Announcements


The two first two lectures (Monday 21st and Tuesday 22nd January 2019, at 3pm) are cancelled. These will be replaced by two extra lectures at 4pm on Tuesday 29th January and Tuesday 12th February.

Forum

General


This course is part of the MAGIC core.

Description

This course is intended to provide an introduction to the theory of partial differential equations (pdes).
Definitions and examples are given of first, second and higher order pdes and also systems of first order pdes. The focus is on developing practical methods that will be applicable in applied mathematics.

Semester

Spring 2019 (Monday, January 21 to Friday, March 29)

Hours

  • Live lecture hours: 20
  • Recorded lecture hours: 0
  • Total advised study hours: 80

Timetable

  • Mon 15:05 - 15:55
  • Tue 15:05 - 15:55

Prerequisites

No prior knowledge of PDEs is required, but experience with vector calculus and general undergraduate methods courses would be very helpful.

Syllabus

  • Notation, definitions. Symbol of a pde and of systems.
  • Examples from applied mathematics.
  • Method of characteristics for first order PDEs
  • Classification of second order PDEs, and reduction to normal form
  • Wave equation and separation of variables
  • Fourier series and Fourier transforms
  • Sturm-Liouville systems
  • Nonlinear PDEs

Lecturer


Alice Thompson
Email Alice.Thompson@manchester.ac.uk
Phone 0161-3068951
Photo of Alice Thompson


Bibliography


An Introduction to Partial Differential Equations, 2nd. editionM. Renardy and R.C. Rogers


Note:

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Assessment



The assessment for this course will be via a single take-home paper issued on 28 April 2019 and due by 12 May 2019. There will be five questions each with equal weight; you will need to answer the equivalent of 2.5 questions perfectly to pass.

No assignments have been set for this course.

Files


Files marked L are intended to be displayed on the main screen during lectures.

Week(s)File
Complete_notes_MAGIC058.pdf
MAGIC058_Example_Sheet_1.pdf
MAGIC058_Example_Sheet_1_Solutions.pdf
MAGIC058_Example_Sheet_2.pdf
MAGIC058_Example_Sheet_2_Solutions.pdf
MAGIC058_Example_Sheet_3.pdf
MAGIC058_Example_Sheet_3_Solutions.pdf
MAGIC058_Example_Sheet_4.pdf
MAGIC058_Example_Sheet_4_Solutions.pdf
MAGIC058_Example_Sheet_5.pdf
MAGIC058_Example_Sheet_5_Solutions.pdf
MAGIC058_Example_Sheet_6.pdf
MAGIC058_Example_Sheet_6_Solutions.pdf
MAGIC058_Example_Sheet_7.pdf
MAGIC058_Example_Sheet_7_Solutions.pdf
MAGIC058_Example_Sheet_8.pdf
MAGIC058_Example_Sheet_8_Solutions.pdf
MAGIC058_Example_Sheet_9.pdf
MAGIC058_Example_Sheet_9_Solutions.pdf
Provisional_complete_notes.pdf
011_February.pdfL
0Announcements.pdf
0Lecture_01_28_01_2019_Visualizer.pdf
0Lecture_02_29_01_2019_Visualizer.pdf
0Lecture_03_29_01_2019_Visualizer.pdf
0Lecture_04_04_02_2019_Visualizer.pdf
0Lecture_05_05_02_2019_Visualizer.pdf
0Lecture_06_11_02_2019_Visualizer.pdf
0Lecture_07_12_02_2019_Visualizer.pdf
0Lecture_08_12_02_2019_Visualizer.pdf
0Lecture_09_18_02_2019_Visualizer.pdf
0Lecture_10_19_02_2019_Visualizer.pdf
0Lecture_11_25_02_2019_Visualizer.pdf
0Lecture_13_04_03_2019_Visualizer.pdf
0Lecture_14_05_03_2019_Visualizer.pdf
0Lecture_15_11_03_2019_Visualizer.pdf
0Lecture_16_12_03_2019_Visualizer.pdf
0Lecture_17_18_03_2019_Visualizer.pdf
0Lecture_18_19_03_2019_Visualizer.pdf
0Lecture_19_25_03_2019_Visualizer.pdf
0Lecture_20_26_03_2019_Visualizer.pdf
0Notes_section_1.pdf
0Notes_section_2.pdf
0Notes_section_3.pdf
0Notes_section_4.pdf
0Notes_section_5.pdf
0Notes_section_6.pdf
0Notes_section_7_part_1.pdf
0Notes_section_7_part_2.pdf
0PDE handout 1.pdfL


Recorded Lectures


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