2017/18 Undergraduate Module Catalogue

PHYS1300 Maths 2- Multivariable Calculus

10 creditsClass Size: 180

Module manager: Prof Helen Gleeson
Email: H.F.Gleeson@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2017/18

Pre-requisite qualifications

'A' Level Physics and Maths or equivalent

This module is not approved as a discovery module

Objectives

On completion of this module you should be able to:

- determine the limit of a sequence;
- 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;
- solve second order, linear, ordinary differential equations with constant coefficients and understand the relationship with SHM equations;
- determine the partial derivatives of functions of two and three variables and 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
- evaluate multivariable integrals in Cartesian, cylindrical and spherical polar coordinate systems;
- find the gradient (grad) of a scalar field and understand its physical uses;
- find the divergence and curl of a vector field;
- evaluate grad, div and curl in Cartesian, cylindrical and spherical polar coordinate systems;
- find the Laplacian of scalar and vector fields;
- determine the flux of a vector field across a surface and use the Divergence theorem to evaluate flux across a closed surface.

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

Series, including : l’Hopital’s rule, convergence of sequences and series, Taylor’s theorem, Taylor and MacLaurin series, Fourier theorem, Fourier series

Second order differential equations, including homogeneity, general solutions to homogeneous differential equations, particular integrals, applications to mechanics and simple harmonic motion


Multi-Variable calculus, including : partial differentiation, stationary points of multi-variable functions, multiple integration, multiple variable calculus in Cartesian, cylindrical and spherical polar coordinate systems

The ‘del’ operator including: the gradient of scalar fields, the divergence and curl of vector fields, the Laplacian, the del operator in Cartesian, cylindrical and spherical polar coordinate systems

Flux and the Divergence theorem including: the definition of flux across a surface, evaluating flux through surface integrals, the Divergence theorem for flux across closed surfaces

Teaching methods

Delivery type	Number	Length hours	Student hours
Example Class	11	1.00	10.00
Lecture	22	1.00	22.00
Private study hours			68.00
Total Contact hours			32.00
Total hours (100hr per 10 credits)			100.00

Private study

Homework: 33 hours;
Study: 35 hours.

Opportunities for Formative Feedback

10 assignments.

Methods of assessment

Coursework

Assessment type	Notes	% of formal assessment
Assignment	10 assignments submitted during semester and work during examples classes	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 type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	2 hr 00 mins	85.00
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: 23/03/2018

Disclaimer

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