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

# {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

best for quick reference and studying for exams

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 â€“ 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 ODEâ€™s restricted to Article No. 21.15 of Text Book 2

MODULE-2

1.Fourier Series: Periodic functions, Dirichletâ€™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 (ODEâ€™s): Numerical solution of ODEâ€™s of first order and first degree- Taylorâ€™s series method

2. Modified Eulerâ€™s method & Runge – Kutta method of fourth order.

3.Milneâ€™s and Adam-Bashforth predictor and corrector method (No derivations of formulae)-Problems

MODULE-5
1. Numerical Solution of second order ODEâ€™s:- Runge-Kutta method of order IV and Milneâ€™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, Eulerâ€™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: â€śEngineering Mathematicsâ€ť, Oxford University Press, 3rd Reprint, 2016.

Reference Books:

1. C.Ray Wylie, Louis C.Barrett : â€śAdvanced Engineering Mathematics”, 6th Edition, 2. McGrawHill Book Co., New York, 1995.
2. S.S.Sastry: â€śIntroductory Methods of Numerical Analysisâ€ť, 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, â€śA Text Book of Engineering Mathematicsâ€ť, Laxmi Publications. Latest edition, 2014.
5. Chandrika Prasad and Reena Garg â€śAdvanced Engineering Mathematicsâ€ť, Latest edition, Khanna Publishing, 2018.

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