'Complex Analysis and Numerical Methods' is a course offered in the fourth semester of B. Tech. in Civil Engineering program at School of Engineering, Amrita Vishwa Vidyapeetham.
Unit 1
Complex Numbers, Complex Plane, Polar Form of Complex Numbers. Powers and Roots, Derivative. Analytic Functions, Cauchy - Riemann Equations, Laplace Equation, Conformal mapping, Exponential Function, Trigonometric Functions, Hyperbolic Functions, Logarthims, General Power, Linear Fractional Transformation.
Unit 2
Complex Line Integral, Cauchy Integral Theorem, Cauchy Integral Formula, Derivatives of Analytic Functions. Power Series, Taylor Series and Maclaurin Series. Laurent Series, Zeros and Singularities, Residues, Cauchy Residue Theorem, Evaluation of Real Integrals using Residue Theorem.
Unit 3
Numerical Methods: Solution of Equations by iteration methods. Interpolations.
Numerical Integration and Differentiation. (Sections: 19.1-19.5)
TEXTBOOK
- Advanced Engineering Mathematics, E Kreyszig, John Wiley and Sons, Ninth Edition, 2012.
REFERENCE BOOK
- S. Ponnusamy, Foundations of Complex Analysis, 2nd Edition, Narosa Publishing House, 2005.
- R. Roopkumar, Complex Analysis, Pearson Education, 2014, Chennai.
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