# MA231 - Vector Analysis

• Module code: MA231
• Module name: Vector Analysis
• Department: Mathematics Institute
• Credit: 12

## Module content and teaching

###### Principal aims

This module aims to: 1. Teach a practical ability to work with functions of two or three variables and vector fields; 2. Present the theorems of Gauss and Stokes as generalisations of the fundamental theorem of calculus to higher dimensions;3. Establish Cauchy's theorem in complex analysis as a consequence of the Cauchy-Riemann equations and the divergence theorems; 4. Teach those rudiments of complex analysis which follow from Cauchy's theorem, namely, the Cauchy integral formula, Taylor expansions and residue calculus.

###### Principal learning outcomes

On successful completion of this module, a student should: 1. Be able to calculate line, surface and volume integrals in general curvilinear coordinates; 2. Be familiar with and use in a variety of contexts the fundamental results of vector calculus, namely, the divergence theorem and Stokes' theorem; 3. Understand the relation between the existence of a scalar or vector potential of a vector field and the vanishing of the curl or divergence of that vector field and be able to calculate the potential when it exists; 4. Be able to establish the Cauchy-Riemann equations for a complex differentiable function and establish Cauchy's theorem from the integral theorems of vector calculus; 5. Be able to prove Cauchy's integral formula from Cauchy's theorem, and to use the integral formula to establish differentiability and series properties of complex differentiable functions; 6. Be able to calculate Taylor expansions, residues and use them in the evaluation of definite integrals and summation of series.

http://go.warwick.ac.uk/MA231/

###### Other essential notes

Prerequisites: MA127 3D Geometry and Motion or PX129 (Maths/Physics) Worksheets.

## Module assessment

Assessment group Assessment name Percentage
12 CATS (Module code: MA231-12)
D (Assessed/examined work) Assessed Course Work 15%
Examination - April 85%

## Module availability

This module is available on the following courses:

###### Core
• Undergraduate Mathematics and Physics (BSc MMathPhys) (FG33) - Year 2
• Undergraduate Mathematics (BSc) (G100) - Year 2
• Undergraduate Mathematics with Intercalated Year (G101) - Year 2
• Undergraduate Mathematics (MMath) (G103) - Year 2
• Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 2
• Undergraduate Mathematics (MMath) with Study in Europe (G106) - Year 2
• Undergraduate Mathematics and Business Studies (with Intercalated Year) (G1N2) - Year 2
• Undergraduate Mathematics and Physics (BSc) (GF13) - Year 2
• Undergraduate Mathematics and Philosophy with Specialism in Logic and Foundations (GV19) - Year 3
###### Optional Core
• Undergraduate Mathematics and Philosophy with Specialism in Logic and Foundations (GV19) - Year 2
###### Optional
• Undergraduate Mathematics and Statistics (BSc MMathStat) (G1G3) - Year 2
• Undergraduate Mathematics and Statistics (BSc MMathStat) (G1G3) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G300) - Year 2
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G300) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G300) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30A) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30A) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30A) - Year 5
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30B) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30B) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30B) - Year 5
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30C) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30C) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30C) - Year 5
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30D) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30D) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30D) - Year 5
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30E) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30E) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30E) - Year 5
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30F) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30F) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30F) - Year 5
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30G) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30G) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30G) - Year 5
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30H) - Year 3
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30H) - Year 4
• Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30H) - Year 5
• Undergraduate Discrete Mathematics (G4G1) - Year 2
• Undergraduate Discrete Mathematics (G4G3) - Year 2
• Undergraduate Mathematics and Statistics (BSc) (GG14) - Year 2
• Undergraduate Mathematics and Statistics (BSc) (GG14) - Year 3
• Undergraduate Mathematics and Statistics (with Intercalated Year) (GG17) - Year 4
• Undergraduate Mathematics and Economics (GL11) - Year 2
• Undergraduate Mathematics and Economics (GL11) - Year 3
• Undergraduate Mathematics and Economics (with Intercalated Year) (GL12) - Year 2
• Undergraduate Mathematics and Economics (with Intercalated Year) (GL12) - Year 4
• Undergraduate Mathematics,Operational Research,Statistics and Economics (Y602) - Year 2
• Undergraduate Mathematics,Operational Research,Statistics and Economics (Y602) - Year 3
• Undergraduate Mathematics,Operational Research,Statistics,Economics (with Intercalated Year) (Y603) - Year 4