Syllabus Mathematics - 2 - (BE02000011) Total Credits L + T + (PR / 2) Assessment Pattern and Marks Total Marks C Theory Tutorial / Practical ESE (E) PA / CA (M) PA / CA (I) ESE (V) 4 70 30 0 0 100 Unit 1 Module 1 : Matrices : Linear Independence; Row Echelon form (REF)and Reduced Row, Echelon form(RREF) of a Matrix, Rank of a Matrix using REF/RREF; Inverse of a matrix using Gauss-Jordan method; Solution of System of linear equations by elementary row operations; Symmetric, skew symmetric and orthogonal matrices; Eigenvalues and eigenvectors; Diagonalization of matrices; Inverse of a Matrix by Cayley-Hamilton Theorem. (Chapter - 1) Unit 2 Module 2 : First order ordinary differential equations : Exact differential equations, Integrating factors for non-Exact differential equations, linear and Bernoulli’s equations. Equations not of first degree : equations solvable for p, equations solvable for y, equations solvable for x and Clairaut’s type. (Chapter - 2) Unit 3 Module 3 : Ordinary differential equations of higher orders : Higher order linear differential equations with constant and variable coefficients, Euler-Cauchy equations, solution by variation of parameters, method of undetermined coefficients; Classification of Ordinary and Singular points, Power series solutions for ordinary points. (Chapters - 3,4) Unit 4 Module 4 : Complex Variables (Differentiation) : Differentiation, Cauchy-Riemann equations, analytic functions, harmonic functions, finding harmonic conjugate; analyticity of elementary functions (exponential, trigonometric, logarithm) and their properties; (Chapters - 5) Unit 5 Module 5 : Complex Variables (Integration) : Contour integrals, Cauchy-Goursat theorem (without proof), Cauchy Integral formula (without proof); Taylor’s series, zeros of analytic functions, singularities, Laurent’s series; Residues, Cauchy residue theorem (without proof), Rouche’s theorem. (Chapter - 6)
