Engineering Mathematics-3 Syllabus VTU CBCS 2015-16 BE/B.Tech III sem complete syllabus covered here. This will help you understand complete curriculum along with details such as exam marks and duration.
Engineering Mathematics-3 Syllabus VTU CBCS 2015-16
| Subject Code | 15MAT31 | IA Marks | 20 |
|---|---|---|---|
| Number of Lecture Hours/Week | 04 | Exam Marks | 80 |
| Total Number of Lecture Hours | 50 | Exam Hours | 3 |
CREDITS – 04
Course objectives:
- The objectives of this course is to introduce students to the mostly used analytical and numerical methods in the different engineering fields by making them to learn Fourier series, Fourier transforms and Z-transforms, statistical methods, numerical methods to solve algebraic and transcendental equations, vector integration and calculus of variations.
| MODULES | TEACHING HOURS | REVISED BLOOM’S TAXONOMY (RBT) LEVEL |
|---|---|---|
| Module -1 | _ | |
| Fourier Series: Periodic functions, Dirichlet’s condition, Fourier Series of periodic functions with period 2π and with arbitrary period 2c. Fourier series of even and odd functions. Half range Fourier Series, practical harmonic analysis-Illustrative examples from engineering field. | 10 Hours | L1, L2 & L4 |
| Module -2 | _ | |
| Download iStudy App (No Ads, No PDFs) for complete VTU syllabus, results, timetables and all other updates. | 10 Hours | L2, L3 & L4 |
| Module -3 | _ | |
| Statistical Methods: Review of measures of central tendency and dispersion. Correlation-Karl Pearson’s coefficient of correlation-problems. Regression analysis- lines of regression (without proof) –problems Curve Fitting: Curve fitting by the method of least squares- fitting of the curves of the form, y = ax + b, y = ax2 + bx + c and y = aebx . Numerical Methods: Numerical solution of algebraic and transcendental equations by Regula- Falsi Method and Newton-Raphson method. | 10 Hours | L3 |
| Module -4 | _ | |
| Finite differences: Forward and backward differences, Newton’s forward and backward interpolation formulae. Divided differences- Newton’s divided difference formula. Lagrange’s interpolation formula and inverse interpolation formula (all formulae without proof)-Problems. Numerical integration: : Simpson’s (1/3)th and (3/8)th rules, Weddle’s rule (without proof ) –Problems. | 10 Hours | L3 |
| Module -5 | _ | |
| Vector integration: Line integrals-definition and problems, surface and volume integralsdefinition, Green’s theorem in a plane, Stokes and Gauss-divergence theorem(without proof) and problems. Calculus of Variations: Variation of function and Functional, variational problems. Euler’s equation, Geodesics, hanging chain, problems. | 10 Hours | L3 & L4 L2 & L4 |
Course Outcomes: On completion of this course, students are able to:
- Know the use of periodic signals and Fourier series to analyze circuits and system communications.
- Explain the general linear system theory for continuous-time signals and digital signal processing using the Fourier Transform and z-transform.
- Employ appropriate numerical methods to solve algebraic and transcendental equations.
- Αpply Green’s Theorem, Divergence Theorem and Stokes’ theorem in various applications in the field of electro-magnetic and gravitational fields and fluid flow problems.
- Determine the extremals of functionals and solve the simple problems of the calculus of variations.
Question paper pattern:
- The question paper will have ten full questions carrying equal marks.
- Each full question consisting of 16 marks.
- There will be two full questions (with a maximum of four sub questions) from each module.
- Each full question will have sub question covering all the topics under a module.
- The students will have to answer five full questions, selecting one full question from each module.
Graduate Attributes (as per NBA)
- Engineering Knowledge
- Problem Analysis
- Life-Long Learning
- Accomplishment of Complex Problems
Text Books:
- B.S. Grewal: Higher Engineering Mathematics, Khanna Publishers, 43rd Ed., 2015.
- E. Kreyszig: Advanced Engineering Mathematics, John Wiley & Sons, 10th Ed., 2015.
Reference books:
- N.P.Bali and Manish Goyal: A Text Book of Engineering Mathematics, Laxmi Publishers, 7th Ed., 2010.
- B.V.Ramana: “Higher Engineering M athematics” Tata McGraw-Hill, 2006.
- H. K. Dass and Er. RajnishVerma: “Higher Engineerig Mathematics”, S. Chand publishing, 1st edition, 2011.
We links and Video Lectures:
- http://nptel.ac.in/courses.php?disciplineID=111
- http://wwww.khanacademy.org/
- http://www.class-central.com/subject/math
For all other BE/B.Tech 3rd Sem Subject syllabus do follow VTU 3rd Sem BE / B.Tech Syllabus CBCS (2015-16) Scheme for Industrial Engineering and Management Group.
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