# Courses / Module

Toggle Print

## COMPLEX ANALYSIS AND VECTOR CALCULUS

Module code: EE212
Credits: 5
Semester: 2
Department: THEORETICAL PHYSICS
International:
Coordinator: Dr Jonivar Skullerud (THEORETICAL PHYSICS)
Overview

Indicative Syllabus
• Vector Calculus
• Review of vector basics, applications of vectors in physical examples.
• Develop scalar and vector triple product formulae.
• Functions of several variables. Geometric interpretation. Level Curves.
• Partial derivatives. Geometric interpretation of the partial derivative.
• Chain rules for function of several variables.
• Scalar and vector functions. Physical examples.
• Introduce the "Del" vector differential operator.
• The gradient of a scalar field. r-dependent vector and scalar fields. Physical examples.
• Directional Derivative. Examples involving steepest ascent/descent. Directions of zero change.
• Divergence of a vector field.
• The Laplacian operator. Poisson's and Laplace's equation.
• The Curl of a vector field. Conservative vector fields.
• Discussion of Maxwell's equations.
• Derivative of vector functions. Unit tangent, normal, and binormal vectors.
• Curvature, radius of curvature and torsion.
• The Frenet-Serret formulae.
• Velocity and acceleration vectors vectors.
• Line integrals.
• Path independence. Scalar potential of a conservative vector function.
• Complex Analysis
• Basic concepts of complex numbers. Functions of a complex variable.
• The Cauchy-Riemann equations. Analytic functions.
• Harmonic functions. Connection between harmonic functions and analytic functions.
• Solving equations in complex variables.
• Integration of a complex function and line integrals in the complex plane.
• Cauchy's Integral theorem.
• The Cauchy Integral Formula and contour integrals.
• The Cauchy Integral Formula for derivatives.
• Laurent Series and the Residue theorem.

Learning Outcomes

Teaching & Learning methods

Assessment

Autumn Supplementals/Resits

Pre-Requisites

Co-Requisites

Timetable