|Unit – I||Matrices:|
Minors and Cofactors, Adjoint of a square matrix, Inverse of a matrix. Rank of a matrix, Solution of Homogeneous and non-homogeneous linear Equations using Matrix method.
|Unit- II||Eigen Values and Eigen Vectors:|
Vectors, linear combination of vectors, Inner Product of two vectors, characteristic equation, Eigen Vector, Cayley- Hamilton Theorem, Similarity of Matrices, Derogatory and Non-derogatory matrices, Complex Matrices: Hermitian, skew-Hermitian and Unitary matrices and their properties.
|Unit -III||Vector Calculus:|
Vector Differentiation: Vector Operator Del, Gradient, and Geometrical Meaning of gradient, Divergence and Curl.
|Unit – IV||Differential Equations:|
Differential Equations of 1st order and 1st degree and applications
|Unit – V||Linear Differential Equations:|
Linear Differential equations with constant coefficient, Differential equations of higher order and applications.
|Unit -VI||Successive differentiation, Mean Value theorems, Partial differentiation, Euler’s Theorem, Approximation and errors, Maxima and Minima|
|List of Problems|
i) Problem solving based on matrices ii) Problem solving based on Eigen Values and Eigen Vectors iii) Problem solving based on Vector Analysis iv) Problem solving based on Differential Equations
v) Problem solving based on Linear Differential Equations
vi) Problem solving based on Successive Differentiation vii) Problem solving based on Mean Value theorems viii) Problem solving based on Partial differentiation ix) Problem solving based on Euler’s Theorem
x) Problem solving based on Approximation and errors xi)Problem solving based on Maxima and Minima
Engineering Mathematics A tutorial approach by R. R. Singh and Mukul Bhatt, TMH 2010
Text Book of Applied Mathematics Vol I and Vol II. P.N. Wartikar & J.N. Wartikar, Pune Vidyarthi Griha Prakashan
Higher Engineering Mathematics by B. V. Ramana, McGraw-Hill Differential Calculus by Shanti Narayan. S. Chand.
Higher Engineering Mathematics by B.S. Grewal, Khanna Publications
Vector Analysis by Murray Spiegel, McGraw-Hill
Matrices by Vashistha, S. Chand
Download ebook – Applied Mathematics -1