REVISED 2012 Applied Mathematics-II Mumbai University

REVISED 2012 Applied Mathematics-II Mumbai University

REVISED 2012 Applied Mathematics-2 Mumbai University

Syllabus for Applied Mathematics-II 

Prerequisite


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).





Module‐1: 
Beta and Gamma functions, Differentiation under Integral sign and exact 
differential equation: 
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.


Module‐2: 
Differential Calculus 
2.1: Linear differential equations(Review), equation reduciable to linear        form, 
Bernoulli’s equation. 

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 
equation) 


Module‐3: 
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 
Jacobians only).


Module ‐4:
Multiple Integrals with Application and Numerical Integration:‐ 
4.1: Triple integration –definition and evaluation (Cartesian, cylindrical  and spherical 
polar coordinates). 

 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 
(a) Trapezoidal 

(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)  



Recommended Books: 
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
th Ed. 

4: Numerical Analysis by S.S.Sastry, Prentice Hall 

5: Differential Equations, Sheply Ross, Wiley India.