Faculty of Science

Objectives

To provide a rigorous introduction to the fundamentals techniques of applied mathematics and mathematical physics; introduction to computational physics.

Contents

The algebra of complex Numbers: Loci and the Argand diagrams, De’Moivre’s theorem and Euler’s formula; The algebra of matrices: Theory of Determinants, The theory of linear systems of algebraic equations, Method of Gaussian elimination, Rank and linear independence; Introduction to Vector spaces: Basis and dimension change of basis, rank; Vector Algebra: Products of vectors and their applications in physics, solution of vector equations; Vector calculus of a single variable: Differentiation of a vector and the resolution of such derivatives into tangential and normal components with application to physics; Vector Calculus of several variables (Partial differentiation): The differential and partial differential, chain rule and change of variable, extreme and the method of Langrange multipliers, the method of least squares; Vector Field theory: The Div., Grad. And Curl operators, vector identities, the Divergence and Stokes theorem with application in physics; Vector calculus of several variable (Integration): line, Green’s theorem in the plane.