Subject – Applied Mathematics IIClass – F.E. (all Branches of Engineering)MU
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 
4 

Practical 
— 

Tutorial 
1 

Hours 
marks 

Evaluation System  Theory Examination 
3 
100 
Practical and OralExamination 
— 
— 

Oral Examination 
— 
— 

Term Work 
— 
25 

Total 
125 

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 coefficientsComplimentary 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
02
01
02
022.5Integral CalculusDouble Integrals
2.5.1 Double IntegrationDefinition, geometrical interpolation properties and evaluation.
2.5.2 Evaluation of double integrals by changing the order of integration and changing to polar form.
03
062.6Integral CalculusTriple 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.
03
03
02
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
25
• The final certification and acceptance of termwork 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
Griha.
• Advanced Engineering Mathematics. Erwin Kreyszing. wiley India 8th Ed.
• Elementary Differential Equation, E.d. rainville. P.E & R.E Bedient. Prentice Hall, 8th
edition.
all syllabus in single PDF file free download .