Mathematics-II detail syllabus for Common To All (Common), 2018-19 scheme is taken from AKTU official website and presented for AKTU students. The course code (KAS203), and for exam duration, Teaching Hr/Week, Practical Hr/Week, Total Marks, internal marks, theory marks, duration, and credits do visit complete sem subjects post given below.
For all other common 2nd sem syllabus for b.tech 2018-19 scheme aktu you can visit Common 2nd Sem syllabus for B.Tech 2018-19 Scheme AKTU Subjects. The detail syllabus for mathematics-ii is as follows.
Module 1:
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Module 2:
Multivariable Calculus-II
Improper integrals, Beta & Gama function and their properties, Dirichlet’s integral and its applications, Application of definite integrals to evaluate surface areas and volume of revolutions.
Module 3:
Sequences and Series
Definition of Sequence and series with examples, Convergence of sequence and series, Tests for convergence of series, (Ratio test, D’ Alembert’s test, Raabe’s test). Fourier series, Half range Fourier sine and cosine series.
Module 4:
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Module 5:
Complex Variable -Integration
Complex integrals, Contour integrals, Cauchy- Goursat theorem, Cauchy integral formula, Taylor’s series, Laurent’s series, Liouvilles’s theorem, Singularities, Classification of Singularities, zeros of analytic functions, Residues, Methods of finding residues, Cauchy Residue theorem, Evaluation of real integrals of the type (formula ahead :-)) integral 0 to infinite f (cos theta, sin theta) d theta and integral -ve infinite to infinite f(x) dx.
Course Outcomes:
- Understand the concept of differentiation and apply for solving differential equations.
- Remember the concept of definite integral and apply for evaluating surface areas and volumes.
- Understand the concept of convergence of sequence and series. Also evaluate Fourier series
- Illustrate the working methods of complex functions and apply for finding analytic functions.
- Apply the complex functions for finding Taylor’s series, Laurent’s series and evaluation of definite integrals.
Text Books:
- B. V. Ramana, Higher Engineering Mathematics, Tata McGraw-Hill Publishing Company Ltd., 2008.
- B. S. Grewal, Higher Engineering Mathematics, Khanna Publisher, 2005.
- R. K. Jain & S. R. K. Iyenger , Advance Engineering Mathematics , Narosa Publishing -House, 2002.
Reference Books:
- E. Kreyszig, Advance Engineering Mathematics, John Wiley & Sons, 2005.
- Peter V. O’Neil, Advance Engineering Mathematics, Thomson (Cengage) Learning, 2007.
- Maurice D. Weir, Joel Hass, Frank R.Giordano, Thomas, Calculus, Eleventh Edition, Pearson.
- G.B Thomas, R L Finney, Calculus and Analytical Geometry, Ninth Edition Pearson, 2002.
- James Ward Brown and Ruel V Churchill, Fourier Series and Boundary Value Problems, 8th Edition-Tata McGraw-Hill
- D. Poole , Linear Algebra: A Modern Introduction, 2nd Edition, Brooks/Cole, 2005.
- Veerarajan T., Engineering Mathematics for first year, Tata McGraw-Hill, New Delhi, 2008.
- Charles E Roberts Jr, Ordinary Differential Equations, Application, Model and Computing, CRC Press T&F Group.
- Ray Wylie C and Louis C Barret, Advanced Engineering Mathematics, 6th Edition, Tata McGraw-Hill.
- James Ward Brown and Ruel V Churchill, Complex Variable and Applications, 8th Edition, Tata McGraw-Hill.
- P. Sivaramakrishna Das and C. Vijayakumari, Engineering Mathematics, 1st Edition, Pearson India Education Services Pvt. Ltd.
- Advanced Engineering Mathematics By Chandrika Prasad, Reena Garg Khanna Publishing House, Delhi
For detail syllabus of all other subjects of B.Tech Common, 2018-19 scheme do visit Common 2nd Sem syllabus for 2018-19 scheme.
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