Week 10: Introduction to Complex Integrals: Contours and Contour Integrals, Upper Bounds for the Moduli of Contour Integrals
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Complex Variables and Applications, Brown and Churchill, 9th edition pgs 115 - 130, 132 - 139 |
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Course Material
- Week1: Introduction to Complex Numbers, Basic Algebraic Properties
- Week 2: Geometric representation of complex numbers, Modulus and Complex Conjugates, Exponential Form of Complex Number
- Week 3: Arguments of Products and Quotients, Powers and roots of Complex Numbers, Regions in Complex Plane
- Week 4: Introduction to Functions of Complex Variables: Definition, limit and continuity
- Week 5: Derivatives of a Complex valued Function, Rules for Differentiation, Cauchy Riemann Equations in Rectangular Coordinates
- Week 6: Cauchy Riemann Equations in Polar Coordinates, Analytic Function, Harmonic Function
- Week 7: Introduction to Elementary functions: The Exponential and the Logarithmic Function, Branches of Logarithmic function
- Week 8: Introduction to Trigonometric, Hyperbolic and Inverse Trigonometric and Hyperbolic functions
- Week 9: Mid Term
- Week 10: Introduction to Complex Integrals: Contours and Contour Integrals, Upper Bounds for the Moduli of Contour Integrals
- Week 11: Introduction to Cauchy - Goursat theorem, Simply Connected Domains, Multiply Connected Domains
- Week 12: Cauchy Integral Formula, Morera's Theorem, Liouville’s Theorem, . Maximum Modulus Theorem.
- Week 13: Convergence of Sequence and Series, Introduction to Taylor and Maclaurin Series
- Week 14: Laurent Series
- Week 15: Integration and Differentiation of Power Series, Multiplication and division of power series
- Week 16: Isolated Singular Point, Introduction to Residues, Introduction to Cauchy’s residue theorem with applications, Residue at Infinity
- Week 17: The Three Types of Isolated Singular Points, Residue at Poles, Zero of Analytic Function,
- Week 18: Final Term
- Chapters 18
- Department Mathematics
- Teacher
Uzma Ahmad
