MA 2403: MATHEMATICS - III

MA 2403: MATHEMATICS - III

1.      Advance Calculus: Jacobians, Taylor’s and Maclaurin’s series of two variables, Maxima and Minima of functions of two variables, Lagrange’s method of undetermined multipliers and their applications, Elementary ideas of multiple integrals, Change of order of integration, and change of variables in double integral using Jacobians, beta and gamma functions.

2.      Fourier Series and Partial Differential Equations: Expansion of functions in a Fourier series, Half range series Sine and Cosine series and change of interval. Fourier Integral. Formation of partial differential equations, partial differential equations of first order and first degree i.e., Pq + Qq = R, Linear homogenous partial differential equation of nth order with constant coefficient, separation of variables. Application to simple problems of vibrations of string and beam and heat conduction equations.

3.      Laplace, Z and Fourier Transforms: Definition of LT, LT of elementary and periodic functions, properties of LT including LT of derivatives, Inverse Laplace Transform and its properties. Convolution Theorem. Application of LT to ordinary differential equations with constant and variable coefficients, Simultaneous differential equations. Z transforms and its simple properties. Fourier transform and its application to solution of linear PDE.

4.      Graph Theory and Combinational Optimization: Graphs – Definitions and basic properties – Isomorphism, Euler Circuits and Hamiltonian cycle. Digraphs, Trees – properties, spanning tree Kruskal and Prim algorithm. Flow augmented paths – Ford – Fulkerson algorithm, cut sets. Max. Flow min. cut Method theorem.

    

5.      Mathematical Programming Techniques: Simplex Method for Maximization and Minimization. Reyised Simplex Method and Duality Theorem. Non-linear Optimization. Khun-Tucker condition, Fibonacci Search. Quadratic interpolation and Combinational optimization.

Books and References Recommended

1.      Paria G, Ordinary Differential Equations with Laplace Transforms. Scholar’s Publications Indore.

2.      Paria G, Partial Differential Equations and Complex Variables, Scholars Publications Indore.

3.      Erwin. Kreyszig, Advanced Engineering Mathematics, 8^th edition, John Willy and sons Publications, 1999.

4.      Ramana B V, Higher Engineering Mathematics, Tata McGraw Hill Publishing Company Ltd New Delhi, 2006.

5.      B.G. Goodaire and Michael M. Permexter, Discrete Mathematics and Graph Theory.

6.      Ashok Ganguly et al., Engineering Mathematics Vol II, Ramprasad and Sons, Bhopal.

7.      Paria G, A Textbook of Vectors, Scholar’s Publications, Indore.

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