Engineering Mathematics-II

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Subject syllabus

Exactly what you would be recording.

Unit I 
Linear Algebra I: Vector space, subspaces, linear dependence and independence of vectors, 
bases, and dimension, matrices, Rank and nullity of a matrix, rank -nullity theorem (without 
proof), Projection matrix, symmetric, skew-symmetric matrix, Orthogonal and unitary matrix, 
Idempotent matrix, Partition matrix [8] 
Unit II 
Linear Algebra II: Solution of systems of linear equations, Gaussian elimination, 
Eigenvalues and Eigenvectors with applications, Algebraic and geometric multiplicity, 
Determinant and its properties, Projections, LU decomposition, Singular value decomposition, 
Quadratic forms                           [8] 
Unit III 
Ordinary Differential Equations: First order linear and nonlinear differential equations: : 
Separable ODEs, exact ODEs and integrating factor, Bernoulli equations. Homogeneous linear 
ODEs of second (and higher) order with constant coefficients, Euler-Cauchy equations, Wronskian, Solution of non homogeneous linear ODEs: : method of undetermined coefficients, 
Method of variation of parameters  
Unit IV 
Partial Differential Equations: Basic concepts of PDEs, heat, wave, and Laplace equation 
and their solution by method of separating variables, D’Alembert’s solution of wave equation