Week 1:Linear Algebra 1 : vectors, linear vector spaces, inner product, C-S inequality, linear independence, row-reduction
Week 2:Linear Algebra 2 : Matrices, determinants, span, basis, orthonormal basis, subspaces, linear operators.
Week 3: Linear Algebra 3: Direct sum, eigenvalues and eigenvectors, unitary, Hermitian, normal operators, transformations, defective matrices, diagonalization.
Week 4: Fourier Series and Transforms: periodic functions, series expansion, Fourier coefficients, Completeness relation, Fourier transforms.
Week 5: Ordinary Differential Equations 1: Introduction, Separable variables, orthogonal trajectories, linear first-order ODEs, Wronksian, exact ODEs, auxiliary equation.
Week 6: Ordinary Differential Equations 2: Inhomogeneous second order ODEs, method of undetermined coefficients, vibrations in mechanical systems, forced vibrations, resonance, linear superposition.
Week 7: Ordinary Differential Equations 3: Laplace transforms, Solving ODEs using Laplace transforms, Dirac Delta function.
Week 8: Ordinary Differential Equations 4: Green's function method, power series method, Frobenius method.
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