A Presentation on APPLIED MATHEMATICS (9030)

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

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

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.

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.

Learning Structure Application Procedure Concept Facts

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

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

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.

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.

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

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

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.

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

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

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 )

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)

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