Applied Mathematics E book-Notes-Tutorial
Here is the full syllabus covered in the attached ebooks.
Elementary differentiation -Definition, limit and continuity, elementary differentiation, standard forms, methods of differentiation. Elementary integration- standard forms, integration by substitution, integration by parts, integration by partial fraction.
Taylorís and Maclaurinís expansions; indeterminate form; curvature ,asymptotes, function of two or more independent variables, partial differentiation, homogeneous functions and Eulerís theorem, total derivatives, derivative of an implicit function, change of variables, Jacobians, maxima and minima.
Rectification of standard curves, double and triple integrals, change of order of integration, Gamma and Beta functions, application of double and triple integrals to find area and volume.
Ordinary differential equations: Exact and Bernoulliís differential equations, equations reducible to exact form by integrating factors, equations of first order and higher degree, Differential equations of higher orders, methods of finding complementary functions and particular integrals, method of variation of parameters, simultaneous linear differential equations with constant coefficients.
Matrices: Elementary transformations, rank of a matrix, reduction to normal form, inverse of a matrix, consistency and solution of linear equations, Eigen values and Eigen vectors, Cayley-Hamilton theorem, diagonalisation of matrices.
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