Mathematics-4
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Mathematics-4 Syllabus — Unit-wise Content
The official GTU curriculum for Mathematics-4 (subject code 2140001) as prescribed for Nano · Semester 4 divides the course into 5 units, covering 29 listed topics. The unit-wise breakdown below is read from the GTU syllabus document for this subject code, so you can check what the course actually covers before deciding which papers to attempt.
Download the official syllabus PDF (2140001)Unit 1 Complex Numbers and Functions
- Limits of Functions
- Analytic functions Cauchy-Riemann Equations
- Necessary and Sufficient condition for analyticity
- Properties of Analytic Functions
- Laplace Equation
- Harmonic Functions
- Finding Harmonic Conjugate functions Exponential
- Hyperbolic functions and its properties
- Multiple valued function and its branches: Logarithmic function and Complex Exponent function
Unit 2 Complex Integration
- Line Integrals (contour integral) and its properties
- Line integrals of single valued functions
- Line integrals of multiple valued functions (by choosing suitable branches)
- Cauchy- Goursat Theorem
- Cauchy Integral Formula
- Liouville Theorem
- Fundamental Theorem of Algebra
- Maximum Modulus Theorems
Unit 3 Power Series
- Convergence (Ordinary
- Absolute) of power series
- Taylor and Laurent Theorems
- Laurent series expansions
- Zeros of analytic functions
- Singularities of analytic functions and their classification Residues: Residue Theorem
- Rouche’s Theorem
- Argument Principle
Unit 4 Applications of Contour Integration
- Evaluation of various types of definite real integrals using contour integration method
Unit 5 Conformal Mapping and its applications
- Mappings by elementary functions
- Mobius transformations
- Schwarz- Christoffel transformation
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