MTL101: Linear Algebra & Differential Equations (4 Credits)
Vector spaces over Q, R and C, subspaces, linear independence, linear span of a set of vectors, basis and dimension of a vector space, sum and direct sum. Systems of linear (homogeneous and non-homogeneous) equations, matrices and Gauss elimination, elementary row operations, row space, column space, null space and rank of a matrix. Linear transformation, rank-nullity theorem and its applications, matrix representation of a linear transformation, change of basis and similarity. Eigenvalues and eigenvectors, characteristic and minimal polynomials, Cayley-Hamilton theorem (without proof) and applications. Review of first order differential equations, Picard’s theorem, linear dependence and Wronskian. Dimensionality of space of solutions, linear ODE with constant coefficients of second and higher order, Cauchy-Euler equations, Method of undetermined coefficients and method of variation of parameters. Boundary Value Problems: Sturm-Liouville eigenvalue problems. System of linear differential equations with constant coefficients, fundamental matrix, matrix methods. Power Series and its convergence, power series method, Fourier series, Laplace Transform Method.
Grading is usually absolute, however in our sem, the average was very low and cutoffs were lowered (cutoff for 10 was in low 70s) .
Easier course than MTL100, only thing required is consistency. Don't take it lightly though.
Very similar to the MTH102 course in IITK, you can find extra resources here if you wish.
3b1b's Essence of Linear Algebra playlist might be useful for being able to visualize the various concepts from the LA portion.