Differentiable functions and Cauchy-Riemann Equations
Course Material
- Introduction: The algebra of complex numbers, Book
- Geometric representation of complex numbers
- Powers and roots of complex numbers
- Functions of Complex Variables, limit and continuity
- Differentiable functions and Cauchy-Riemann Equations
- Analytic functions, Entire functions, Harmonic functions
- Elementary functions: The exponential, Trigonometric functions, Hyperbolic
- Elementary functions: The exponential, Trigonometric functions, Hyperbolic, Logarithmic and Inverse elementary functions
- Mid Term Exam
- Open mapping theorem, Maximum modulus theorem
- Contours and contour integrals, Cauchy-Goursat theorem
- Cauchy integral formula, Lioville’s theorem, Morerea’s theorem
- Series: Power series, Radius of convergence and analyticity, Taylor’s series, Integration and differentiation of power series
- Laurent’s series and residues
- Poles and residues: Zero, singularities, Poles and Residues, Types of singular points, Calculus of residues
- Poles and residues: Zero, singularities, Poles and Residues, Types of singular points, Calculus of residues
- Contour integration, Cauchy’s residue theorem with applications, Mobius transforms, Conformal mappings
- Final Term Exams
- Chapters 18
- Department Mathematics(SCB)
- Teacher
Ms. Ammara Nazar
