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## 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 Timetable 