Fourier Series and Prentice Hall

DETAILED SYLLABI OF
B.Tech DEGREE PROGRAMME IN
ELECTRONICS AND COMMUNICATION
ENGINEERING
(Applicable from 2010 Admission onwards)

DEPARTMENT OF ELECTRONICS AND
COMMUNICATION ENGINEERING

NATIONAL INSTITUTE OF TECHNOLOGY CALICUT

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MA 1001: MATHEMATICS I
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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.

Reference:
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Kreyszig E, ‘Advanced Engineering Mathematics’ 8th Edition, John Wiley & Sons New York, (1999)
Piskunov,

References: Koontz, H., and Weihrich, H., Essentials of Management: An International Perspective, 8th ed., McGraw Hill, 2009. Hicks, Management: Concepts and Applications, Cengage Learning, 2007. Mahadevan, B., Operations Management, Theory and Practice, Pearson Education Asia, 2009. Kotler, P., Keller, K.L, Koshy, A., and Jha, M., Marketing Management, 13th ed., 2009. Khan, M.Y., and Jain, P.K., Financial Management, Tata-Mcgraw Hill, 2008. Patterson D.A. & Hennessy J.L., "Computer Organization and Design", Morgan Kaufmann Publishers, 2002 John.P.Hayes “Computer Architecture and Organization”, McGraw-Hill International Editions, Computer Science Series, 1998. Morris Mano “Computer System Architecture”, Prentice-Hall India, Eastern Economy Edition, 2009 Carl Hamacher, Zvonko Vranesic & Safwat Zaky, “Computer Organization”, Mc Graw Hill, 2001 Pal Choudhuri P., "Computer Organization and Design", Prentice-Hall India, 2nd Edition, 2003 William Stallings, "Computer Organization and Architecture", Pearson Education, 4th Edition, 2006