## GTU NSM Study Material (2140001) | Maths-IV

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#### Chapter 1 : Complex Numbers and Functions

- Limits of Functions, Continuity, Differentiability, Analytic functions Cauchy-Riemann Equations
- Necessary and Sufficient condition for analyticity
- Properties of Analytic Functions, Laplace Equation, Harmonic Functions
- Finding Harmonic Conjugate functions Exponential, Trigonometric, Hyperbolic functions and its properties
- Multiple valued function and its branches: Logarithmic function and Complex Exponent function

#### Chapter 2 : Complex Integration

- Curves, 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

#### Chapter 3 : Power Series

- Convergence (Ordinary, Uniform, 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

#### Chapter 4 : Applications of Contour Integration

#### Chapter 5 : Conformal Mapping and its applications

#### Chapter 6 : Interpolation

#### Chapter 7 : Numerical integration

#### Chapter 8 : Linear algebraic equation

- Solution of a system of linear equations: implementation of Gaussian elimination and Gauss-Seidel methods
- partial pivoting

#### Chapter 9 : Roots of equation

- Solution of a nonlinear equation: Bisection and Secant methods
- Newton’s method
- rate of convergence
- Power method for computation of Eigen values

#### Chapter 10 : Ordinary differential equations

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#### AS PER OLD SYLLABUS :

(2110014) MATHS – 1 / VCLA

(2110015) MATHS – 2 / VCLA

(2130002) MATHS – 3 / AEM

(2140001) MATHS – 4 / NSM

#### AS PER NEW SYLLABUS :

(3110014) MATHEMATICS – 1

(3110015) MATHEMATICS – 2

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#### For Get Other Mathematics Study Material You Can Go With :

- Calculus / Mathematics – 1 (2110014)
- VCLA / Mathematics – 2 (2110015)
- AEM / Mathematics – 3 (2130002)
- NSM / Mathematics – 4 (2140001)
- New mathematics -2 (3110015)
- New mathematics -1 (3110014)

#### You Can Also Search for Question papers Of All Mathematics.

- New mathematics -2 (3110015)
- Calculus / Mathematics – 1 (2110014)
- VCLA / Mathematics – 2 (2110015)
- AEM / Mathematics – 3 (2130002)
- NSM / Mathematics – 4 (2140001)

#### If You Want To More Then You Can Also Search for Other Engineering Maths Like

**AS PER OLD SYLLABUS :**

- (2110014) MATHS – 1 / VCLA
- (2110015) MATHS – 2 / VCLA
- (2130002) MATHS – 3 / AEM
- (2140001) MATHS – 4 / NSM

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