Mathematics-I detail syllabus for Common To All (Common), 2018-19 scheme is taken from AKTU official website and presented for AKTU students. The course code (KAS103), 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 1st sem syllabus for b.tech 2018-19 scheme aktu you can visit Common 1st Sem syllabus for B.Tech 2018-19 Scheme AKTU Subjects. The detail syllabus for mathematics-i is as follows.
Module 1:
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Module 2:
Differential Calculus- I
Introduction to limits, continuity and differentiability, Rolle’s Theorem, Lagrange’s Mean value theorem and Cauchy mean value theorem, Successive Differentiation (nth order derivatives), Leibnitz theorem and its application, Envelope, Involutes and Evolutes, Curve tracing: Cartesian and Polar co-ordinates
Module 3:
Differential Calculus-II
Partial derivatives, Total derivative, Euler’s Theorem for homogeneous functions, Taylor and Maclaurin’s theorems for a function of one and two variables, Maxima and Minima of functions of several variables, Lagrange Method of Multipliers, Jacobians, Approximation of errors.
Module 4:
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Module 5:
Vector Calculus
Vector differentiation: Gradient, Curl and Divergence and their Physical interpretation, Directional derivatives, Tangent and Normal planes.
Vector Integration: Line integral, Surface integral, Volume integral, Gauss’s Divergence theorem, Green’s theorem, Stoke’s theorem ( without proof) and their applications.
Course Outcomes:
- Remember the concept of matrices and apply for solving linear simultaneous equations.
- Understand the concept of limit, continuity and differentiability and apply in the study of Rolle,s , Lagrange,s and Cauchy mean value theorem and Leibnitz theorems .
- Identify the application of partial differentiation and apply for evaluating maxima, minima, series and Jacobians.
- Illustrate the working methods of multiple integral and apply for finding area, volume, centre of mass and centre of gravity.
- Remember the concept of vector and apply for directional derivatives, tangent and normal planes. Also evaluate line, surface and volume integrals.
Text Books:
- B. V. Ramana, Higher Engineering Mathematics, Tata Mc Graw-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.
- 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.
- Ray Wylie C and Louis C Barret, Advanced Engineering Mathematics, Tata Mc-Graw-Hill; Sixth Edition.
- P. Sivaramakrishna Das and C. Vijayakumari, Engineering Mathematics, 1st Edition, Pearson India Education Services Pvt. Ltd
- Advanced Engineering Mathematics. Chandrika Prasad, Reena Garg, 2018.
- Engineering Mathemathics – I. Reena Garg, 2018.
For detail syllabus of all other subjects of B.Tech Common, 2018-19 scheme do visit Common 1st Sem syllabus for 2018-19 scheme.
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