B.Tech DEGREE PROGRAMME IN
ELECTRONICS AND COMMUNICATION
(Applicable from 2010 Admission onwards)
DEPARTMENT OF ELECTRONICS AND
NATIONAL INSTITUTE OF TECHNOLOGY CALICUT
MA 1001: MATHEMATICS I
Module 1 (12 hours)
Preliminary Calculus : Partial differentiation, Total differential and total derivative, Exact differentials, Chain rule, Change of variables, Minima and Maxima of functions of two or more variables. Infinite Series : Notion of convergence and divergence of infinite series, Ratio test, Comparison test, Raabe’s test, Root test, Series of positive and negative terms, Idea of absolute convergence, Taylor’s and Maclaurin’s series.
Module 2 (17 hours)
First order ordinary differential equations: Methods of solution, Existence and uniqueness of solution, Orthogonal Trajectories, Applications of first order differential equations. Linear second order equations: Homogeneous linear equations with constant coefficients, fundamental system of solutions, Existence and uniqueness conditions, Wronskian, Non homogeneous equations, Methods of Solutions, Applications.
Module 3 (13 hours)
Fourier Analysis : Periodic functions - Fourier series, Functions of arbitrary period, Even and odd functions, Half Range Expansions, Harmonic analysis, Complex Fourier Series, Fourier Integrals, Fourier Cosine and Sine Transforms, Fourier Transforms.
Module 4 (14 hours)
Gamma functions and Beta functions, Definition and Properties. Laplace Transforms, Inverse Laplace Transforms, shifting Theorem, Transforms of derivatives and integrals, Solution of differential Equations, Differentiation and Integration of Transforms, Convolution, Unit step function, Second shifting Theorem, Laplace Transform of Periodic functions.
Kreyszig E, ‘Advanced Engineering Mathematics’ 8th Edition, John Wiley & Sons New York, (1999) Piskunov, ‘Differential...