# MMath&Phys Mathematics and Physics

Year of entry: 2023

## Course unit details:Introduction to Vector Calculus

Unit code MATH11411 10 Level 1 Semester 1 No

### Overview

This unit introduce students to the calculus of functions depending on more than one variable, while emphasising its usefulness in physical applications.

### Aims

The unit aims to introduce students to multivariable calculus, without assuming prior knowledge of linear algebra, while emphasising its usefulness in physical applications.

### Learning outcomes

On the successful completion of the course, students will be able to:

• Evaluate vector products in two and three-dimensions. Evaluate square-matrix and vector products. Compute determinants of 2x2 and 3x3 real matrices.
• Evaluate and manipulate functions of more than one variable. Sketch contours of functions of two variables near critical points. Sketch two-dimensional vector fields. Construct, evaluate and interpret partial derivatives of scalar and vector-valued functions of one, two and three variables.
• Find and classify critical points of functions of two variables
• Differentiate scalar and vector fields and physically interpret the associated operators; grad, curl and div.
• Construct, evaluate and interpret definite integrals of functions of two and three variables.
• Determine whether a given vector field is conservative or solenoidal.
• Verify specific examples of the classic integral theorem(s) of vector calculus in three dimensions; Green’s theorem, the divergence theorem and Stokes’ theorem.

Method Weight
Other 20%
Written exam 80%

### Feedback methods

There are supervisions in alternate weeks which provide an opportunity for students' work to be marked and discussed and to provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.

### Study hours

Scheduled activity hours
Lectures 22
Tutorials 5
Independent study hours
Independent study 73

### Teaching staff

Staff member Role
David Silvester Unit coordinator
Richard Hewitt Unit coordinator