# Course Identification

Physics module: Mathematics of physics
20226161

## Lecturers and Teaching Assistants

Prof. Shimon Levit
Dr. Dan Klein

## Course Schedule and Location

2022
First Semester
Tuesday, 15:00 - 17:30, Musher, Lab 3
05/10/2021
30/04/2022

## Field of Study, Course Type and Credit Points

Science Teaching (non thesis MSc Track): Lecture; Obligatory; Regular; 3.00 points

1st year

No

No

Hebrew

## Attendance and participation

Obligatory

Numerical (out of 100)

100%

Examination

N/A
N/A
-
N/A

N/A
N/A
-
N/A

N/A

## Syllabus

1. Hyperbolic Functions. Taylor Series. Gaussian Integrals. The Dirac Delta Function. Spherical and Cylindrical Coordinates
2. Complex Numbers and Complex Functions. Definition of a Complex Number. Basic Complex Arithmetics. The Complex Plane. Complex Exponentials and General Complex Functions.
3. Vectors and Vector Analysis. Vectors and Their Transformations. Transformation Matrices. Addition and Multiplication of Vectors. Why Physics Uses Vectors? Rotational Invariance. Tensors. Integrals of Vectors. Derivatives of Vectors. The Gradient. The Laplacian. Divergence and Curl. Useful Identities and Calculation Tips.
4. Systems of Linear Algebraic Equations. Matrices and Determinants. Two Linear Equations. Conditions on Determinants for Solution to Exist. Eigenvalues and Eigenvectors. Product of 2 £ 2 Matrices. Functions of 2 £ 2 Matrices. System of n Equations and its Matrix Form. Determinant of an n£n Matrix. Cramer's Formula and Existence of Solutions. Eigenvalues and Eigenvectors of n£n Matrices. Product of n £ n Matrices.
5. Ordinary Differential Equations (ODE). Linear ODE with Constant Coefficients. Linear Second Order ODE with Non Constant Coefficients. Systems of Linear ODE's. Coupled Oscillators.

## Learning Outcomes

Upon successful completion of the course students will be able to:

Demonstrate enough proficiency in the topics taught in the course to enable them cope with the demanding curriculum of the physics courses in the program.