{Mod1-mod5 ALL IN ONE notes}MATHS-M3(18MAT31)-Transform Calculus, Fourier Series and Numerical Techniques(18MAT31)

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

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SYLLABUS

MODULE-1

1. Laplace Transform: Definition and Laplace transforms of elementary functions (statements only). 

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. Inverse Laplace Transform: 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

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

MODULE-2

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

2. Half range Fourier series.

3. Practical harmonic analysis

MODULE-3

1.Fourier Transforms: Infinite Fourier transforms, Fourier sine and cosine transforms. Inverse Fourier transforms. Problems. 

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

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

MODULE-4

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

2. Modified Euler’s method & Runge - Kutta method of fourth order. 

3.Milne’s and Adam-Bashforth predictor and corrector method (No derivations of formulae)-Problems

MODULE-5

1. Numerical Solution of second order ODE’s:- 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 

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

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.