1. A Presentation on APPLIED MATHEMATICS (9030)

2. Subject Title : Applied Mathematics Course Name: Second Year
Subject Title : Applied Mathematics Course Name: Second Year Engineering Diploma Course Code : EE/EJ Semester : Third Subject Abbr : AMT Subject Code : 9030

3. Examination Scheme Teaching Scheme TH TU PR 04 -- PAPER HRS TH TEST PROR TW
TOTAL 03 80 20 --
100

4. Rationale
Since 21st century man has developed new disciplines like Information technology , Genetic engineering , Biotechnology etc. on the basis of Mathematics. Thus the study of this subject is necessary to develop the skills essential for these new disciplines in the student. The study of mathematics is necessary to develop in the student the skills essential for studying new technological development. This subject introduces some applications of engineering, through which the student can understand the link of Mathematics with engineering principles.

5. Objectives The students will be able to:
Apply Mathematical term, concept, principals, and different methods
Apply Mathematical methods to solve technical problems,
Execute management plans with precision.
Use Mathematical techniques necessary for daily and practical problems.

6. Learning Structure
Application
Procedure
Concept
Facts

7. Application:-
Apply the principles of Mathematics to solve problems in Electrical and Electronics Field

8. Procedure
Methods of finding integration definite integration and its properties.
Methods of solving differential equation of first order and first degree.
Use of Laplace transform for solving problems of Differential Equations.
Use of Fourier series for expansion of function at the given intervals.
Methods for finding approximate roots by using bisection, Regula-falsi, Newton-Raphson method, Gauss elimination method, Jacobi and Gauss-seidal methods

9. Concept
Integration of standard functions. Rules of integration. Integration by parts, partial fractions.
Order, degree of differential equation.
Laplace Transform of standard functions, properties. Inverse L. T. Convolution theorem.
Eular’s formula for Fourier series expansion.
Higher order algebraic equations. Upper and lower triangular matrix, iterative methods.

10. Facts First order differentiation.
Definition of integration as anti derivative.
Integration.
Definition of differential equation.
Definition of Laplace transform and Inverse Laplace transform.
Definition of periodic, even and odd functions.
Relation between degree of equation and roots. Relation between no. of unknowns and equations.

11. Sr . No. Name of Books Author Publication 1 Engineering Mathematics
P.Kandasamy,K. Thilagavathy
S.Chand &Company Ltd 2
Advanced Engineering Mathematics
Erwin Kreyszig 3
Engineering Mathematic
S.Arumugam, A.Somasundram
Scitech Publication 4
Electonic Mathematic
S. P. Deshpande, P. N. Kulkarni 5
S.S. Sastry
Prentice Hall India PV Ltd 6
Higher Engineering Mathematics
B.S . Grewal
Khanna Publishers 7
Elements of Probability & S tatistics
A. P. Baisnab
Tata Mc Graw Hill publishing company LTD 8
Introductory Methods of Numerical Analysis 9
Discrete Mathematics
Olympia Nieodemi
CBS Publishres & Distibutots 10
Mathematics for Polytechnic students
S. P. Deshpande
Pune Vidyarthi Griha Publication 11
B.V. Mane
Everest Publishing House 12
Numerical Mathematical Analysis
James B. Scarborough
Oxford & IBH publishing company LTD 13
H.Tatas:A text of Applied Mathematics
B.S.Tyagi
International Publication 14
Mathematical Statistics
John E.Freund 15
Engineering Mathematics-I
R.M Baphana
Technovo Publication

12. 16
Applied Mathematics I , II , III
P N Wartikar
J N wartikar 17
Mathematics & Statistics
Suranjan Saha
New Central Book Agency (p)LTD. 18
Engineering Mathematics
Gupta
MACMILLAN INDIA LTD. 19
Advanced Calculas
Widder
Prentice Hall India PV Ltd 20
Mathematics for Diploma in Engineering Student -
Shrish Pra
21.
Trigonometry
S.L.Loney
S.Chand Publication
22.
Higher Algebra
H.S.Hall &S.R.Knight
Metric Edition
23.
College Algebra
Frc.G.Valles
Charotar Publication
24.
Applied Mathematics
B.M.Patel & others
Nirali Publication
25.
A.M.Kulkarni
Central Techno Publication
26.
G.V.Kumbhojkar
Phadke Publication 27
Sameer Shah
Tech-Max Publication

13. 9030 0910-I 3 Hours / 80 Marks Seat No. Instructions-
For Theory 80 marks MSBTE conducting examination at end of semester
MSBTE Question Paper Format
9030
0910-I
3 Hours / 80 Marks Seat No.
Instructions-
All Questions are compulsory.
Answer each next main Question on a new page.
Figures to the right indicate full marks.
Assume suitable data, if necessary.
Use of Non-programmable Electronic Pocket Calculator is permissible.

14. Attempt any EIGHT of the following [ marks 16 ]
Q 1.
Attempt any EIGHT of the following [ marks 16 ] a)
Integration ( Substitution) b)
Integration (Trigonometric) c)
Integration (Formulae) d)
Definite Integration e)
Differential equations (Formation, Solution, Order & Degree of D.E.) f)
Differential equations ( Variable Separable) g) h)
Transform ( linearity property) i)
Transform ( first shifting property) j)
Inverse Transform

15. Attempt any Three of the following [ marks 12]
Q 2.
Attempt any Three of the following [ marks 12] a)
Differential equations b)
( Variable Separable /Reducible Variable Separable) c)
(Homogeneous/Exact /Linear/ Bernoulli’s D.E.) d)
Application of D.E.
Q 3.
Attempt any Three of the following [ marks 12 ]
Laplace Transform
( linearity property/Trigonometry)
( first shifting property)
Inverse Laplace Transform
( first shifting property/ Partial fraction)
Solution of D.E. using Laplace Transform

16. Attempt any Three of the following [ marks 16]
Q 4.
Attempt any Three of the following [ marks 16] a)
Integration b) c)
Definite Integration d) e)
Application of Integration f)
Q 5.
Attempt any Three of the following [ marks 12 ]
Fourier Series
Numerical Methods
(Bisection/ Regula - falsi / Newton- Raphson method )

17. Attempt any Four of the following [ marks 12]
Q 6.
Attempt any Four of the following [ marks 12] a)
Numerical Methods
(Bisection/ Regula - falsi / Newton- Raphson method ) b)
( Gauss elimination/Gauss-seidel/JacobiMethod) c) d)

18. Thank you Mr. Vikas N. Bachhav Presented By :- Lecturer in Mathematics
K. K. Wagh Polytechnic, Nashik
Thank you