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AU Mathematics II Sem II
No Units Titles Sub Titles Chapters
1 Unit 1 Linear Algebra Rank of a matrix, Eigen values, Eigen vectors of a Matrix, Cayley Hamilton theorem, Consistency of equations, Matrix invertion, Gaussian elimination scheme, Cholesky factorization, Jacobi and Gauss-Seidal iterative methods for solving simultaneous equations, Eigen value solution using forward iteration, Inverse itrration, Hermitian and skew Hermitian forms, Unitary Matrix, Functions of a Matrix, Quadratic forms and conical forms VIEW CHAPTERS
2 Unit 2 Differential Equations of First Order and its Applications Formation of differential equation, Solution of a differential equation, Geometrical meaning, Equations of the first order and first degree, Variables separable, Homogeneous equations, Linear equations, Bernoulli s equation, Exact equations, Equation reducible to exact equations, Equations of the first order and higher degree, Calirut s equation, Geometric applications, Orthogonal trajectories, Physical applications, Simple electric circuits, Heat flow, Chemical applications, Newton s law of cooling VIEW CHAPTERS
3 Unit 3 Linear Differential Equations Higher order linear differential equations with constant coefficients, Deflection of beams, Simple harmonic motion, Oscillatory electric circuits VIEW CHAPTERS
4 Unit 4 Series Solution of Differential Equations Frobenis method, Special function as solution from series, Bessel equation, Bessel functions of first and second kind, Equation reducible to Bessel s equations, Legender s equations, Legender polynomial, Rodrigues formula, Generating functions, Recurrence relation, Orthonogolity relation for Bessel functions and Legendre polynomial VIEW CHAPTERS
5 Unit 5 Laplace Transforms Transforms of elementary functions, Properties of Laplace transforms, Existence conditions, Inverse transforms, Transform of derivatives, Transform of Integrals, Multiplication s by  t  division by  t , Convolution theorem, Application to ordinary differential equations and simultaneous linear equations with constant coefficients, Unit step function, Impulse functions and periodic functions VIEW CHAPTERS
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