University of Mumbai

Class – F.E. (all Branches of Engineering)

Subject – Applied Mathematics -II

all syllabus in single PDF file free download 

Periods per week (01 Period of 60 minutes) Lecture







Evaluation System Theory Examination



Practical and OralExamination

Oral Examination

Term Work





Sr. No. Detailed Syllabus: Hrs
Prerequisite: –Idea of curve tracing in Cartesian. Parametric and Polar forms. Standardcurves such as Straight lines.  Circles, Parabolas. Hyperbola, Catenary Clssoid, Astroid, Cycloid, Lommscate of Bernoulli, Cardiode, concept of Solid Geometry- Planes, Spheres, cones, Cylinders, Parabolloids, 02
2.1 Beta and Gamma functions, Differentiation under integral sign.2.1.1     Definition of Beta and Gamma functions and properties2.1.2     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 degree2.2.1     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


3.   LF = e f ( x ) dx  wheref x) = ∂y x


N −∂M


4. I.F.+ e ∫ g ( y ) dy whereg (Y 0 = ∂x  M M



2.2.2     Lmeat differential equations and differential equations reducible to the linear form

2.2.3     Numerical solutions of differential equations using Taylor’s series method.






















Details of Syllabus –


2.3 Numerical solutions of differential equations of first order and first 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 functions, particular integrals of differential equations of the type

f(D)y =X where X is eax    sin (ax+b), cos (az+b),xn, eax V, xV03





032.4Linear Differential equations with variable coefficients. Method of variation of parameters and Rectification.

2.4.1     Cauchy’s homogeneous Linear differential equation and Lavender’s differential equation.

2.4.2      Method of variation of parameters

2.4.3      Simple application of differential equations of first and second order to electrical and mechanical engineering 0roblems (no formulation of differential equation)

2.4.4     Rectification of plane curves










022.5Integral Calculus-Double Integrals

2.5.1     Double Integration-Definition, geometrical interpolation properties and evaluation.

2.5.2    Evaluation of double integrals by changing the order of integration and changing to polar form.



062.6Integral Calculus-Triple Integral and application of double and triple integrals, computer oriented techniques.

2.6.1     Triple Integration- definition and evaluation (Cartesian, Cylindrical

and Spherical polar coordinates), concept of Jacobeans.

2.6.2     Applications of double integrals to compute Volume

2.6.3     Computer oriented techniques in problem soling using Scilab.







Theory Examination:

1.        Question paper will comprise of total 7 questions, each of 20 marks.

2.         Only 5 questions need to be solved.

3.         Q, 1 will be compulsory and based on entire syllabus

4.         Remaining questions will be mixed in nature (e.g. suppose Q.2 has part (a) form, module 3 then part (b) will be form any module other then module3)

5.         In question paper weightage of each module will be proportional to number of

respective lecture hours as mentioned in the syllabus.

Term Work.

•        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 of 1st  order and 1st degree

•        Test (at least one)                                                                           : 05 Marks


•                The final certification and acceptance of term-work ensures the satisfactory performance of laboratory work and minimum passing in the term –work.

Recommended Books:

• Higher Engineering Mathematics. Dr. B.S. Grewal. Khanna Publications

• Differential Equation. Ross.. wiley India. 3rd Ed.

• A textbook of Applied Mathematics, P.N. & J.N. Wartikar. volume 1 & @ . Pune vidyarthi


• Advanced Engineering Mathematics. Erwin Kreyszing. wiley India 8th Ed.

• Elementary Differential Equation, E.d. rainville. P.E & R.E Bedient. Prentice Hall, 8th


all syllabus in single PDF file free download