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MA1011 Methods of Applied Mathematics I

MA1011 Methods of Applied Mathematics I

Credits: 20 Convenor: Dr. J. Levesley Semester: 1 (weeks 1 to 12)
Prerequisites:
Assessment: Weekly exercises and computer practical: 40% Examination: 0%
Lectures: 33 Problem Classes: 10
Tutorials: none Private Study: 85
Labs: 11 Seminars: none
Project: none Other: none
Surgeries: 11 Total: 150

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. Compute vector and Cartesian equations of lines and planes, including tangent planes of surfaces. Compute directional derivatives. Find and characterise stationary points on surfaces. Calculate the lenght of a curve in space. Compute and change the order of integration in double integrals.

Students should be able to use a computer to solve some simple differetial equatons, assess the approximating power of the Taylor series, calculate the length a curve, and the volume under a surface.

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 do some vector geometry, and will learn how to perform partial differentiations, how to use the chain rule, and how to find a directional derivative. They will learn how to find local and global maxima and minima, as well as learn how to distinguish these from saddle points. Students will learn how to use integration to compute the length of a curve, and the volume under a surface.

Students will use the computer to reinforce their geometric feel for processes such as differentiation and integration by numerically solving differential equations and numerically computing integrals. They will also explore the approximation power of Taylor series.

Syllabus

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. Compute vector and Cartesian equations of lines and planes, including tangent planes of surfaces. Compute directional derivatives. Find and characterise stationary points on surfaces. Calculate the length of a curve in space. Compute and change the order of integration in double integrals.

Students should be able to use a computer to solve some simple differential equatons, assess the approximating power of the Taylor series, calculate the length a curve, and the volume under a surface.

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: MA1051 Newtonian Dynamics Up: ModuleGuide03-04 Previous: MA1002 Vectors and ODEs

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Last updated: 2004-02-21
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