Courses / Module

Toggle Print

Module COMPLEX ANALYSIS AND VECTOR CALCULUS

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

Open Learning Outcomes
 
Open Teaching & Learning methods
 
Open Assessment
 
Open Repeat options
 
Open Pre-Requisites
 
Open Co-Requisites
 
Open Timetable
 
Back to top Powered by MDAL Framework © 2019
V5.2.0 - Powered by MDAL Framework © 2019