Unit – IMatrices:

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- IIEigen 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 -IIIVector Calculus:

Vector   Differentiation:   Vector   Operator   Del,   Gradient,   and Geometrical Meaning of gradient, Divergence and Curl.

Unit – IVDifferential Equations:

Differential Equations of 1st order and 1st degree and applications

Unit – VLinear Differential Equations:

Linear Differential equations with constant coefficient, Differential equations of higher order and applications.

Unit -VISuccessive differentiation, Mean Value theorems, Partial differentiation, Euler’s Theorem, Approximation and errors, Maxima and Minima
Problem Solving
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

Text Books:

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

 

References:

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