Course Identification

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.

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.

Lecture Notes