Complex Variables and Numerical Methods
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Complex Variables and Numerical Methods Syllabus — Unit-wise Content
The official GTU curriculum for Complex Variables and Numerical Methods (subject code 2141905) as prescribed for Auto · Semester 4 divides the course into 4 units, covering 24 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 (2141905)Unit 1 Complex Numbers and Functions
- De Moivre’s Theorem
- Roots of a complex number
- Hyperbolic functions and their properties
- Multi-valued function and its branches: Logarithmic function and Complex Exponent function Limit
- Continuity and Differentiability of complex function
- Analytic functions
- Cauchy-Riemann Equations
- Necessary and Sufficient condition for analyticity
- Properties of Analytic functions
- Laplace Equation
- Harmonic Functions
- Harmonic Conjugate functions and their Engineering Applications
Unit 2 Complex Integration
- Line Integral(contour integral) and its properties
- Cauchy- Goursat Theorem
- Cauchy Integral Formula
- Liouville Theorem (without proof)
- Maximum Modulus Theorems(without proof)
Unit 3 Power Series
- Absolute) of power series
- Taylor and Laurent Theorems (without proof)
- Laurent series expansions
- zeros of analytic functions
- Singularities of analytic functions and their classification Residues: Residue Theorem
- Rouche’s Theorem (without proof)
Unit 4 Applications of Contour Integration
- Evaluation of various types of definite real integrals using contour
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