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Department of Mathematics



Next: MA1011 Methods of Applied Mathematics I Up: ModuleGuide03-04 Previous: MA1001 Multivariate Calculus

MA1002 Vectors and ODEs

MA1002 Vectors and ODEs

Credits: 10 Convenor: Dr. J. Levesley Semester: 1 (weeks 2 to 6)
Prerequisites:
Assessment: Weekly exercises and computer practical: 40% Examination: 0%
Lectures: 15 Problem Classes: 5
Tutorials: none Private Study: 45
Labs: 5 Seminars: none
Project: none Other: none
Surgeries: 5 Total: 75

Subject Knowledge

Aims

This module aims to introduce the student to fundamental methods in applied mathematics, to give the student experience in using the computer to solve mathematical problems, and to reinforce A level calculus skills.

Learning Outcomes

Know how to solve the following differential equations: first order separable; first order linear; second order linear with constant coefficients. Compute partial derivatives, use the chain rule. Be able to compute the Taylor series of a function. Perform simple operations with vectors.

Students should be able to use a computer to solve some simple differetial equatons and assess the approximating power of the Taylor series.

Methods

Lectures, computer classes, problem classes.

Assessment

Marked problem sheets, computer practical portfolio, examination.

Subject Skills

Aims

To provide students with computing skills and develop written communication skills and problem solving skills.

Learning Outcomes

Students will have used a computer to solve some simple mathematical problems, and recorded their findings in a portfolio. Students will have improved their ability ot solve problems both using pencil and paper and a computer.

Methods

Lectures, computer classes, problem classes.

Assessment

Marked problem sheets, marked computer practical portfolio.

Explanation of Pre-requisites

This modules will assume that the student has a firm grasp of all the material in the core A-level syllabus. In particular, a thorough understanding of A-level calculus will be required: differentiation and integration of standard functions (polynomials, radicals, trigonometric, exponential and logarithmic functions) together with rules for dealing with products and compositions of functions. The module will also assume a knowledge of trigonometry, including standard trigonometric identities.

Course Description

In this course we present a number of standard mathematical methods which can be used for solving simple differential equations. They will see how a function can be approximated using Taylor series.

Students will use the computer to reinforce their geometric feel for processes such as differentiation and integration by numerically solving differential equations.

Syllabus

Know how to solve the following differential equations: first order separable; first order linear; second order linear with constant coefficients. Be able to compute the Taylor series of a function. Perform simple operations with vectors.

Students should be able to use a computer to solve some simple differential equatons and assess the approximating power of the Taylor series.

Reading list

Recommended:

C. H. Edwards and D. E. Penney, Calculus, Pearson Education, 2002.

Background:

J. Stewart, Calculus, Thompson Learning, 2003.

G. B. Thomas, Calculus, Addison Wesley, 2000.

Resources

Problem sheets, computer rooms, lecture rooms.

Module Evaluation

Module questionnaires, module review, year review.

Next: MA1011 Methods of Applied Mathematics I Up: ModuleGuide03-04 Previous: MA1001 Multivariate Calculus

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Last updated: 2004-02-21
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