MA5151 Advanced Mathematical Methods Lecture Notes Syllabus Book Previous 2 13 15 Marks Anna University Important Question Bank With Answers Regulation 2017 Study Materials Pdf Ppt

MA5151 Advanced Mathematical Methods Lecture Notes Syllabus Book Previous  2 13 15 Marks  Anna University Important Question Bank With Answers Regulation 2017 Study Materials Pdf Ppt

MA5151 ADVANCED MATHEMATICAL METHODS

UNIT I LAPLACE TRANSFORM TECHNIQUES FOR PARTIAL DIFFERENTIAL EQUATIONS

Laplace transform : Definitions – Properties – Transform error function – Bessel’s function – Dirac delta function – Unit step functions – Convolution theorem – Inverse Laplace transform : Complex  inversion formula – Solutions to partial differential equations : Heat equation – Wave equation.

UNIT II FOURIER TRANSFORM TECHNIQUES FOR PARTIAL DIFFERENTIAL EQUATIONS

Fourier transform : Definitions – Properties – Transform of elementary functions – Dirac delta function – Convolution theorem – Parseval’s identity – Solutions to partial differential equations : Heat equation – Wave equation – Laplace and Poisson’s equations.

UNIT III CALCULUS OF VARIATIONS

Concept of variation and its properties – Euler’s equation – Functional dependant on first and higher order derivatives – Functionals dependant on functions of several independent variables – Variational problems with moving boundaries – Isoperimetric problems – Direct methods – Ritz and Kantorovich methods.

UNIT IV CONFORMAL MAPPING AND APPLICATIONS

Introduction to conformal mappings and bilinear transformations – Schwarz Christoffel  transformation – Transformation of boundaries in parametric form – Physical applications : Fluid flow and heat flow problems.

UNIT V TENSOR ANALYSIS

Summation convention – Contravariant and covariant vectors – Contraction of tensors – Inner product – Quotient law – Metric tensor – Christoffel symbols – Covariant differentiation – Gradient - Divergence and curl.

REFERENCES :

1. Andrews L.C. and Shivamoggi, B., "Integral Transforms for Engineers”, Prentice Hall ofIndia Pvt. Ltd., New Delhi, 2003.

2. Elsgolc, L.D., “Calculus of Variations", Dover Publications Inc., New York, 2007.

3. Kay, D. C., "Tensor Calculus”, Schaum's Outline Series, Tata McGraw Hill Edition, 2014.

4. Mathews, J. H., and Howell, R.W., “Complex Analysis for Mathematics and Engineering",5th Edition, Jones and Bartlett Publishers, 2006.

5. Naveen Kumar, “An Elementary Course on Variational Problems in Calculus ", Narosa Publishing House, 2005.

6. Ramaniah. G. “Tensor Analysis”, S. Viswanathan Pvt. Ltd., 1990.

7. Saff, E.B and Snider, A.D, “Fundamentals of Complex Analysis with Applications in Engineering, Science and Mathematics", 3rd Edition, Pearson Education, New Delhi, 2014.

8. Sankara Rao, K., “Introduction to Partial Differential Equations”, Prentice Hall of India Pvt. Ltd., New Delhi, 1997.

9. Spiegel, M.R., “Theory and Problems of Complex Variables and its Applications”, 

Schaum’s Outline Series, McGraw Hill Book Co., 1981.

MA5151 Advanced Mathematical Methods Lecture Notes Syllabus Book Previous  2 13 15 Marks  Anna University Important Question Bank With Answers Regulation 2017 Study Materials Pdf Ppt