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2014/15 Undergraduate Module Catalogue

PHYS1300 Maths 2

10 creditsClass Size: 154

Module manager: Dr Anne Ghesquiere
Email: a.ghesquiere@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2014/15

Pre-requisite qualifications

'A' Level Physics and Maths or equivalent

Module replaces

PHYS1160

This module is not approved as a discovery module

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.
- estimate the error in a function of two variables.

Learning outcomes
Manipulate numerical and other quantitative information, and apply manipulative skills to the solution of problems.

Skills outcomes
Basic 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. Finding stationary points, testing for maxima , minima and saddle points.

Teaching methods

Delivery typeNumberLength hoursStudent hours
Example Class101.0010.00
Lecture221.0022.00
Private study hours68.00
Total Contact hours32.00
Total hours (100hr per 10 credits)100.00

Private study

Homework: 33 hours;
Study: 35 hours.

Opportunities for Formative Feedback

5 assignments.

Methods of assessment


Coursework
Assessment typeNotes% of formal assessment
Assignment6 assignments submitted during semester15.00
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 mins85.00
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: 27/03/2015

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