# Summer School on Mathematical Physics

August 08, 2023 to August 31, 2023, Virtual

We are offering a comprehensive 26-hour online course (13 lectures of 2 hours) designed to instil fundamental mathematical techniques to undergraduate students pursuing physics. This initiative is organised under the auspices of the KRG's Ministry of Higher Education and Scientific Research in partnership with the University of Garmian, the Kurdish Mathematical Society and Iraq's chapter of Global STEM Initiative.

The course will be instructed by the esteemed Professor Ebrahim Karimi, who is the director of the University of Quantum Institute (NexQT) and a respected member of the University of Ottawa's academic staff in Canada.

Upon the successful culmination of the course, participants will receive a certificate of completion. To be eligible for this recognition, participants are required to maintain an online presence for at least 80% of the course duration and consistently accomplish the given class assignments.

The course will be delivered in English. The primary resource for this course will be the 6th edition of “Mathematical Methods in Physics”, authored by George Arfken.

For an efficient learning experience, a dedicated Google Classroom will be set up, and all class sessions will be conducted via Zoom Meeting. This provides learners with a robust and interactive environment, promoting engagement and comprehension.

The course content and schedule:

Vector Analysis

Tuesday (8 August 2023) from 12:00 EST to 14:00 EST

Wednesday (9 August 2023) from 12:00 EST to 14:00 EST

Thursday (10 August 2023) from 12:00 EST to 14:00 EST

Homework 1 [Deadline Aug. 17]. Deadline is Extended!

Definitions; Elementary; Approach; Rotation of the coordinate axes; Scalar or Dot Product; Vector or Cross Product; Triple Scalar Product; Triple Vector Product; Gradient, ∇; Divergence, ∇.A; Curl, ∇×A; Successive Applications of ∇; Vector Integration; Gauss’ Theorem; Stokes’ Theorem; Potential Theory; Gauss’ Law, Poisson’s Equation; Dirac Delta Function; Helmholtz’s Theorem Contents

Vector Analysis in Curved Coordinates and Tensors

Tuesday (15 August 2023) from 12:00 EST to 14:00 EST

Wednesday (16 August 2023) from 12:00 EST to 14:00 EST

Thursday (17 August 2023) from 12:00 EST to 14:00 EST

Homework 2 [Deadline Aug. 21]

Orthogonal Coordinates in R3; Differential Vector Operators; Special Coordinate Systems: Introduction; Circular Cylinder Coordinates; Spherical Polar Coordinates; Tensor Analysis; Contraction, Direct Product; Quotient Rule; Pseudotensors, Dual Tensors; General Tensors; Tensor Derivative Operators

Determinants and Matrices

Tuesday (22 August 2023) from 12:00 EST to 14:00 EST

Wednesday (23 August 2023) from 12:00 EST to 14:00 EST

Thursday (24 August 2023) from 12:00 EST to 14:00 EST

Homework 3 [Deadline Aug. 28]

Determinants; Matrices; Orthogonal Matrices; Hermitian Matrices, Unitary Matrices; Diagonalization of Matrices; Normal Matrices

Group Theory

Tuesday (29 August 2023) from 12:00 EST to 14:00 EST

Wednesday (30 August 2023) from 12:00 EST to 14:00 EST

Thursday (31 August 2023) from 12:00 EST to 14:00 EST

Homework 4 [Deadline Sept 5]

Introduction to Group Theory; Generators of Continuous Groups; Orbital Angular Momentum; Angular Momentum Coupling; Homogeneous Lorentz Group; Lorentz Covariance of Maxwell’s Equations; Discrete Groups; Differential Forms

Participants who can not join Google Classrooms, they can submit their assignments to one of the following emails:

1st Classroom's moderator : mpsc.m2@garmian.edu.krd

2nd Classroom's moderator : mpsc.m3@garmian.edu.krd

3rd Classroom's moderator : mpsc.m4@garmian.edu.krd

4th Classroom's moderator : mpsc.m5@garmian.edu.krd