Code

:

140001


Common Name

:

MIV


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, CauchyRiemann 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). CauchyGoursat 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 GaussSeidel 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  McGrawHill (2003)



Complex analysis
J. M. Howie  SpringerVerlag (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  McGrawHill, 1980.



Introduction to Numerical Analysis (2nd Edition)
C. E. Froberg  AddisonWesley, 1981



Exam Papers
GTU Result
 16,351  12,689  77.60  3,662  22.40  123 
 30,865  25,350  82.13  5,515  17.87  454 
 39,498  20,738  52.50  18,760  47.50  60 
 43,658  34,611  79.28  9,047  20.72  1,255 