Department of Physics

10ΥΚΟ10 Basic Mathematical Methods

Course webpage:  https://eclass.uoa.gr/courses/PHYS338

Course outline

Course content

• Complex numbers. Geometrical representation. De Moivre’s theorem. Connection with geometry.
• Vectors and vector operations (addition-subtraction, inner and outer product) with applications to kinematics and geometry. Use of indices and summation convention.
• Matrices. Matrix operations. Matrices as transformations in two or three dimensions. The determinant as volume ratio. Operations on determinants and solution of linear algebraic systems. Inverse matrices. Rotation matrices in two dimensions.
• Eigenvectors and eigenvalues of 2x2 and 3x3 matrices. Matrix diagonalization. Invariance of the trace and determinant.
• Vector spaces as an algebraic structure. Linear independence. Basis. Dimension. Subspaces.
• Metric spaces. Vector orthogonalization.