MA-111 Applied Mathematics-I
Teaching Scheme			Credit	Marks Distribution			Duration of End Semester Examination
L	T	P		Internal Assessment	End Semester Examination	Total
3	1	0	4	Maximum Marks: 40	Maximum Marks: 60	100	3 Hours
				Minimum Marks: 16	Minimum Marks: 24	40

Unit - I

Linear Algebra: Review of matrices , Row reduced echelon form , Inverse using Gauss Jordan method and rank of a matrix , Solution of linear system of equations; Gaussian elimination, LU decomposition method. Vector space, subspaces, basis and dimension , Linear dependence & Independence of vectors , rank-nullity theorem , Eigen values, Eigen vectors , diagonalization. Cayley Hamilton Theorem (without proof), quadratic & canonical forms.

Unit - II

Calculus: Rolle’s theorem , Lagrange’s mean value theorem (without proof) , improper integrals , beta and gamma functions. Functions of several variables , Limits and continuity , partial derivatives , total derivative , Euler ‘s theorem , Jacobian , maxima and minima , Lagrange ‘s method of multipliers , Taylor ‘s & Maclaurin‘s Theorem.

Unit - III

Multiple Integrals and applications: Double integral , change of order of integration , Polar coordinates , graphing of polar curves , Change of variables , Applications of double integrals to areas and volumes , evaluation of triple integral .

Unit - IV

Functions of Complex variables: Introduction to elementary complex functions (exponential , trigonometric & hyperbolic , inverse trigonometric & hyperbolic , logarithmic) , Analytic functions , Cauchy-Riemann equations.

Complex integration: Cauchy’s theorem , Cauchy’s integral formula , Taylor’s & Laurent’s series , zeros & singularities , Cauchy’s residue theorem.