The book covers all the "must-know" topics required for university exams and competitive tests like the CSIR-NET or GATE. From the Cauchy-Riemann equations to the Residue Theorem and Conformal Mappings, it leaves no stone unturned. 3. Abundant Solved Examples
Week 1: Complex numbers, topology, holomorphic functions basics. Week 2: Power series, convergence, Taylor expansions. Week 3: Complex integration, Cauchy theorem/formula. Week 4: Morera’s theorem, uniform convergence, families of analytic functions. Week 5: Singularities, Laurent series, residue calculus applications. Week 6: Rouche’s theorem, argument principle, analytic continuation. Week 7: Conformal mapping fundamentals, Riemann mapping theorem overview. Week 8: Review, problem-solving, and selected advanced topics from the book. foundation of complex analysis by ponnusamy pdf top