Course: MTH6151 - Partial Differential Equations - 2023/24

Topic outline

Select topic General

General

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- Select activity Announcements
  
  Announcements Forum
- Select activity Module forum
  
  Module forum
- Select activity Important module information
  
  Important module information Page
- Select activity 2017 Coursenotes by Juan A. Valiente Kroon
  
  2017 Coursenotes by Juan A. Valiente Kroon File
  
  1.5 MB
- Select activity Q-Review Recordings
  
  Q-Review Recordings External tool
Select topic January Final Exam (open on January 5th 10:00am))

January Final Exam (open on January 5th 10:00am))
This handwritten assessment is available for a period of 3 hours and 30 minutes in total, within which you must submit your solutions. This time frame includes 30 minutes for scanning and submitting your solution. You may log out and in again during that time, but the countdown timer will not stop. If your attempt is still in progress at the end of the set time slot, any file you have uploaded will be automatically submitted.
The assessment is intended to be completed within 3 hours.
In completing this assessment:
You may use books and notes.
You may use calculators and computers, but you must show your working
for any calculations you do.
You may use the Internet as a resource, but not to ask for the solution to
an exam question or to copy any solution you find.
You must not seek or obtain help from anyone else.
- Select activity Semester A final assessment
  
  Semester A final assessment Quiz
Select topic Courworks

Courworks
There will be 3 coursework through out the semester. They will consists of selected questions from the problem sets given after every week's lectures. The problem sets can be found in the corresponding tag of each week on the QMplus page.
The due dates and the proportion they make up in final marks are as follows:
Coursework 1 (5%): Due on Friday, October 13, 2023
Coursework 2 (10%): Due on Friday, November 17, 2023
Coursework 3 (5%): Due on Friday, December 8, 2023
- Select activity Coursework 1 (5%), due on October 13, Friday , 23:59pm
  
  Coursework 1 (5%), due on October 13, Friday , 23:59pm Assignment
- Select activity Coursework 1 solutions
  
  Coursework 1 solutions File
  
  6.5 MB
- Select activity Coursework 2 (10%), due on November 17, Friday , 23:59pm
  
  Coursework 2 (10%), due on November 17, Friday , 23:59pm Assignment
- Select activity Coursework 2 solutions
  
  Coursework 2 solutions File
  
  17.7 MB
- Select activity Coursework 3 (5%), due on December 8, Friday , 23:59pm
  
  Coursework 3 (5%), due on December 8, Friday , 23:59pm Assignment
- Select activity Coursework 3 solutions
  
  Coursework 3 solutions File
  
  12.2 MB
Select topic What's it like to be a Math Phd (mini-talk by Jordan Marajh and Evelyn Yoczira Lira Torres)

What's it like to be a Math Phd (mini-talk by Jordan Marajh and Evelyn Yoczira Lira Torres)
- Select activity Mini-Talk slides for October 11, 2023
  
  Mini-Talk slides for October 11, 2023 File
  
  1.2 MB
Select topic Week 1 - Introduction to PDEs

Week 1 - Introduction to PDEs
Lecture Hours:
September 25th 9:00am-11:00am
September 27th 11:00am-1:00pm
- Select activity Week 1 lecture notes
  
  Week 1 lecture notes File
  
  151.0 KB
- Select activity Review of some ODE techniques
  
  Review of some ODE techniques File
  
  4.1 MB
- Select activity Problem set 1
  
  Problem set 1 File
  
  90.8 KB
- Select activity Selected solutions to Problem set 1
  
  Selected solutions to Problem set 1 File
  
  851.3 KB
Select topic Week 2 -First order PDEs

Week 2 -First order PDEs
Lecture Hours:
October 2nd 9:00am-11:00am
October 4th 11:00am-12:00pm
Seminar Hour:
October 4th 12:00pm-1:00pm
- Select activity Week 2 lecture notes
  
  Week 2 lecture notes File
  
  235.1 KB
- Select activity Problem set 2
  
  Problem set 2 File
  
  79.5 KB
- Select activity Selected solutions to Problem set 2
  
  Selected solutions to Problem set 2 File
  
  838.4 KB
- Select activity Selected Solutions to Problem set 2 (continued)
  
  Selected Solutions to Problem set 2 (continued) File
  
  2.5 MB
- Select activity PS2 Q9 solutions
  
  PS2 Q9 solutions File
  
  1.7 MB
Select topic Week 3 - Classification of second order PDEs and derivation of the wave equations

Week 3 - Classification of second order PDEs and derivation of the wave equations
- Select activity Week 3 lecture notes
  
  Week 3 lecture notes File
  
  276.4 KB
- Select activity Problem set 3
  
  Problem set 3 File
  
  96.9 KB
- Select activity Selected solutions to Problem set 3
  
  Selected solutions to Problem set 3 File
  
  825.8 KB
Select topic Week 4 - Wave equations on the real lines and conservation of energy

Week 4 - Wave equations on the real lines and conservation of energy
- Select activity Week 4 lecture notes
  
  Week 4 lecture notes File
  
  201.2 KB
- Select activity Problem set 4
  
  Problem set 4 File
  
  101.7 KB
- Select activity Selected solutions to Problem set 4
  
  Selected solutions to Problem set 4 File
  
  453.2 KB
Select topic Week 5 - Wave equations on half line and intervals

Week 5 - Wave equations on half line and intervals
- Select activity Week 5 lecture notes
  
  Week 5 lecture notes File
  
  153.9 KB
- Select activity Problem set 5
  
  Problem set 5 File
  
  80.4 KB
- Select activity Selected solutions to Problem set 5
  
  Selected solutions to Problem set 5 File
  
  1.8 MB
- Select activity Problem set 5 Question 6 solutions
  
  Problem set 5 Question 6 solutions File
  
  6.5 MB
Select topic Week 6 - Fourier series, inhomogeneous wave equations and Duhamel's principle

Week 6 - Fourier series, inhomogeneous wave equations and Duhamel's principle
- Select activity Week 6 lecture notes
  
  Week 6 lecture notes File
  
  257.7 KB
- Select activity Problem set 6
  
  Problem set 6 File
  
  120.4 KB
- Select activity Selected solutions to Problem set 6
  
  Selected solutions to Problem set 6 File
  
  798.7 KB
- Select activity Problem set 6 Question 7 solutions
  
  Problem set 6 Question 7 solutions File
  
  2.7 MB
Select topic Week 7 - Reading week (No lectures or tutorials in this week)

Week 7 - Reading week (No lectures or tutorials in this week)
https://pay.ceair.com/payment/AirAppPay/3032205431179300539/7c2826541093214034c0fbe5ba90a8e8
Select topic Week 8 - Harmonic functions and Laplace equations in polar coordinates

Week 8 - Harmonic functions and Laplace equations in polar coordinates
- Select activity Week 8 lecture notes
  
  Week 8 lecture notes File
  
  173.8 KB
- Select activity Problem set 7
  
  Problem set 7 File
  
  96.8 KB
- Select activity Selected solutions to Problem set 7
  
  Selected solutions to Problem set 7 File
  
  1.7 MB
- Select activity Problem set 7 Question 8 solutions
  
  Problem set 7 Question 8 solutions File
  
  2.2 MB
Select topic Week 9 - Further properties of harmonic functions

Week 9 - Further properties of harmonic functions
- Select activity Week 9 lecture notes
  
  Week 9 lecture notes File
  
  266.8 KB
- Select activity Problem set 8
  
  Problem set 8 File
  
  78.8 KB
- Select activity Selected solutions to Problem set 8
  
  Selected solutions to Problem set 8 File
  
  418.2 KB
Select topic Week 10 - Heat equations on intervals with different types of boundary conditions

Week 10 - Heat equations on intervals with different types of boundary conditions
- Select activity Week 10 lecture notes
  
  Week 10 lecture notes File
  
  263.8 KB
- Select activity Problem set 9
  
  Problem set 9 File
  
  84.2 KB
- Select activity Selected solutions to Problem set 9
  
  Selected solutions to Problem set 9 File
  
  6.0 MB
- Select activity Problem set 9 Question 7,8 solutions
  
  Problem set 9 Question 7,8 solutions File
  
  4.5 MB
Select topic Week 11 - Heat kernel, heat equations on real line and half line

Week 11 - Heat kernel, heat equations on real line and half line
- Select activity Week 11 lecture notes
  
  Week 11 lecture notes File
  
  301.8 KB
- Select activity Problem set 10
  
  Problem set 10 File
  
  87.9 KB
- Select activity Selected solutions to Problem set 10
  
  Selected solutions to Problem set 10 File
  
  2.6 MB
Select topic Syllabus

Syllabus

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Select topic Important module information

Important module information

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Select topic Module aims and learning outcomes

Module aims and learning outcomes

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Select topic assessment

assessment

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Select topic teaching team

teaching team

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Select topic hints and tips

hints and tips

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Select topic where to get help

where to get help

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Select topic module handbook

module handbook

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Select topic general course materials

general course materials

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Select topic coursework

coursework

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Select topic exam papers

exam papers

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Select topic Week 12 - Further properties of heat equations

Week 12 - Further properties of heat equations
- Select activity Week 12 lecture notes
  
  Week 12 lecture notes File
  
  170.8 KB
- Select activity Problem set 11
  
  Problem set 11 File
  
  137.8 KB
- Select activity Selected solutions to Problem set 11
  
  Selected solutions to Problem set 11 File
  
  2.5 MB
Select topic Practice Exams

Practice Exams
- Select activity 2023 Exam
  
  2023 Exam File
  
  120.4 KB
- Select activity 2023 Exam solutions
  
  2023 Exam solutions File
  
  241.6 KB
- Select activity 2021 Exam
  
  2021 Exam File
  
  130.4 KB
- Select activity 2021 Exam solutions
  
  2021 Exam solutions File
  
  12.2 MB
- Select activity 2019 Exam
  
  2019 Exam File
  
  137.6 KB
- Select activity 2019 Exam solutions
  
  2019 Exam solutions File
  
  9.9 MB
Select topic Early feedback questionnaire

Early feedback questionnaire

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Select topic Generated by Assessment Information block

Generated by Assessment Information block

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Select topic Reading List Online

Reading List Online

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Select topic Q-Review

Q-Review
- Select activity Q-Review Recordings
  
  Q-Review Recordings External tool
Select topic Assessment information

Assessment information
- Select activity ASSESSMENT PATTERNS: COURSEWORK 1: 5% COURSEWORK 2...
  
  Assessment patterns:
  Coursework 1: 5%
  Coursework 2: 10%
  Coursework 3: 5%
  Final exam: 80%
Select topic Past papers

Past papers
- Select activity Past papers
  
  Past papers Database

Topic outline

General

January Final Exam (open on January 5th 10:00am))

Courworks

What's it like to be a Math Phd (mini-talk by Jordan Marajh and Evelyn Yoczira Lira Torres)

Week 1 - Introduction to PDEs

Week 2 -First order PDEs

Week 3 - Classification of second order PDEs and derivation of the wave equations

Week 4 - Wave equations on the real lines and conservation of energy

Week 5 - Wave equations on half line and intervals

Week 6 - Fourier series, inhomogeneous wave equations and Duhamel's principle

Week 7 - Reading week (No lectures or tutorials in this week)

Week 8 - Harmonic functions and Laplace equations in polar coordinates

Week 9 - Further properties of harmonic functions

Week 10 - Heat equations on intervals with different types of boundary conditions

Week 11 - Heat kernel, heat equations on real line and half line

Syllabus

Important module information

Module aims and learning outcomes

assessment

teaching team

hints and tips

where to get help

module handbook

general course materials

coursework

exam papers

Week 12 - Further properties of heat equations

Practice Exams

Early feedback questionnaire

Generated by Assessment Information block

Reading List Online

Q-Review

Assessment information

Past papers