Engineering Mathematics-III detailed syllabus scheme for B.Tech Automobile Engineering (AE), 2017-18 onwards has been taken from the DBATU official website and presented for the Bachelor of Technology students. For Subject Code, Course Title, Lecutres, Tutorials, Practice, Credits, and other information, do visit full semester subjects post given below.
For all other DBATU Syllabus for Automobile Engineering 3rd Sem 2017-18, do visit AE 3rd Sem 2017-18 Onwards Scheme. The detailed syllabus scheme for engineering mathematics-iii is as follows.
Engineering Mathematics-III Syllabus for Automobile Engineering (AE) 2nd Year 3rd Sem 2017-18 DBATU
Pre-requisite:
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Course outcomes:
At the end of the course, students will be able to
- Comprehend the fundamental knowledge of the Laplace and inverse Laplace transform: and their derivatives for elementary functions (K2, A2)
- Apply the properties of Laplace and inverse Laplace transforms to solve simultaneous linear and linear differential equations with constant coefficients (K3, A4)
- Conceptualize the definitions and properties of Fourier transforms (K2, A4)
- Solve boundary value problems using Fourier transforms (K3, A3)
- Find the series solutions of the linear differential equations using Frobenius method (K2, A2, S3)
- Find the solutions of partial differential equations governing real-world problems (K2, A4)
- Conceptualize limit, continuity, derivative and integration of complex functions (K2, A4)
- Evaluate complex integrals useful in real-world problems (K5, A4, S4)
Unit 1
Laplace Transform Definition: conditions for existence; Transforms of elementary functions; Properties of Laplace transforms: Linearity property, first shifting property, second shifting property, transforms of functions multiplied by tn, scale change property, transforms of functions divided by t, transforms of integral of functions, transforms of derivatives; Evaluation of integrals by using Laplace transform; Transforms of some special functions: periodic function, error function, unit step function .
Unit 2
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Unit 3
Fourier Transform Definitions: integral transforms; Fourier integral theorem (without proof); Fourier sine and cosine integrals; Complex form of Fourier integrals; Fourier sine and cosine transforms; Properties of Fourier transforms; Convolution theorem for Fourier Transforms; Application to boundary value problems.
Unit 4
Series Solutions of Differential Equations and Special Functions Validity of series solution; Series solutions about ordinary and singular point; Frobenius method; Series solution of Bessel equation; Recurrence relations for Bessel function; Generating function for Bessel function; Orthogonality of Bessel function.
Unit 5
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Unit 6
Calculus of Complex Functions Limit and continuity of f(z); Derivative of f( z ) – Cauchy-Riemann equations; Analytic functions; Harmonic functions – orthogonal system; Conformal transformations; complex integration -Cauchys theorem, integral formula; Residue theorem.
Text Books:
- B. S. Grewal, Higher Engineering Mathematics, Khanna Publishers, New Delhi.
- P. N. Wartikar and J. N. Wartikar, A Text Book of Applied Mathematics (Vol. I and II), Pune Vidyarthi Griha Prakashan, Pune.
- Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons, New York.
- Dr. B. B. Singh, A course in Engineering Mathematics (Vol. III), Synergy Knowledgeware, Mumbai.
Reference Books:
- B. V. Ramana, Higher Engineering Mathematics, Tata McGraw-Hill Publications, New Delhi.
- N. P. Bali and N. Ch. Narayana Iyengar, A Text Book of Engineering Mathematics, Laxmi Publications (P) Ltd., New Delhi.
- Peter O Neil, A Text Book of Engineering Mathematics, Thomson Asia Pvt. Ltd., Singapore.
- C. R. Wylie and L. C. Barrett, Advanced Engineering Mathematics, Tata McGraw-Hill Publishing Company Ltd., New Delhi.
- Dr. B. B. Singh, Integral Transforms and their Engineering Applications, Synergy Knowledge ware, Mumbai.
For detail syllabus of all other subjects of Automobile Engineering (AE) 3rd Sem 2017-18 regulation, visit AE 3rd Sem Subjects syllabus for 2017-18 regulation.