Bihar Engineering University, Bihar, Civil Engineering Semester 2, Mathematics –II (Differential Equations) Syllabus

Unit - 1 First Order Ordinary differential Equations

Module 3

First order ordinary Differential Equation

3.1 Exact Differential Equation

3.2 Linear differential equation

3.3 Bernoulli equation

3.4 Eulers equation

3.5 Equation not of first degree

3.6 Clairauts equation

Unit - 2 Ordinary Differential Equation of higher orders

Module 3

Ordinary Differential Equation of higher orders

3.1 Second order Linear Differential equation with variable coefficient

3.2 Method of variation of Parameters

3.3 Cauchy Euler Equation

3.4 Power Series solution

3.5 Legendre’s Equation

3.6 Bessel function

Unit - 3 Partial Differential equation

Module 3C

Partial Differential equation First order

3.1 First Order Partial differential equation

3.2 Solution of first order linear and nonlinear partial differential equation

Unit - 4 Partial Differential Equation- Higher Order

Module 3D

Partial Differential Equation Higher Order

3.1 Solution to homogenous and non homogenous linear partial differential equation second and higher order by CF and PI

3.2 Flows Vibrations Diffusion

3.3 Second order linear equation and their classification

3.4 Initial and Boundary condition

3.6 Duhamel’s Principle for One Dimensional Wace Equation

3.7 Method of separation of variables

3.8 Laplacian in plane Cylindrical and Spherical polar coordinates

Unit - 5 Complex Variables: Differentiation

Module 4A

Complex Variables Differentiation

4.1 Differentiation

4.2 Cauchy Riemann Equation

4.3 Analytic Function

4.4 Harmonic Function

4.5 Finding harmonic conjugate

4.6 Elementary Analytic Function

4.7 Conformal mappings

4.8 Mobius Transformation

Unit - 6 Complex variable integration

Module 4 B

Complex variable integration

4.1 Contour integral

4.2 Cauchy Goursat Theorem

4.3 Cauchy integral formula

4.4 Liouvilles Theorem and Maximum modulus Theorem

4.5 Taylors series

4.6 Singularities

4.7 Laurents series

4.8 Residue

4.9 Cauchy Residue theorem

Unit - 7 Application of Complex integration by residues

Amalgamation of Firms

Module 4C

Application of Complex integration by residues

4.1Evaluation of definite integrals

4.2 Improper Integral

Unit - 8 Numerical Methods-I

MODULE 5A

NUMERICAL METHODS – 1

5.1 SOLUTION OF POLYNOMIAL AND TRANSCENDENTAL EQUATIONS – BISECTION METHOD NEWTONRAPHSON METHOD AND REGULAFALSI METHOD

5.2 FINITE DIFFERENCES

5.3 RELATION BETWEEN OPERATORS

5.4 INTERPOLATION USING NEWTON’S FORWARD AND BACKWARD DIFFERENCE FORMULAE.

5.5 INTERPOLATION WITH UNEQUAL INTERVALS NEWTON’S DIVIDED DIFFERENCE AND LAGRANGE’S FORMULAE.

5.6 Numerical differentiation

5.7 NUMERICAL INTEGRATION TRAPEZOIDAL RULE AND SIMPSON’S 13RD AND 38 RULES.

Unit - 9 Numerical method – II

Module 5 B

Numerical method – 2

5.1 ORDINARY DIFFERENTIAL EQUATIONS

5.2 TAYLOR’S SERIES

5.3 EULER AND MODIFIED EULER’S METHODS.

5.4 RUNGE KUTTA METHOD OF FOURTH ORDER FOR SOLVING FIRST AND SECOND ORDER EQUATIONS.

5.5 MILNE’S AND ADAM’S PREDICATORCORRECTOR METHODS.

5.6 PARTIAL DIFFERENTIAL EQUATIONS