# Applied Mathematics II (REVISED 2007)

ENGINEERING SEM 2
Applied Mathematics -II
Syllabus In Detail:-
Prerequisite: -    02 hr
Idea of curve tracing in Cartesian. Parametric and Polar forms. Standard
curves such as Straight lines.    Circles, Parabolas. Hyperbola, Catenary
Clssoid, Astroid, Cycloid, Lommscate of Bernoulli, Cardiode, concept of
Solid Geometry- Planes, Spheres, cones, Cylinders, Parabolloids,
2.1         Beta and Gamma functions, Differentiation under integral sign.
06hr
2.1.1    Definition of Beta and Gamma functions and properties
2.1.2    Relation between Beta and Gamma functions (with proof),
duplication formula (with proof)
2.1.3    Differentiation under the integral sign with constant limits of
integration.
2.2         Differentiation  Equations of first order and first degree
04hr

2.2.1    Exact differential equations and those which can be reducible to the
exact form by using integrating factors (four rules)
1.  Homogeneous differential equations
2.  F(xy)ydx+g (xy)xdy=0
? M   ? N
-------------
?f (x)dx              ?y  ?x
3.  LF = e        wheref (x) =
N
?N -?M

?g (y )dy             ?x   ?M
4. I.F.+  e       whereg(Y0 =
M

2.2.2    Lmeat differential equations and differential equations reducible to             03
the linear form
2.2.3    Numerical solutions of differential equations using Taylor’s series              01
method.

2.3         Numerical solutions of differential equations of first order and first 03 hr
degree, Differential equations of order n.
2.3.1    Euler’s method, Modified Euler’s method, Runge Kutta method of 4th

order. Comparison of numerical solutions with the exact solutions.
2.3.2    Linear differential equations with constant coefficients-Complimentary                03
functions, particular integrals of differential equations of the type
ax                               n  ax      V
f(D)y =X where X is e           sin (ax+b), cos (az+b),x , e      V, x
2.4         Linear Differential equations with variable coefficients. Method of
variation of parameters and Rectification.

2.4.1     Cauchy’s homogeneous Linear differential equation and Lavender’s                     02
differential equation.
2.4.2      Method of variation of parameters                                                   01
2.4.3      Simple application of differential equations of first and second order              02
to electrical and mechanical engineering 0roblems (no formulation of
differential equation)
2.4.4     Rectification of plane curves                                                        02
2.5         Integral Calculus-Double Integrals
2.5.1     Double Integration-Definition, geometrical interpolation properties    03 hr
and evaluation.
2.5.2    Evaluation of double integrals by changing the order of integration         06hr
and changing to polar form.
2.6         Integral Calculus-Triple Integral and application of double and triple
integrals, computer oriented techniques.

2.6.1     Triple Integration- definition and evaluation (Cartesian, Cylindrical      03hr
and Spherical polar coordinates), concept of Jacobeans.
2.6.2     Applications of double integrals to compute Volume                              03hr
2.6.3     Computer oriented techniques in problem soling using Scilab.              02 hr

•      Attendance ( Theory  and Theory)                                               : 05 Marks
•       Tutorials covering entire portion                                             : 05 Marks
•      Programming Assignments using Scilab                                           : 05 Marks
-Curve Tracing. Intersection of surfaces. evaluation of
double and Triple Integrals. Solution of Differential equations
st              st
of 1   order and 1   degree
•      Test (at least one)                                                            : 05 Marks
25
•      The final certification and acceptance of term-work ensures the satisfactory performance
of laboratory work and minimum passing in the term –work

REFERENCE BOOKS

• Higher Engineering Mathematics. Dr. B.S. Grewal. Khanna Publications
rd
• Differential Equation. Ross.. wiley India. 3   Ed.
• A textbook of Applied Mathematics, P.N. & J.N. Wartikar. volume 1 & @ . Pune vidyarthi
Griha.
th
• Advanced Engineering Mathematics. Erwin Kreyszing. wiley India 8   Ed.
• Elementary Differential Equation, E.d. rainville. P.E & R.E Bedient. Prentice Hall, 8th

edition.