Guru Gobind Singh Indraprastha University, Delhi, Computer Engineering Semester 2, Applied Mathematics-II Syllabus

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Unit - 1 Partial differentiation and its Applications

Unit1

Partial differentiation and its Applications

1.1. Partial differentiation and its Applications Partial derivatives of first and second order.

1.2. Euler‘s theorem for homogeneous functions

1.3. Derivatives of Implicit Functions

1.4. Total derivatives Change of variables.

1.5 Change of variable

1.6. Jacobian

1.7. Taylor‘s theorem for function of two variableswithout proof

1.8. Error and approximation

1.9. Extreme values of function of several variables maxima minima saddle points

1.10 Lagrange method of undetermined multipliers

1.11. Partial differential equations Formulation

1.12. Solution of first order equations Lagrange’s equations

1.13. Charpit‘s method.

Unit - 2 Laplace Transformation

Unit2

Laplace Transformation

2.1. Laplace Transformation Definition Laplace transformation of basic functions existence condition for Laplace transformation

2.2. Properties of Laplace transformation Linearity scaling and shifting

2.3. Unit step function Impulse Function Periodic Functions

2.4. Laplace transformation of derivatives Laplace transformation of integrals

2.5. Convolution theorem

2.6. Inverse Laplace transformation

2.7. Solution of ordinary Differential equations.

Unit - 3 Complex Function

Unit3

Complex Function

3.1. Complex functions Definition derivative

3.2. Analytic function

3.3. Cauchy Riemann equation without proof

3.4. Conformal and bilinear mapping

3.5. Complex integration complex line integration

3.6. Cauchy’s integral theorem and integral formula without proof

3.7. Zeroes and singularities Taylor’s and Laurent’s series

3.8. Residues Residue theorem

3.9 Evaluation of real and definite integrals Integration around the unit circle

3.10 Integration around a small semi circle and integration around rectangular contours.

Unit - 4 Multiple integrals

Unit4

Multiple integrals

4.1. Multiple integrals Double Integrals

4.2. Change of order of integration

4.3. Triple integrals

4.4. Vector calculus scalar and vector functions

4.5. Gradient divergence and curl

4.6. Directional derivative

4.7. Line integrals surface integrals volume integrals

4.8. Green’s theorem Stokes theorem and Gauss divergence theorem Without proof

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