## Mathematics-I

18HS0830

UNIT – I

Matrices: Inverse and rank of a matrix; System of linear equations; Symmetric,skew-symmetric and orthogonal matrices; Eigen values and eigen vectors; Diagonalization of matrices; Cayley-Hamilton Theorem, and Orthogonal transformation.

UNIT – II

Calculus: Evaluation of definite and improper integrals; Applications of definite integrals to evaluate surface areas and volumes of revolutions; Beta and Gamma functions and their properties. Rolle’sTheorem, Mean value theorems (without proof) Taylor’s and Maclaurin’s theorems.

UNIT – III
Multivariable Calculus : (Differentiation) Limit, continuity and partial derivatives, total derivative; Maxima, minima and saddle points; Method of Lagrange multipliers; Gradient,directional derivatives, curl and divergence.

UNIT – IV
Sequences and Series: Convergence of sequence and series, tests for convergence(Geometric test, P- test, limit comparison test, D’ Alember ratio test, Cauchy’ s nth root test); Power series, Taylor’s series, series for exponential, trigonometric and logarithm functions.

UNIT-V
Fourier series: Determination of Fourier coefficients- Fourier series- Even and functions, Fourier Series in an arbitrary interval, Periodic function, Half range sine and cosine series,