REVISED 2012 Applied Mathematics-II Mumbai University
Syllabus for Applied Mathematics-II
Idea of Curve tracing in cartesian, parametric and polar forms. Straight
lines, Circles, Parabolas, Hyperbola, Catenary, Cissoid, Astroid, Cycloid,
Lemniscate of Bernoulli, Cardiode. Concept of Solid Geometry ‐Planes,
Spheres, Cones, Cylinders, Paraboloids (Tracing of curves by using SciLab).
Beta and Gamma functions, Differentiation under Integral sign and exact
1.1: Beta and Gamma functions and its properties. Differentiation under integral
sign with constant limits of integration.
1.2: Rectification of plane curves.
1.3: Differential Equation of first order and first degree‐Exact differential
equations, Equations reducible to exact equations by integrating factors.
2.1: Linear differential equations(Review), equation reduciable to linear form,
2.2: Linear Differential Eqaution with constant coeffiecient‐ Complimentary function,
particular integrals of differential equation of the type f(D)y = X where X is eax,sin(ax+b),
cos (ax+b), xn, eaxV, xV.
2.3: Cauchy’s homogeneous linear differential equation and Legendre’s
differential equation, Method of variation of parameters.
2.4: Simple application of differential equation of first order and second order to
electrical and Mechanical Engineering problem (no formulation of differential
Numerical solution of ordinary differential equations of first order and
first degree and Multiple Integrals‐
3.1 :(a)Taylor’s series method (b)Euler’s method
(c) Modified Euler method (d) Runga‐Kutta fourth order formula (SciLab
programming is to be taught during lecture hours)
3.2:Multiple Integrals‐Double integration‐definition, Evaluation of Double Integrals,
Change of order of integration, Evaluation of double integrals by changing the order
of integration and changing to polar form (Examples on change of variables by using
Multiple Integrals with Application and Numerical Integration:‐
4.1: Triple integration –definition and evaluation (Cartesian, cylindrical and spherical
4.2: Application to double integrals to compute Area, Mass, Volume. Application of
triple integral to compute volume.
4.3: Numerical integration‐Different type of operators such as shift, forward,
backward difference and their relation. Interpolation, Newton iterpolation, Newton‐
Cotes formula(with proof). Integration by
(b) Simpson’s 1/3rd
(c) Simpson’s 3/8th rule (all with proof).
(Scilab programming on (a) (b) (c) (d) is to be
taught during lecture hours)
1: A text book of Applied Mathematics, P. N. Wartikar and J. N. Wartikar, Vol –I and II by
Pune Vidyarthi Graha.
2: Higher Engineering Mathematics, Dr.B. S. Grewal, Khanna Publication
3: Advanced Engineering Mathematics, Erwin Kreyszig, Wiley Eastern Limited,9
4: Numerical Analysis by S.S.Sastry, Prentice Hall
5: Differential Equations, Sheply Ross, Wiley India.