# Mathematics II - PH312

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## Module delivery information

Location Term Level1 Credits (ECTS)2 Current Convenor3 2020 to 2021
Canterbury
Spring 4 15 (7.5) DR G Dobre

## Overview

Differential Equations: Solving differential equations, separable equations, linearity, homogeneity, first and second order equations, particular integrals. Boundary and initial values, auxiliary equations with complex roots, coefficients and terms, examples from physics.

Partial Derivatives: functions of two variables , partial derivatives, directional derivatives, functions many variables, higher derivatives, function of a function, implicit differentiation, differentiation of an integral w.r.t a parameter, Taylor expansions, stationary points.

Elementary multivariate Calculus: the chain rule, Multiple integrals, integrals over rectangles/irregular areas in the plane, change of order of integration.

Polar Coordinates: Cylindrical polar coordinates in two and three dimensions, integrals, spherical coordinates, solid angle.

Introduction to Vector Calculus : Gradients, Divergence, Gauss's theorem, Curl, Stokes' theorem.

## Details

### Contact hours

24 lecture hours and 12 hours workshop sessions.

Total study time: 150 hours, including contact hours and 114 independent learning hours.

### Availability

This is not available as a wild module.

## Method of assessment

Coursework 30% comprising two in course test and weekly home work involving problem solving, and two one hour class test. Final (written, unseen, 2hrs) exam 70%.

Engineering Mathematics (7th Ed.); Stroud, K.A. & Booth, D.J. (2013)

See the library reading list for this module (Canterbury)

## Learning outcomes

• Solve problems in physics using appropriate mathematical tools
• Present and interpret information graphically
• Make use of appropriate texts, research-based materials or other learning resources as part of managing their own learning.
• Problem-solving skills, in the context of both problems with well-defined solutions and open-ended problems; an ability to formulate problems in precise terms and to identify key issues, and the confidence to try different approaches in order to make progress on challenging problems. Numeracy is subsumed within this area..
• Analytical skills – associated with the need to pay attention to detail and to develop an ability to manipulate precise and intricate ideas, to construct logical arguments and to use technical language correctly.

## Notes

1. Credit level 4. Certificate level module usually taken in the first stage of an undergraduate degree.
2. ECTS credits are recognised throughout the EU and allow you to transfer credit easily from one university to another.
3. The named convenor is the convenor for the current academic session.