# Fourier Series and Prentice Hall

**Topics:**Fourier series, Fourier transform, Partial differential equation

**Pages:**143 (23670 words)

**Published:**January 2, 2013

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, ‘Differential and Integral Calculus, MIR Publishers, Moscow (1974). Wylie C. R. & Barret L. C ‘Advanced Engineering Mathematics’ 6th Edition, McGraw Hill, New York, (1995).

Thomas G. B. ‘Calculus and Analytic Geometry’ Addison Wesley, London (1998).

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MA 1002: MATHEMATICS II

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Module 1 (14 hours)

Linear Algebra I: Systems of Linear Equations, Gauss’ elimination, Rank of a matrix, Linear independence, Solutions of linear systems: existence, uniqueness, general form. Vector spaces, Subspaces, Basis and Dimension, Inner product spaces, Gram-Schmidt orthogonalization, Linear Transformations.

Module 2 (14 hours)

Linear Algebra II: Eigen values and Eigen vectors of a matrix, Some applications of Eigen value problems, Cayley-Hamilton Theorem, Quadratic forms, Complex matrices, Similarity of matrices, Basis of Eigen vectors – Diagonalization.

Module 3 (13 hours)

Vector Calculus I: Vector and Scalar functions and fields, Derivatives, Curves, Tangents, Arc length, Curvature, Gradient of a Scalar Field, Directional derivative, Divergence of a vector field, Curl of a Vector field.

Module 4(15 hours)

Vector Calculus II: Line Integrals, Line Integrals independent of path, Double integrals, Surface integrals, Triple Integrals, Verification and simple applications of Green’s Theorem, Gauss’ Divergence Theorem and Stoke’s Theorem.

Reference:

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Kreyzig E, Advanced Engineering Mathematics, 8th Edn, John Wiley & Sons, New York (1999). Wylie C. R & Barrret L. C, Advanced Engineering Mathematics, 6th Edn, Mc Graw Hill, New York (1995). Hoffman K & Kunze R, Linear Algebra, Prentice Hall of India, New Delhi (1971).

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PH 1001: PHYSICS

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Module 1 (6 hours)

Theory of Relativity: Frames of reference, Galilean Relativity, Michelson-Morley experiment, postulates of Special Theory of Relativity, Lorentz transformations, simultaneity, length contraction, time dilation, velocity addition, Doppler effect for light,...

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