.2,14.3 H3.1,H3.2,H3.3 | Introduction,
Statement of the Convergence Theorem,
Fourier Cosine and Sine Series,
Exam review and solved examples, weeks 5-6.
Midterm 1 Sample Exam PDF source |
Week 7: Feb 17, 19 | Exam 1 Weeks 1-6 | Monday Holiday, President's Day. No classes.
EXAM 1 on Wednesday.
Midterm Exam 1 Problem statements and student solutions |
Week 8: Feb 24, 26 | EPH 14.4,14.5,14.6 H3.4,H3.5,H3.6 | Term-by-Term Differentiation of Fourier Series,
Term-By-Term Integration of Fourier Series,
Complex Form of Fourier Series |
Week 9: Mar 3, 5 | EPH 15.1 to 15.4 H4.1 to H4.4 | Introduction, Derivation of a Vertically Vibrating String, Boundary Conditions, Vibrating String with Fixed Ends |
Week 10: Mar 8-16 | Spring Break | Sat 8 March to Sun 16 March. No classes. |
Week 11: Mar 17, 19 | EPH 15.5 H4.5,H7.4 | Vibrating Membrane,
Separating the time variable, Helmholtz equation, Eigenvalue problems.
Solved examples, wave equation. Reference: Haberman Section 7.4 (PDF) Background Sections on orthogonality and projections. References: EPH 4.6, 4.9, 4.10 |
Week 12: Mar 24, 26 | EPH 16.1,16.2,16.3 H10.1,H10.2,H10.3 | Introduction, Heat Equation on an Infinite Domain, Fourier Transform Pair |
Week 13: Mar 31 and Apr 2 | EPH 16.4,16.5 H10.4,H10.5 | Fourier Transform and the Heat Equation, Parseval Identity.
Midterm Exam 2 Sample Exam Problems only (PDF) and Solutions (PDF) |
Week 14: Apr 7, 9 | EPH 16.6,Exam 2 H10.6 |
Fourier Sine and Cosine Transforms:
The Heat Equation on Semi-Infinite Intervals.
Worked Examples Using Transforms, part I.
Exam review and solved examples, weeks 7-12.
Midterm Exam 2, Wednesday, covers weeks 7-12. See Week 13 sample exam. Exam 2 Problems, answers and solutions |
Week 15: Apr 14, 16 | EPH 16.6,16.7 H10.6,H10.7 | Worked Examples Using Transforms, Part II. Additional examples: Welding torch, Shannon's theorem on signals |
Week 16: Apr 21, 23, 25 | Final Exam Review | Exam review for the final exam, weeks 1-15.
Final Exam outline, problem types Sample final exam questions and solutions Final Exam Friday 25 April, 10:15am in WEB 1250. Last Day for Extra Credit is May 1, 6pm under the door 113 JWB. Final exam questions and 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 S2014.
syllabus (244K pdf) - The textbook for the course is Haberman, fifth edition. See the syllabus for details and alternate editions.
- 3150 format suggestions for reports
How to improve your written work. Writing reports. ( 84K pdf)
Maple, Matlab and Mathematica Tutorials
Sample Maple Code for 3150
The text directory contains copy-and-paste maple sources.Click Here for directory access
Click Here for a guide to the text files
Maple Tutorials
- Maplesoft Quick Reference Cards Click Here
- Douglas Meade's Quick Reference Card for Maple 12 to 17 Click Here
- A rookie maple tutorial for the impatient from Indiana University Click Here
- Maple programming examples by topic from Kettering University Click Here
- Utah Maple tutorial 2014 in html format
Used in LCB115 maple intro lectures.
Click Here - How to use maple 17 under unix, windows, OS/X (text)
Here - Maple graphics and low speed internet
Maple at home - Peter Stone's Maple Resource page for undergraduate math topics Click Here
Matlab Tutorials
- A one-page pdf Matlab cheat sheet from Strang's linear algebra course at MIT Click Here
- A matlab tutorial at MIT, contains basic information. No video camera, only code examples and text information. Link is HERE
- Mathworks matlab tutorials and documents are HERE. Register for the short tutorials, then try a few using your univ of Utah computer account. Matlab has a site license valid for all campus computers.
Mathematica Tutorials
- Printed or free PDF tutorials on special topics are available at Wolfram Research: HERE
- New users can start with John McLoone's YouTube video (2010) HERE
- A complete set of short tutorial videos are available at Wolfram Research, addressing special topics HERE
- Wolfram videos and screencasts cover a wide range of applications and interests. See Wolfram Broadcast Videos
Due Dates, Homework Problems, Reading
Problems, problem notes, answers.
Please see the LECTURE LINKS, organized by week. The problems due, the extra credit problems, and the PDF source for the problem statements are located there. There is just one source of information.
Professor Will Nesse has produced video lectures on the 3150 topics, the plan to do them all. A simple way to find the videos is to search "William Nesse" on YouTube. Here's the direct link to the YouTube channel: Will Nesse 3140 Channel on YouTube
Homework Package Due Dates
HW1 Assigned in week 1, due Wednesday week 2 HW2 Assigned in week 2, due Wednesday week 3 HW3 Assigned in week 3, due Wednesday week 4 HW4 Assigned in week 4, due Wednesday week 5 HW5 Assigned in week 5, due Wednesday week 6 HW6 Assigned in week 6, due Wednesday week 8 Week 7 Exam 1, HW recess HW7 Assigned in week 8, due Wednesday week 9 HW8 Assigned in week 9, due Wednesday week 11 Week 10, Spring Break HW9 Assigned in week 11, due Wednesday week 12 HW10 Assigned in week 12, due Wednesday week 13 HW11 Assigned in week 13, due Wednesday week 15 Week 14 Exam 2, HW recess HW12 Assigned in week 15, due Wednesday week 16New homework for the next week is posted either Wednesday or Thursday, assuming no one wants to do HW in advance of the lectures.
Friday problem sessions in WEB 1250 at 11:50am will discuss HW due the next week. For example, Friday of Week 4 would discuss HW4, which is due the next Wednesday in Week 5. Blackboard photos of the Friday session are posted in the Lecture Links.
Required HW Problems are keyed to the textbook problems, but they are independent of any book, appearing only in PDF files at this website.
References in the PDF problems are to Haberman 4E or 5E, Edwards-Penney DE and BVP and Asmar PDE and BVP, all editions. The textbooks are available in the LCB Math Center.
Studying Ahead. Please look at these recommended problems, none of which are due, but they will appear in required HW (PDF files). Abbreviations: H=Haberman 4E or 5E. EPH=Edwards-Penney-Haberman hybrid text, special edition for the University of Utan 2014.
EXERCISES H 1.2 or EPH 12.2: 1, 2b, 4b, 7, 8 EXERCISES H 1.3 or EPH 12.3: 2, 3 EXERCISES H 1.4 or EPH 12.4: 1d, 1f, 1h, 2a, 4, 7a, 8 EXERCISES H 1.5 or EPH 12.5: 1a, 2, 3a, 3e, 7, 11, 13 EXERCISES H 2.2 or EPH 13.2: 2a, 2b, 4a, 4b EXERCISES H 2.3 or EPH 13.3: 1a, 1c, 1f, 2b, 2c, 3c, 4, 5, 6, 7, 8 EXERCISES H 2.4 or EPH 13.4: 1, 2, 3, 4 EXERCISES H 2.5 or EPH 13.5: 1a, 1c, 1e, 2a, 3, 4, 5a, 5c, 6a, 7b, 9, 15b, 22 EXERCISES H 3.2 or EPH 14.2: 1b, 1d, 1f, 2a, 2c, 2f, 4 EXERCISES H 3.3 or EPH 14.3: 1a, 1d, 2a, 2d, 5c, 7, 10, 13, 18 EXERCISES H 3.4 or EPH 14.4: 1a, 2, 3a, 6, 8, 9 EXERCISES H 3.5 or EPH 14.5: 1c, 4, 7 EXERCISES H 3.6 or EPH 14.6: 1 [this section appears later in editions before 4E] EXERCISES H 4.2 or EPH 15.2: 2, 5 EXERCISES H 4.3 or EPH 15.3: 1, 2 EXERCISES H 4.4 or EPH 15.4: 1a, 1b, 2c, 3b, 6, 7, 8, 9, 11, 13 EXERCISES H 4.5 or EPH 15.5: 1 EXERCISES H 4.6 or EPH 15.6: 3, 4 EXERCISES H 10.2 or EPH 16.2: 1, 2 EXERCISES H 10.3 or EPH 16.3: 1, 2, 3, 5, 6, 7, 11, 18 EXERCISES H 10.4 or EPH 16.4: 1, 2, 3a, 4a, 5c, 7c, 8, 11 EXERCISES H 10.5 or EPH 16.5: 1, 2, 3, 5, 10, 11, 12 EXERCISES H 10.6 or EPH 16.6: 1a, 2b, 3, 11a, 12a, 15, 18 EXERCISES H 10.7 or EPH 16.7: 1, 2
Exams
Gustafson's 3150 Midterm and Final Exams Spring 2014
These sources will be posted after the exam is graded.- Midterm Exam 1, Problem statements and student solutions
- Midterm Exam 2, Problem statements and student solutions
- Final Exam 25 April 2014, questions and student solutions
Gustafson's 3150 Midterm and Final Exam Samples Spring 2014
These sources will be posted when available, due to the change of textbook and the re-ordering of topics.- Sample Midterm exam 1, Gustafson's 3150 course S2014.
Midterm 1 Sample Exam PDF source, Problems only
Midterm 1 review Problem 5, Blackboard photos Wednesday, 12 Feb 2014
Midterm 1 review, Problems 1,2,3 Blackboard photos Friday, 14 Feb 2014
Midterm 1 review 4pm in WEB L105, Problems 4,5 Blackboard photos Tuesday, 18 Feb 2014 - Sample Midterm Exam 2, Gustafson's 3150 course S2014.
Sample Midterm Exam 2 Problems only (PDF) and Solutions (PDF)
Midterm Exam 2 review, Blackboard photos Friday, 4 Apr 2014
Midterm Exam 2 Review Blackboard photos Monday, 7 Apr 2014
Midterm Exam 2 Review Blackboard photos Tuesday, 8 Apr 2014
Xerox copy, Sample exam 2 solutions - Sample Final Exam, Gustafson's 3150 course S2014.
Final Exam outline, problem types
Sample final exam questions and [pending] solutions
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
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
Professor William Nesse has produced video lectures on the 3150 topics, the plan to do them all. A simple way to find the videos is to search "William Nesse" on YouTube. Here's the direct link to the YouTube channel: Will Nesse 3140 Channel on YouTube
Tutoring in WEB 1622 is staffed every weekday: Times and Staff WEB1622
Lecture links Weeks 1 to 4
- Week 1 Haberman
Conveyor belt problem, advection equation
HW1 is due Tuesday of Week 2. Problem list for HW1
HW1 homework problem statements PDF source
Fourier's text, Analytical Theory of Heat, 1878 Translation to English
Advection equation answer check. Fourier's solution to the rod problem.
Blackboard photos Monday, 6 Jan 2014
Derivations H1.2, heat equation. Boundary conditions H1.3.
Blackboard photos Wednesday, 8 Jan 2014
Problem session on HW1. Blackboard photos Friday, 10 Jan 2014 - Week 2 Haberman
HW2 is due Wednesday of Week 3. Problem list for HW2
HW2 homework problem statements PDF source
Equilibrium solutions, H1.4. Heat equation in 3D, derivation, H1.5. Blackboard photos Monday, 13 Jan 2014
Fourier's Law derivation, Gradient Theorems H1.6, Orthogonality H2.3 Appendix, Coordinates polar, cylindrical, spherical H1.5. Extra proofs. Blackboard photos Wednesday, 15 Jan 2014
Details for the Laplace equation in polar coordinates. Here, original from Professor Michael Wilson, UVM.
Friday problem session. Problems XC-H1.5-14, H1.5-2, H1.4-7. H1.4-2, H1.4-1, H1.3-2(c). Blackboard photos Friday, 17 Jan 2014
Edit: Photo3 answer is off by factor A (rod cross-sectional area). The error is using dx instead of A*dx in the integral. - Week 3 Haberman
HW3 is due Wednesday of Week 4. Problem list for HW3
HW3 homework problem statements PDF source
Linearity, Heat equation for the Rod, Separation of variables H2.1, H2.2, H2.3 Blackboard photos Wednesday, 22 Jan 2014
Friday problem session WEB 1250, HW3 Blackboard photos Friday, 24 Jan 2014 - Week 4 Haberman
HW4 is due Wednesday of Week 5. Problem list for HW4
HW4 homework problem statements PDF source
Superposition, Rod Problem, Orthogonality Blackboard photos Monday, 27 Jan 2014
Rod formula, orthogonality revisted, Fourier formulas for sines and cosines Blackboard photos Wednesday, 29 Jan 2014
Friday problem session WEB 1250, HW4 Blackboard photos Friday, 31 Jan 2014
Solution notes for H2.4-4
Solution notes for H2.4-6a
Lecture links Weeks 5 to 8
- Week 5 Haberman
HW5 is due Wednesday of Week 6. Problem list for HW5
HW5 homework problem statements PDF source
Rod Problemwith insulated ends. Laplace's Equation and steady-state heat in a plate.
Blackboard photos Monday, 3 Feb 2014
Cauchy-Euler differential equations, background: How to solve r^2R''+rR'+cR=0
Laplaces equation, rectangle, disk. Blackboard photos Wednesday, 5 Feb 2014
Friday problem session on HW5, H2.5. Blackboard photos Friday, 7 Feb 2014 - Week 6 Haberman
Midterm 1 Sample Exam PDF source
Directory of Sample midterm solutions
HW6 is due Wednesday of Week 8, because of the midterm exam Problem list for HW6
HW6 homework problem statements PDF source
Maximum principle, Fourier series, Fourier Convergence. Blackboard photos Monday, 10 Feb 2014
Graphing u(r,theta) in HW5 Problem H2.5-5b
Maple code PDF for r^10 cos(3 theta)
Matlab code MuPad text for r^10 cos(3 theta) with instructions.
Matlab Examples in MuPad
Midterm 1 review Problem 5, H3.2 Example 1, Fourier sine series Blackboard photos Wednesday, 12 Feb 2014
Midterm 1 review, Problems 1,2,3 Blackboard photos Friday, 14 Feb 2014 - Week 7 Haberman
Monday 17 February is a Holiday, President's Day, no classes.
Midterm Exam 1 is Wednesday 19 February.
Midterm 1 Sample Exam PDF source
Midterm 1 review 4pm in WEB L105, Problems 4,5 Blackboard photos Tuesday, 18 Feb 2014
Problem session Friday 21 February was canceled. - Week 8 Haberman
HW6 is due this Wednesday, Week 8, Problem list for HW6
HW6 homework problem statements PDF source
HW7 is due Wednesday of Week 9, Problem list for HW7
HW7 homework problem statements PDF source
Wednesday, 26 Feb 2014. Fourier sine and cosine series, Gibbs demo with maple source
Blackboard photos Wednesday, 26 Feb 2014
Friday problem session, H3.3, HW7 Blackboard photos Friday, 28 Feb 2014
HW8 is due Wednesday of Week 11, Problem list for HW7
HW8 homework problem statements PDF source
Lecture links Weeks 9 to 12
- Week 9 Haberman
HW8 is due Wednesday of Week 11, Problem list for HW8
HW8 homework problem statements PDF source
Monday, 3 Mar 2014. Fourier sine and cosine series, differentiation and integration term-by-term, wave equation for a vibrating string
Blackboard photos Monday, 3 Mar 2014
Wednesday, 5 Mar 2014. d'Alembert's solution for the infinite string, wave equation for a vibrating finite string, boundary conditions, separation of variables.
Blackboard photos Wednesday, 5 Mar 2014
Friday problem session, H3.4, HW8, Differentiation-integration of Fourier series
Blackboard photos Friday, 7 Mar 2014 - Week 10 Spring Break
Nothing due until Wed of week 11. - Week 11 Haberman
HW9 is due Wednesday of Week 12, Problem list for HW9
HW9 homework problem statements PDF source
Monday, 17 Mar 2014. Wave Equation in dimensions 2 and 3. Derivation details. Application: Solve by separation of variables the rectangular drumhead problem with speed g=0 and shape f=x(L-x)(H-y)$.
Blackboard photos Monday, 17 Mar 2014
Reference for the rectangular drumhead problem, Haberman Section 7.4 (PDF)
Wednesday, 19 Mar 2014. Separating the t-variable. Helmholtz equation.
Blackboard photos Wednesday, 19 Mar 2014 Friday problem session, H4.2-1, H4.2-2, H4.4-1, H4.4-2, H4.4-7, H4.4-11, Blackboard photos Friday, 21 Mar 2014 Background references on orthogonality and projections, EPH 4.6,EPH 4.9,EPH 4.10 - Week 12 Haberman
HW10 is due Friday of Week 13, Problem list for HW10
HW10 homework problem statements PDF source
Monday, 24 Mar 2014. Heat equation on -infinity to infinity. Fourier Transform pair.Impulse train.
Blackboard photos Monday, 24 Mar 2014
Wednesday, 26 Mar 2014. Fourier Transform pair. Impulse train again. Fourier transform magnitude and phase.
Blackboard photos Wednesday, 26 Mar 2014
Xray Glasses demo for Signal, Magnitude and Phase. What Fourier transforms do for you. See also the Friday session, photos 1 and 2.
Source files and PDF, 26 Mar 2014
Friday problem session, 28 Mar 2014. Fourier coefficients and the Fourier transform F(w). Problems H10/EPH16: Section 2 - 1,2; Section 3 - 1,2,3,5,6 [7,8 not discussed]
Blackboard photos Friday, 28 Mar 2014
Lecture links Weeks 13 to 16
- Week 13 Haberman
HW11 is due Friday of Week 14, Problem list for HW11
HW11 homework problem statements PDF source
Monday, 31 Mar 2014. Heat equation on -infinity to infinity. Fourier Transform pair. Fourier's Transform method, heat equation. Heat kernel. Gaussian transform table.
Blackboard photos Monday, 31 Mar 2014
Midterm Exam 2 Sample Exam Problems only (PDF) and Solutions (PDF)
Fourier transform: solutions to Problem 1a, 1b are in the April 4 blackboard photos (see below).
Wednesday, 2 Apr 2014. Magnitude plots and Fourier coefficients. Thermal energy diffusion example, H10.4. Parseval Identity. Fourier sine and cosine transforms.
Blackboard photos Wednesday, 2 Apr 2014
Friday, 4 Apr 2014. Exam review. No problems from HW11. See April 11.
Blackboard photos Friday, 4 Apr 2014 - Week 14 Haberman
Homework recess. This is exam week. HW11 due next Monday 14 April (HW11 from Week 13).
Monday Exam Review Blackboard photos Monday, 7 Apr 2014
Exam review was Monday at 4pm in OSH 113.
Tuesday Exam Review Blackboard photos Tuesday, 8 Apr 2014
Exam review was Tuesday at 4pm in WEB L105.
Problem session HW11, Blackboard photos Friday, 11 Apr 2014 - Week 15 Haberman
Homework recess. Last week of lectures. HW11 due Monday 14 April (HW11 from Week 13).
Monday: Shannon theorems. Signal reconstruction. Dirac impulse. Riemann-Stieltjes integral. Riemann-Lebesgue lemma.
Blackboard photos Monday, 14 Apr 2014
Wednesday: Cochlea, Ikcd cartoon, magnitude/phase, sound/frequency tuning, klingon alphabet, Shannon interpolation example Projection (html)
Fourier transform, Sine and Cosine Transform Projection slides (PDF)
Welding Torch examples, Fourier transform, Dirac impulse, Nyquist-Shannon Projection slides (PDF)
Fermi National Accelerator Lab reference tables for the Fourier Transform (PDF)
Dirac impulse topics, Blackboard photos Wednesday, 16 Apr 2014 - Week 16 Haberman
Final exam review. Sample final from week 15.
Solutions to Problems 1 and 2, Blackboard photos Monday, 21 Apr 2014
Solutions to Problems 4 and 5, Blackboard photos Wednesday, 23 Apr 2014
Final Exam outline, problem types
Sample final exam questions and solutions
Final Exam Friday 25 April, 10:15am in WEB 1250.