MATHEMATICAL METHODS Ebook, presentation and lecture notes covering full semester syllabus
The topics covered in the attached e-books are:
UNIT I - Matrices and Linear systems of equations: Elementary row transformations-Rank-Echelon form, Normal form Solution of Linear Systems Direct Methods- LU Decomposition- LU Decomposition from Gauss Elimination Solution of Tridiagonal Systems-Solution of Linear Systems
UNIT II - Eigen values, eigen vectors properties Cayley-Hamilton Theorem - Inverse and powers of a matrix by Cayley-Hamilton theorem Diagonolization of matrix. Calculation of powers of matrix Modal and spectral matrices.
UNIT III - Real matrices Symmetric, skew - symmetric, orthogonal, Linear Transformation Orthogonal Transformation. Complex matrices: Hermitian, Skew-Hermitian and Unitary forms- Reduction of quadratic form to canonical form.
UNIT IV - Solution of Algebraic and Transcendental Equations: Introduction The Bisection Method The Method of False Position The Iteration Method Newton-Raphson Method.
UNIT V - Curve fitting
UNIT VI - Numerical solution of Ordinary Differential equations
UNIT VII - Fourier Series
UNIT VIII - Formation of partial differential equations by elimination of arbitrary constants and arbitrary functions