## MATH2365 Vector Calculus

### 15 creditsClass Size: 150

Module manager: Dr O.G. Harlen
Email: oliver@maths.leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2008/09

### Pre-requisite qualifications

(MATH1015 and (MATH1932 or MATH1960)) or equivalent.

### This module is mutually exclusive with

 MATH2420 Multiple Integrals and Vector Calculus

Module replaces

MATH2360

This module is approved as an Elective

### Module summary

Vector calculus is the extension of ordinary one-dimensional differential and integral calculus to higher dimensions. As such it provides the mathematical framework for the study of a wide variety of physical systems, such as fluid mechanics and electromagnetism that can be described by vector and scalar fields.

### Objectives

On completion of this module, students should be able to:

a) calculate vector and scalar derivatives of vector and scalar fields using the grad, div and curl operators in Cartesian and in cylindrical and spherical polar coordinates;
b) use suffix notation to manipulate Cartesian vectors and their derivatives;
c) calculate multiple integrals in two and three dimensions including changing variables using Jacobians;
d) calculate line and surface integrals and use the various integral theorems.

### Syllabus

1. Vector Calculus: grad, div, curl and the operator. The directional derivative and Laplacian operators.
2. Suffix notation: representation of vectors and their products using suffix notation. The Kronecker delta and alternating tensors. Grad, div and curl in suffix notation. Use of suffix notation to manipulate products and combinations of vector differentials.
3. Double and triple integrals of scalars. Change of order of integration for double integrals over non-rectangular domains. Transformation of coordinates: the Jacobian. Cylindrical and spherical polar coordinates.
4. Scalar line and surface integrals of vectors in 3 dimensional space. Parameterisation of lines and surfaces, tangent and normal vectors. Evaluation of line and surface integrals. Other forms of line and surface integrals.
5. Exact differentials and conservative fields. The divergence and Stokes' theorems.
6. Orthogonal curvilinear coordinates. Grad, div and curl in cylindrical and spherical polar
coordinates.

### Teaching methods

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

 Delivery type Number Length hours Student hours Example Class 11 1.00 11.00 Lecture 33 1.00 33.00 Private study hours 106.00 Total Contact hours 44.00 Total hours (100hr per 10 credits) 150.00

### Private study

Studying notes between lectures: 52 hours.
Doing problems: 40 hours.
Exam preparation: 14 hours.

### Opportunities for Formative Feedback

regular problems sheets

### Methods of assessment

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

Coursework
 Assessment type Notes % of formal assessment Problem Sheet . 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) 3 hr 85.00 Total percentage (Assessment Exams) 85.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated