Transform Calculus, Fourier Series and Numerical Techniques(18MAT31)-CBCS 2018 scheme

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*SYLLABUS*MODULE-1

1.

**Definition and Laplace transforms of elementary functions (statements only).***Laplace Transform:*Laplace transforms of Periodic functions (statement only) and unit-step function – problems Discussion restricted to the problems as suggested in Article No.21.1 to 21.5, 21.7,21.9, 21.10 & 21.17 of Text Book 2. 3L

2.

**Definition & problems, Convolution theorem to find the inverse Laplace Transforms(without Proof) and Problems Discussion restricted to problems as suggested in Article No.21.12 & 21.14 of Text Book 2. 3L***Inverse Laplace Transform:* 3.

**. Application of Laplace transforms to solve ODE’s restricted to Article No. 21.15 of Text Book 2***Solution of linear differential equations using Laplace Transforms*MODULE-2

1.

**: Periodic functions, Dirichlet’s condition. Fourier series of periodic functions period and arbitrary period.***Fourier Series*2.

*Half range Fourier series.*3.

*Practical harmonic analysis*MODULE-3

**: Infinite Fourier transforms, Fourier sine and cosine transforms. Inverse Fourier transforms. Problems.**

*1.Fourier Transforms*2.

**: Difference equations, basic definition, ztransform-definition, standard z-transforms, damping and shifting rules, initial value and final value theorems (without proof) and problems.***Difference equations and Z-transforms*3.

**( RBT Levels: L1 & L2)***Inverse z-transform-problems and applications to solve difference equations.*MODULE-4

1.

**Numerical solution of ODE’s of first order and first degree- Taylor’s series method***Numerical Solutions of Ordinary Differential Equations (ODE’s):*2.

*Modified Euler’s method & Runge – Kutta method of fourth order.*3.

**(No derivations of formulae)-Problems***Milne’s and Adam-Bashforth predictor and corrector method*MODULE-5

1.

**Runge-Kutta method of order IV and Milne’s predictor and corrector method.(No derivations of formulae). Discussion and problems as suggested in Article No.32.12 of Text Book 2. 3L***Numerical Solution of second order ODE’s:-*2.

**Variation of function and functional, variational problems, Euler’s equation.***Calculus of Variations:*3.

**Geodesics,**hanging chain, problems

*Text books:* 1. E. Kreyszig: Advanced Engineering Mathematics, John Wiley & Sons, 10th Ed.(Reprint), 2017.

2. B.S. Grewal: Higher Engineering Mathematics, Khanna Publishers, 44th Ed., 2017.

3. Srimanta Pal & Subobh C Bhunia: “Engineering Mathematics”, Oxford University Press, 3rd Reprint, 2016.

__Reference Books:__1. C.Ray Wylie, Louis C.Barrett : “Advanced Engineering Mathematics”, 6th Edition, 2. McGrawHill Book Co., New York, 1995.

2. S.S.Sastry: “Introductory Methods of Numerical Analysis”, 11th Edition, Tata McGraw-Hill, 2010

3. B.V.Ramana: “Higher Engineering Mathematics” 11th Edition, Tata McGraw-Hill, 2010.

4. N.P.Bali and Manish Goyal, “A Text Book of Engineering Mathematics”, Laxmi Publications. Latest edition, 2014.

5. Chandrika Prasad and Reena Garg “Advanced Engineering Mathematics”, Latest edition, Khanna Publishing, 2018.