Intermediate Partial Differential Equations I (Mathematics 436)


LECTURER: Professor G. E. Swaters, Department of Mathematical & Statistical Sciences, CAB 537 and CCIS 3-265.

Email: gswaters@ualberta.ca

OTHER CONTACT INFORMATION: See my URL at https://sites.ualberta.ca/~gswaters.

OFFICE HOURS: Tuesday & Thursday as needed (or else by appointment).

STUDENTS WITH SPECIAL NEEDS: Students with learning challenges will find that the University has a friendly, well-organized office dealing with these challenges. The web site link is Academic Success Centre. Eligible students have both rights and responsibilities with regard to accessibility-related accommodations. Consequently, scheduling exam accommodations in accordance with Academic Success Centre deadlines and procedures is essential. Please note adherence to procedures and deadlines is required for U of A to provide accommodations. Contact the Academic Success Centre for further information.

TEXTBOOK: Partial Differential Equations of Applied Mathematics, 3rd Edition by Erich Zauderer. The University of Alberta Library has online access to the textbook at

http://login.ezproxy.library.ualberta.ca/login?url=http://onlinelibrary.wiley.com/book/10.1002/9781118033302

LECTURE TIME & LOCATION: Tuesday & Thursday 12:30-13:50pm in ESB 1-33. Cells phones are to be turned off during the lectures.

SECTION URL: https://sites.ualberta.ca/~gswaters/teaching/436.html

EXAMINATION POLICY: The Midterm will be in class on Thursday, October 28th, 2021. If a student has an acceptable excuse for missing the midterm, the weight of the midterm will be transferred to the final. There will be no deferred midterm. For an excused absence where the cause is religious belief, a student must contact the instructor within two weeks of the start of classes to request accommodation for the term (including the final exam, where relevant). Adequate documentation is required to substantiate the student request.

The Final Examination will be held on Tuesday, December 21st, 2021 from 9-11am, and hopefully will be held in the classroom. A student who cannot write the final examination due to incapacitating illness, severe domestic affliction or other compelling reasons can apply for a deferred final examination.  Students who failed at the start of term to request exam accommodations for religious beliefs are expected to follow the normal deferred final examination process.  Such an application must be made to the student’s Faculty office within two working days of the missed examination and must be supported by a Statutory Declaration or other appropriate documentation (Calendar section 23.5.6).  Deferred examinations are a privilege and not a right; there is no guarantee that a deferred examination will be granted.  Misrepresentation of Facts to gain a deferred examination is a serious breach of the Code of Student Behaviour.  

The date and location of the final examination is set by the Registrar and takes precedence over the final examination date reported in this document.  Students must verify this date on BearTracks when the Final Exam Schedule is posted.

 

The course website contains links to previous years’ midterms, finals and their solutions.

THE USE OF CELL PHONES, CALCULATORS & COMPUTERS IS NOT PERMITTED IN THE EXAMINATIONS.

GENERAL COURSE DESCRIPTION: The principal purpose of this course is to provide an intermediate level discussion of partial differential equations. It is assumed that the student has mastered the material in Mathematics 337 or its equivalent.

DETAILED DESCRIPTION: Basically, the course covers Chapter 2 through to Chapter 4 in Zauderer. Of particular note we are interested in developing an introduction to nonlinear pdes.

ASSIGNMENTS: There will be 5 assignments, which will be assigned every two to three weeks depending on the pace of completion of individual sections from the textbook. The assignment questions will be posted on my MATH 436 website. The completed assignments must be handed in on the due date in class. Late assignments will not be marked and a grade of zero will be assigned.

GRADING:  Assignments (20%), Midterm (30%) and Final Examination (50%). An overall course mark of 50% or more guarantees a passing grade of at least D. An overall course mark of 90% or more guarantees a grade of at least A.

ACADEMIC INTEGRITY: The University of Alberta is committed to the highest standards of academic integrity and honesty. Students are expected to be familiar with these standards regarding academic honesty and to uphold the policies of the University in this respect. Students are particularly urged to familiarize themselves with the provisions of the Code of Student Behaviour (online at www.governance.ualberta.ca) and avoid any behaviour, which could potentially result in suspicions of cheating, plagiarism, misrepresentation of facts and/or participation in an offence. Academic dishonesty is a serious offence and can result in suspension or expulsion from the University.

ADDITIONAL INFORMATION:

Policy about course outlines can be found in §23.4(2) of the University Calendar.

Audio or video recording of lectures, labs, seminars or any other teaching environment by students is allowed only with the prior written consent of the instructor or as a part of an approved accommodation plan. Recorded material is to be used solely for personal study, and is not to be used or distributed for any other purpose without prior written consent from the instructor.

    

Lecture Schedule

Week of

Monday

Tuesday

Wednesday

Thursday

Friday

August 29

 

No class

 

Introduction

 

September 5

 

2.1

 

2.1 & 2.2

 

12

 

2.2

 

2.2 & 2.3

 

19

 

2.3

 

3.1

 

26

 

3.1 & 3.2

 

No class

 

October 3

 

3.2 & 3.3

 

3.3 & 3.4

 

10

 

3.4

 

3.5

 

17

 

3.5 & 3.6

 

3.6

 

24

 

Review

 

Midterm

 

31

 

4.1

 

4.2

 

November 7

 

Reading

 

Reading

 

14

 

4.3

 

4.4

 

21

 

4.4 & 4.5

 

4.5

 

28

 

4.6

 

4.6 & 4.7

 

December 5

 

4.7

 

No class

 

 

  


Assignments and Examinations

Assignment #1 (Due September 23rd) solution

2.1.1, 2.1.4, 2.2.1, 2.2.2, 2.2.5

Assignment #2 (Due October 14th) solution

2.2.19, 2.2.26, 2.3.3, 2.3.6

Assignment #3 (Due November 16th) solution

3.1.5, 3.1.6, 3.1.7, 3.3.2, 3.3.6

Assignment #4 (Due December 2nd) solution

3.3.12, 3.3.19 (HINT: To find the general solution first put the system into normal form), 3.3.20, 3.4.7, 3.5.4

Midterm and its solution

Final and its solution

 


 

 

Additional Resources

2006 Midterm and its solution

2006 Final and its solution

2008 Midterm and its solution

2008 Final and its solution

2010 Midterm and its solution

2010 Final and its solution

2014 Midterm and its solution

2014 Final and its solution

2015 Midterm and its solution

2015 Final and its solution

2016 Midterm and its solution

2016 Final and its solution

2017 Midterm and its solution

2017 Final and its solution

2018 Midterm and its solution

2018 Final and its solution

2019 Midterm and its solution

2019 Final and its solution

 

 

Example for linear Method of Characteristics (MOC) - PDF handout

Animation of first MOC example (right-click for menu):

 

Another example for linear Method of Characteristics (MOC) - PDF handout

Animation of second MOC example (right-click for menu):

 

Example solution to the wave equation (with Dirichlet initial data) - PDF handout

Animation of example solution to the wave equation (with Dirichlet initial data) (right-click for menu):

 

Example solution to the wave equation (with Neumann initial data) - PDF handout

Animation of example solution to the wave equation (with Neumann initial data) (right-click for menu):

 

Shock formation example - PDF handout

Animation of shock formation example (right-click for menu):

 

Shock wave example - PDF handout

Animation of shock wave example (right-click for menu):

 

 


 

 

Unofficial Final Grades

 

The average final grade was A.

 

ID

Grade

1573829

A

1496691

B-

1561315

C

1496351

B

1523322

A+

1574325

A

1635903

A+

1636986

A

1307580

B+

1570877

A

1531316

B+

1528926

A+

1398066

W

1560558

A