Linear Algebra Semester 3 Institute of Engineering and Technology, AU HOME Credit: 3-0-1-4 Class Contact Hours: Tuesday and Thursday 14.00 to 16.00. Instructor: Ratnik Gandhi Prerequisite: Discrete Mathematics Objective and Outcomes ·         Learn basic linear algebraic techniques and utilize them for modeling and solving engineering problems. Contents: 1          The geometry of linear equations      2          Elimination with matrices      3          Matrix operations and inverses          4          LU and LDU factorization        5          Transposes and permutations 6          Vector spaces and subspaces 7          The nullspace: Solving Ax = 0 8          Rectangular PA = LU and Ax = b 9          Row reduced echelon form    10        Basis and dimension   11        The four fundamental subspaces 12        Graphs and networks  13        Orthogonality 14        Projections and subspaces      15        Least squares approximations            16        Gram-Schmidt and A = QR 17        Properties of determinants    18        Formulas for determinants     19        Applications of determinants 20        Eigenvalues and eigenvectors            21        Diagonalization           22        Markov matrices        23        Differential equations 24        Symmetric matrices   25        Positive definite matrices       26        Matrices in engineering 27        Similar matrices         28        Singular value decomposition 29        Fourier series, FFT, complex matrices           30        Linear transformations           31        Choice of basis 32        Linear programming  33        Numerical linear algebra       34        Computational science             How? We shall devote 2 weeks (roughly 6 to 8 hours) for a chapter of Gilbert Strang book.   4 Sessions a week: -          2 hours of problem solving with the facilitator -          1 hour of instructions -          1 hour of problem solving/ working on projects(in team) Activities: -          Problem solving -          Team project (3 weeks + 7 weeks) -          Computer Programming -          Competition   Evaluation:                                                                                                   -          Exams-10% of questions will come from homework/tutorial assignment -          Projects   Primary references: 1.      Gilbert Strang (Chronology and content): Book and Video Lectures 2.      David C Lay (Applications and Problems)