Week 6: Differentiable functions, the Cauchy-Riemann equations
Churchill, R.V., & Brown, J.W. (2013). Complex variables & applications (9th ed.). New York: McGraw-Hill.
Page # 45-56
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Course Material
- Week 1: Introduction: The algebra of complex numbers
- Week 2: Geometric representation of complex numbers
- Week 3: Polar form of complex numbers, Powers & roots of complex numbers
- Week 4: Functions of Complex Variables
- Week 5: Limit and continuity of complex functions
- Week 6: Differentiable functions, the Cauchy-Riemann equations
- Week 7: Analytic functions, entire functions, harmonic functions
- Week 8: Elementary functions: The exponential, Trigonometric functions, Hyperbolic, Logarithmic & Inverse elementary functions
- Week 9: Mid Term Exam
- Week 10: Complex Integrals: Contours & contour integrals, antiderivatives, independence of path
- Week 11: Cauchy-Goursat theorem, Cauchy integral formula, Lioville’s theorem, Morerea’s theorem
- Week 12: Maximum Modulus Principle, Series: Power series, Radius of convergence & analyticity
- Week 13: Taylor’s & Laurent’s series
- Week 14: Integration & differentiation of power series, isolated singular points
- Week 15: Cauchy’s residue theorem with applications
- Week 16: Types of singularities & calculus of residues, Zeros & Poles, Mobius transforms
- Week 17: Conformal mappings & transformations
- Week 18: Final Term Exam
- Chapters 18
- Department Mathematics
- Teacher
Dr. Javaria Farooq
