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Mathematics-4

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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
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




Books

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

Sem20102011201220132014
4Dec - 2010
27-11-2010


Jun - 2010
15-06-2010


Nov - 2011
21-11-2011


Jun - 2011
02-06-2011


Dec - 2012
30-12-2012


May - 2012
18-05-2012


Dec - 2013
17-12-2013


May - 2013
05-06-2013


Jun - 2014
12-06-2014


Jun - 2014
12-06-2014



GTU Result

ExamTotalPassPass %FailFail %AA
16,35112,68977.603,66222.40123
30,86525,35082.135,51517.87454
39,49820,73852.5018,76047.5060
43,65834,61179.289,04720.721,255


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