Madhyanchal Professional University, MP, Information Technology Semester 2, Mathematics-2 Syllabus

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Unit - 1 Ordinary Differential Equations I

Module 1

Ordinary Differential Equations1

1.1 Differential equations of first order and first degree Leibnitz’s Bernoulli’s and exact

1.2. Differential equations of first order and higher degree

1.3. Higher order differential equations with constant coefficients

1.4. Homogeneous linear differential equations

1.5. Simultaneous differential equations

Unit - 2 Ordinary differential Equations II

Module 2

Ordinary Differential Equations2

2.1. Second order linear differential equations with variable coefficients

2.2. Method of variation of parameters

2.3. Power series solutions

2.4. Legendre polynomials

2.5. Bessel functions for the first kind and their properties

Unit - 3 Partial Differential Equations

Module 3

Partial differential equations

3.1. Formulation of partial differential equations

3.2. Linear and Nonlinear partial differential equations

3.3. Homogeneous linear partial differential equations with constant coefficients

Unit - 4 Functions of Complex Variable

Module 4

Functions of complex variable

4.1. Analytic function Harmonic conjugate

4.2. CauchyRiemann equations Without proof

4.3. Line integral

4.4. CauchyGoursat theorem without proof

4.5. Cauchy integral formula without proof

4.6. Singular points Poles residues Residue theorem

4.7. Application of residue theorem for evaluation of real integrals unit circle

Unit - 5 Vector Calculus

Module 5

Vector calculus

5.1. Differentiation of vectors

5.2. Scalar and vector point function

5.3. Gradient Geometric meaning of gradient

5.4. Directional derivative

5.5. Divergence and curl

5.6. Line integral

5.7. Surface integral and volume integral

5.8. Gauss divergence stokes and green theorems

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Other Subjects of Semester-2
Basic of mechanical engineering
Basic civil engineering & mechanics
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