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DEF intro 16 - Lecture notes 1-24

Module

Calculus and Linear Algebra

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Students shared 7 documents in this course
Academic year: 2018/2019
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Wacko Waldo
University of Nottingham
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University of Nottingham

APPLIED MATHEMATICS

G12DEF Differential Equations and Fourier Analysis

Lecturer: Dr Richard S Graham

Introduction to the Lecture Course

This module provides an introduction to Fourier series, integral transforms and other methods of solving linear ordinary, and partial, differential equations. These methods will be used to solve some standard equations that occur frequently throughout applied mathematics. A synopsis of the syllabus is outlined below.

Topics

  • Introductory definitions ~1 lecture
  • Properties of linear differential equations ~1 lecture
  • Series solutions to linear ODEs ~3 lectures
  • Introduction to Legendre and Bessel functions ~2 lectures
  • Periodic functions ~3 lectures
  1. Representation by Fourier Series
  2. Solutions of periodically forced ODEs
  • Introduction to PDEs ~5 lectures
  1. Solution using separation of variables
  2. Spherical Harmonics
  • The Fourier Transform ~3 lectures
  • The Laplace Transform ~3 lectures

Method of Teaching The course consists of two lectures and one workshop per week. For times and location of the lectures and workshops see the central timetabling website. The workshop sessions will alternate between example classes, where I will go through example problems on the board, and problem classes where individual help with the course material will be available from post-grad teaching assistants and myself. These start with an examples class on Wednesday 3rd February. Many examples will be covered in lectures, but the best way to learn is by doing it yourself. The unassessed coursework, along with the problem classes, provide a good chance to do this. Additional problem sheets, an example class test, previous years’ coursework and past exam papers are also available from the module’s moodle webpage.

Method of Assessment 90% of the course mark will be based on a 2 hour written examination in which you are expected to complete four questions from a possible five. The remaining 10% is based on a class-test. For the date and location of this class-test see the module’s moodle page. The test will last 40 minutes, will have 8 questions (with no choice of questions) and will cover material up the end of slide 78, along with material from the revision questions. The reassessment mark for the module (if required) will be based 100% on the written resit exam, which will be in August.

Webpage There is a moodle webpage for this module where you can find example sheets, lecture notes, recorded lectures, my office hours etc. The website will be updated throughout the course.

G12DEF Differential Equations and Fourier Analysis

Book Lists

Author Title Publisher Library No. Recommended Texts

W E Boyce and R C DiPrima

Elementary Differential Equations and Boundary Value Problems

Wiley QA 371

R V Churchill and J W Brown

Fourier Series and Boundary Value Problems

McGraw-Hill QA 404

E Kreyszig Advanced Engineering Mathematics Wiley TA 330

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DEF intro 16 - Lecture notes 1-24

Module: Calculus and Linear Algebra

7 Documents
Students shared 7 documents in this course

University: University of Nottingham

Was this document helpful?
University of Nottingham
APPLIED MATHEMATICS
G12DEF Differential Equations and Fourier Analysis
Lecturer: Dr Richard S Graham
Introduction to the Lecture Course
This module provides an introduction to Fourier series, integral transforms and other methods of
solving linear ordinary, and partial, differential equations. These methods will be used to solve
some standard equations that occur frequently throughout applied mathematics. A synopsis of the
syllabus is outlined below.
Topics
• Introductory definitions ~1 lecture
• Properties of linear differential equations ~1 lecture
• Series solutions to linear ODEs ~3 lectures
• Introduction to Legendre and Bessel functions ~2 lectures
• Periodic functions ~3 lectures
1. Representation by Fourier Series
2. Solutions of periodically forced ODEs
• Introduction to PDEs ~5 lectures
1. Solution using separation of variables
2. Spherical Harmonics
• The Fourier Transform ~3 lectures
• The Laplace Transform ~3 lectures
Method of Teaching
The course consists of two lectures and one workshop per week. For times and location of the
lectures and workshops see the central timetabling website. The workshop sessions will alternate
between example classes, where I will go through example problems on the board, and problem
classes where individual help with the course material will be available from post-grad teaching
assistants and myself. These start with an examples class on Wednesday 3rd February. Many
examples will be covered in lectures, but the best way to learn is by doing it yourself. The
unassessed coursework, along with the problem classes, provide a good chance to do this.
Additional problem sheets, an example class test, previous years’ coursework and past exam papers
are also available from the module’s moodle webpage.
Method of Assessment
90% of the course mark will be based on a 2 hour written examination in which you are expected to
complete four questions from a possible five. The remaining 10% is based on a class-test. For the
date and location of this class-test see the module’s moodle page. The test will last 40 minutes, will
have 8 questions (with no choice of questions) and will cover material up the end of slide 78, along
with material from the revision questions. The reassessment mark for the module (if required) will
be based 100% on the written resit exam, which will be in August.
Webpage
There is a moodle webpage for this module where you can find example sheets, lecture notes,
recorded lectures, my office hours etc. The website will be updated throughout the course.

Students also viewed

Related documents