Module and Programme Catalogue

Search site

Find information on

2005/06 Undergraduate Module Catalogue

PHYS1160 Differential Calculus and Infinite Series

10 creditsClass Size: 100

Module manager: Professor M D Savage
Email: m.d.savage@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2005/06

Pre-requisite qualifications

A Level Mathematics or equivalent

Pre-requisites

PHYS1150 or equivalent

This module is not approved as an Elective

Objectives

On completion of this module you should be able to:
- solve second order, linear, ordinary differential equations with constant coefficients;
- solve the SHM equation and the damped and forced SHM equations;
- determine the limit of a sequence;
- sketch the graphs of simple functions;
- test a series for convergence;
- determine the Taylor/Maclaurin series for a function of a single variable;
- determine the Fourier half range and full range series for a function, f(x);
- determine the partial derivatives of functions of two and three variables;
- apply the chain rule;
- determine the maxima, minima and saddle points of a function of two variables.

Skills outcomes
Basic mathematical skills in pure mathematics
Ability to solve differential equations
ability to model a physical problemBasic mathematical skills in pure mathematics
Ability to solve differential equations
ability to model a physical problem


Syllabus

Ordinary Differential Equations:
Second order, linear ODE's, principle of superposition. Solution of homogeneous equations with constant coefficients; the complementary function. Solution of inhomogeneous equations; finding particular integrals; the general solution as a combination of the complementary function and a particular integral. Application to Newtonian mechanics; simple harmonic motion, forced and damped oscillations.
Limits and Curve Sketching
Concept of a limit; L'hopital's rule; limit of a sequence and a series. Convergence of sequences and series
Curve sketching by finding stationary points, asymptotes and various limits of functions.
Series
Power series, Maclaurin series, Taylor series and Taylor's theorem. Fourier series, half and full range series.
Several Variable Calculus
Functions of two and three variables, partial differentiation, chain rule. Maxima , minima and saddle points of functions of several variables.

Teaching methods

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

Lectures: 22 x 1 hour;


Example classes: 10 x 1 hour.

Private study

Reading: 28 hours;
Examples: 40 hours.

Opportunities for Formative Feedback

5 assignments.

Methods of assessment

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

1 x 2 hour written examination at the end of the semester: 85%;
5 assignments submitted during the semester: 15%.

Reading list

The reading list is available from the Library website

Last updated: 16/08/2007

Disclaimer

Browse Other Catalogues

Errors, omissions, failed links etc should be notified to the Catalogue Team.PROD

© Copyright Leeds 2019