The Department of Physics

Course Description

This course will introduce students to mathematical methods that will be used in advanced level Physics courses, as well as various applications in Physics. This course will focus on the following: Distribution functions, Sampling theory, Applications in Physics. Cartesian and Curvilinear Coordinate Systems, Vector Analysis, Complex Variable Theory, Fourier Series Analysis, Differential Equations (up to second order), and Applications of these methods in Physics. Through in-class discussions, and problem solving sessions, Students would have an opportunity to improve their ability to reason through challenging situations using basic principles to develop appropriate solutions. Assessment and evaluation is done in the form of in-course tests and a Final examination.

CONTENT

This course will focus on the following:
Vector analysis: Vector multiplication & applications; differentiation/integration of vectors; directional derivatives; Divergence & curl; the Laplacian; line integrals; Green’s theorem; the divergence theorem & Stokes’ theorem & their application in problem solving. Probability & Statistics: Conditional Probability; Bayes Theorem; Random variables. Complex Numbers: Rectangular/polar/complex exponential equivalents of Z; conjugate of Z and its utility; exponential functions of Z; Trig. Functions of Z; Hyperbolic functions; logarithms of Z; complex roots and powers of Z; differentiation/integration of complex expressions; applications of complex numbers in physics. Probability & Statistics: Probability distributions (Poisson, Binomial, Normal); Sampling theory; Probability distributions, Sample means, sample error. Coordinate Systems: Introduction to coordinate systems; Coordinate transformations. Differential Equations: Definitions: ordinary/partial differential equations; order & degree of differential equations; methods of solution of first order equations; Methods of solving second order equations; Applications of differential equations in physics. Fourier series: Advantages over power series expansion; trigonometric/complex exponential equivalents of a Fourier series; Fourier coefficients; Even and odd functions; applications of Fourier series in physics.

GOALS/AIMS

• To enable students to develop a good understanding of the mathematical principles and methods required for more advanced studies of physics.
• To produce graduates with good critical thinking and problem solving skills enabling them to apply mathematical theory to the study and analysis of phenomena in physics.

LEARNING OUTCOMES

After successfully completing this course, students should be able to:

• Apply mathematical principles to the study and analysis of phenomena in physics.
• Analyze and organize information
• Communicate ideas and information
• Apply mathematical ideas and techniques
• Solve problems.

Assessment