PHYS 301

 
Polar Form of Complex Numbers, Triangle Inequality. Curves and Regions in complex Plane. Roots. Euler Formulae, Demoivre’s Theorem.  Limits. Derivatives. Analytic Functions. Cauchy-Riemann Equations. Laplace’s Equation. Rational Functions. Exponential Functions. Trigonometric and Hyperbolic Functions. Logarithmic Function and General Power Line Integral in the Complex Plane. Basic Properties of the Complex Line Integral. Cauchy’s Integral Theorem. Evaluation of Line Integrals by Indefinite Integration. Cauchy’s Integral Formula. The Derivatives of an Analytic Function. Function Represented by Power Series. Taylor Series and Taylor Series of Elementary Functions. Practical Methods for Obtaining Power Series. Uniform Convergence. Laurent Series. Analyticity at Infinity. Zeros and Singularities. The Residue Theorem. Evaluation of Real Integrals