Kavayitri Bahinabai Chaudhari North Maharashtra University, Maharashtra, Civil Engineering Semester 2, Mathematics –II Syllabus

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UNIT - 3 FUNCTION OF COMPLEX VARIABLE

3.1 Differentiation

3.2 CauchyRiemann equations

3.3 Analytic functions

3.4 Harmonic functions finding harmonic conjugate

3.5 Zeros of analytic functions singularities

3.6 Cauchy Integral formula without proof

3.7 Cauchy Residue theorem without proof

Unit - 1 First order ordinary differential equations

1.1 Exact equations Equations reducible to exact

1.2 Linear and Bernoulli’s equations Integrating Factor

1.3 Equations not of first degreeequations solvable for p equations solvable for y equations solvable for x and Clairaut’s type.Equation solvable for p.

Unit - 2 Linear differential equations

2.1 Linear Differential Equations with constant coefficients

2.2 Method to find Particular Integral by shortcut methods

2.3 Method of variation of parameters

2.4 CauchyEuler equation

2.5 Legendre’s Equations

Unit - 4 Numerical methods

4.1 Solution of Ordinary differential equations by Taylor’s series and Picard’s method

4.2 RungeKutta method of fourth order for solving first order equations

4.3 Numerical integration Trapezoidal rule and Simpson’s 13rd and 38 rules

Unit - 5 Multivariable Calculus (Integration)

5.1 Double integrals limits Given and limits not given by Cartesian and Polar coordinates

5.2 Triple integration by spherical polar coordinates

5.3 Applications areas and volumes

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Other Subjects of Semester-2
Physics
Programming for problem solving
Basic electrical & electronics engineering
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