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2008/09 Undergraduate Module Catalogue

MATH1970 Differential Equations

10 creditsClass Size: 200

Module manager: Professor A.V. Mikhailov
Email: sashamik@maths.leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2008/09

Pre-requisites

MATH1960Calculus

This module is mutually exclusive with

MATH1400Modelling with Differential Equations
MATH1460Mathematics for Geophysical Sciences 1
MATH1932Calculus, ODEs and Several-Variable Calculus

This module is approved as an Elective

Module summary

Differential equations provide a powerful mathematical method for modelling physical, chemical and biological phenomena. This introduction to the theory of differential equations cover basic methods for solving ordinary differential equations, that is, equations in which the functions depend on a single variable.

Objectives

On completion of this module, students should be able to:

a) Solve a variety of first-and second-order differential equations;
b) Derive and solve ODEs arising from applications..


Syllabus

1. Introduction. Basic definitions, examples. Geometrical interpretation. Graphical and numerical solutions.
2. First order ordinary differential equations: Linear equations, separable equations. Homogeneous equations, Bernoulli equation. Change of variables. Exact equations.
3. Second order linear ordinary differential equations. Equations with constant coefficients. equations with non-constant coefficients. Homogeneous equations: principle of superposition, solution space, basis, Wronskians, Abel¿s identity. Method of reduction of order. Inhomogeneous equations, methods of undetermined coefficients, variation of parameters.
4. Systems of linear ordinary differential equations: Homogeneous solutions. Fundamental solution matrix. Wronskians. Inhomogeneous systems. Variation of parameters.
5. Phase plane methods: Introduction. Critical points. Stability. Matrix exponential.

Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Delivery typeNumberLength hoursStudent hours
Lecture211.0021.00
Tutorial111.0011.00
Private study hours68.00
Total Contact hours32.00
Total hours (100hr per 10 credits)100.00

Opportunities for Formative Feedback

Regular example sheets.

Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information


Coursework
Assessment typeNotes% of formal assessment
In-course Assessment.15.00
Total percentage (Assessment Coursework)15.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated


Exams
Exam typeExam duration% of formal assessment
Standard exam (closed essays, MCQs etc)2 hr 00 mins80.00
Standard exam (closed essays, MCQs etc)0 hr 00 mins5.00
Total percentage (Assessment Exams)85.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 31/03/2009

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