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Code : 140001 Common Name : M-IV Year : 2 Sem : 4
Theory Hours : 3 Practical Hours : 0 Tutorial Hours : 2 Credits : 5
Exam Marks : 70 Midsem Marks : 30 Practical Marks : 50 Total : 150

Syllabus Topics

Complex numbers and functions
Limits of Functions, Continuity, Differentiability, Analytic functions, Cauchy-Riemann Equations, Necessary and Sufficient condition for analyticity, Properties of Analytic Functions, Laplace Equation, Harmonic Functions, Finding Harmonic Conjugate functions Exponential, Trigonometric, Hyperbolic functions and its properties. Multiple valued function and its branches: Logarithmic function and Complex Exponent function

Complex Integration
Curves, Line Integrals (contour integral) and its properties. Line integrals of single valued functions, Line integrals of multiple valued functions (by choosing suitable branches). Cauchy-Goursat Theorem, Cauchy Integral Formula, Liouville Theorem, Fundamental Theorem of Algebra, Maximum Modulus Theorems

Power Series
Convergence (Ordinary, Uniform, Absolute) of power series, Taylor and Laurent Theorems, Laurent series expansions. Zeros of analytic functions. Singularities of analytic functions and their classification Residues: Residue Theorem, Rouche’s Theorem, Argument Principle

Applications of Contour Integration
Evaluating various type of definite real integrals using contour integration method

Conformal Mapping and its applications
Mappings by elementary functions, Mobius transformations, Schwarz- Christoffel transformation

Interpolation by polynomials, divided differences, error of the interpolating polynomial

Numerical integration
Composite rules, error formulae, Gaussian integration

Linear algebraic equation
Solution of a system of linear equations: implementation of Gaussian elimination and Gauss-Seidel methods, partial pivoting

Roots of equation
Solution of a nonlinear equation: Bisection and Secant methods, Newton’s method, rate of convergence, Power method for computation of Eigen values

Ordinary differential equations
Numerical solution of ordinary differential equations, Euler and Runge- Kutta methods


Complex variables and applicati (7th Edition)

R. V. Churchill and J. W. Brown - McGraw-Hill (2003)

Complex analysis

J. M. Howie - Springer-Verlag (2004).

Complex Variables- Introduction and Applications

M. J. Ablowitz and A. S. Fokas - Cambridge University Press, 1998 (Indian Edition)

Advanced engineering mathematics (8th Edition)

E. Kreyszig - John Wiley (1999).

Elementary Numerical Analysis- An Algorithmic Approach (3rd Edition)

S. D. Conte and Carl de Boor - McGraw-Hill, 1980.

Introduction to Numerical Analysis (2nd Edition)

C. E. Froberg - Addison-Wesley, 1981

Exam Papers

4Dec - 2010

Jun - 2010

Nov - 2011

Jun - 2011

Dec - 2012

May - 2012

Dec - 2013

May - 2013

Jun - 2014

GTU Result

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