# CA2019_Lecture_01_02.pdf - Topic 01 Complex Numbers and its...

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Topic 01 Complex Numbers and its Algebra, Topology of Sets MA201 Mathematics III Instructors: MGPP, DCD, AC, ST IIT Guwahati Instructors: MGPP, DCD, AC, ST Topic 01 Complex Numbers and its Algebra, Topology of Sets 1 / 54
Attendance Policy Attendance in all lecture and tutorial classes is compulsory. Students, who do not meet 75% attendance requirement will not be allowed to write the end semester examination and will be awarded F grade. For attendance in the classes, biometric device or attendance sheets will be circulated. Each student is expected to sign against his/her name only in case of attendance sheets. In case, any student is found marking proxy for some other student, an appropriate disciplinary action will be taken on both students involved in the proxy matter. Random attendance will also be taken. Students must attend all tutorial classes. Roll call attendance will be taken in the tutorial classes. Instructors: MGPP, DCD, AC, ST Topic 01 Complex Numbers and its Algebra, Topology of Sets 2 / 54
Syllabus of Complex Analysis Complex Numbers: Complex numbers and elementary properties. Complex Functions: Limits, continuity and differentiation. Cauchy-Riemann equations. Analytic functions, Harmonic functions. Elementary Analytic functions. Complex Integration: Contour integrals, Anti-derivatives and path independent of contour integrals. Cauchy-Goursat Theorem. Cauchy’s integral formula, Morera’s Theorem. Liouville’s Theorem, Fundamental Theorem of Algebra, Maximum Modulus Principle and its consequences. Power Series: Taylor series, Laurent series. Zeros and Singularities: Zeros of Analytic Functions, Singularities, Argument Principle, Rouche’s Theorem. Residues and Applications: Cauchy’s Residue Theorem and applications. Conformal Mappings: Conformal Mappings, Mobius transformations. Instructors: MGPP, DCD, AC, ST Topic 01 Complex Numbers and its Algebra, Topology of Sets 3 / 54
Complex Analysis Books Text Book: J. W. Brown and R. V. Churchill , Complex Variables and Applications , 7th or 8th Edition, Mc-Graw Hill, 2004. Note: Any Edition is fine. Reference Book: J. H. Mathews and R. W. Howell , Complex Analysis for Mathematics and Engineering , 3rd Edition, Narosa, 1998. Note: Any Edition or Other Publisher is fine. Instructors: MGPP, DCD, AC, ST Topic 01 Complex Numbers and its Algebra, Topology of Sets 4 / 54
Course Website Log on to: with your email username and password. Click on: Mathematics . Click on: MA201 Mathematics-III (July-November 2019) Enrollment key: *** Emailed to the Students Every day log on to the course webpage in moodle to get updates and PPT slides of lectures. Note: Lecture plan along with text book references for complex analysis part is already uploaded. Instructors: MGPP, DCD, AC, ST Topic 01 Complex Numbers and its Algebra, Topology of Sets 5 / 54
Teaching Methodology Both PPT slides and Board will be used for teaching.