MMT-005 IGNOU Solved Assignment 2026-27

Course Scope & Syllabus Overview for MMT-005: Complex Analysis

MMT-005: Complex Analysis is a core course under the IGNOU CBCS curriculum for the M.Sc. (Mathematics with Applications in Computer Science) programme, designed to equip students with rigorous mathematical foundations in complex function theory. This course bridges real and complex analysis, emphasizing analytic functions, contour integration, and residue calculus—critical tools for advanced mathematical modelling in computer science and applied mathematics. The study material ensures alignment with IGNOU’s academic rigor, covering theoretical proofs, computational techniques, and problem-solving strategies that directly correlate with examination expectations.

Key Syllabus Units & Topics

• Block-1: Introduction to Analytic Functions: Covers fundamental concepts such as complex numbers, limits, continuity, and differentiability in the complex plane, including the Cauchy-Riemann equations and their geometric interpretation.
• Block-2: Applications of Analytic Functions: Explores contour integration, Cauchy’s integral theorem, and the residue theorem, with applications in evaluating real integrals and solving differential equations.
• Block-3: Power Series and Laurent Series: Delves into convergence of power series, Taylor and Laurent expansions, and their use in representing analytic functions and isolating singularities.
• Block-4: Conformal Mappings and Schwarz-Christoffel Transformations: Examines bijective analytic functions, Möbius transformations, and their role in solving boundary-value problems in engineering and physics.
• Block-5: Advanced Topics in Complex Analysis: Includes Riemann mapping theorem, Schwarz lemma, and applications to potential theory, providing a bridge to advanced mathematical research.

Frequently Asked Questions

Q: How are marks distributed in the TMA for MMT-005, and what is the minimum pass percentage?
A: The TMA carries 30% weightage in the final grade, with a pass mark of 40% required for each section. Each question is evaluated based on clarity, logical flow, and adherence to IGNOU’s prescribed word limits.

Q: Are there specific guidelines for referencing external sources in the TMA for MMT-005?
A: IGNOU strictly discourages direct copying; solutions must be original and derived from the course material. Citations are only required if referencing standard textbooks (e.g., Ahlfors or Churchill), but original reasoning must dominate the response.