# Vector Calculus - MAT00012I

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• Department: Mathematics
• Module co-ordinator: Dr. Chris Wood
• Credit value: 20 credits
• Credit level: I
• Academic year of delivery: 2019-20
• See module specification for other years: 2016-17

## Module will run

Occurrence Teaching cycle
A Spring Term 2019-20 to Summer Term 2019-20

## Module aims

Part A:

• To deepen and extend the Stage 1 Calculus module, with a more mature look at the fundamental concepts of infinitesimal calculus from the viewpoint of vector-valued functions of many variables.
• To discuss the three essential ingredients of calculus - continuity, differentiability, and integrabilitybringing out the distinctive flavour of each theory, and describing their inter-relationships and applications.
• To gain a deeper understanding of the three famous differential operators of classical vector calculus: div, grad and curl.

Part B:

• To describe the differential calculus of scalar and vector fields in R3.
• To extend the theory of integration to volume integrals and integrals over surfaces in R3.
• To describe the theorems of Stokes and Gauss which link these topics together, and thereby to complete the chain of generalisations of the Fundamental Theorem of Calculus encountered previously.
• To determine when a potential function and vector potential exist, and calculate them.

## Module learning outcomes

At the end of the module you should be able to

Part A:

• Appreciate the concept of continuity for functions of many variables, and recognize a good supply of continuous functions.
• Understand the concept of linear approximation, recognize a wide range of differentiable functions of many variables, and differentiate them.
• Appreciate, and use, the chain rule.
• Integrate vector and scalar fields along contours in n-dimensional spaces.
• Discern when a multi-dimensional vector field is conservative, and construct a potential.
• Find a harmonic conjugate for a harmonic function in the plane.
• Calculate the flux of a vector field through a planar domain.
• Express a line integral as a double integral, and vice versa.

Part B:

• Compute integrals over a variety of regions of space.
• Parametrise a variety of surfaces in space and compute surface integrals of vector fields.
• Use index notation to manipulate vector expressions.
• Work with the fundamental differential operators of vector calculus.
• Understand the relationship between volume integrals and surface integrals, and surface integrals and line integrals.
• Use the integral theorems to move from one type of integral to another.
• Apply the techniques of vector calculus to a range of problems from geometry and physics.
• Determine when a potential function and a vector potential exist, and calculate them.

## Assessment

Task Length % of module mark
University - closed examination
Closed Examination
3 hours 100

None

### Reassessment

Task Length % of module mark
University - closed examination
Closed Examination
3 hours 100

## Module feedback

Information is currently unavailable.