Regulation 2021, Anna University Subject code – MA3452 deals with B.E Aeronautical Engineering 2nd year semester IV Vector Calculus And Complex Functions Syllabus. To prepare for challenging subjects in the field of Aeronautics need a detailed syllabus and preparation strategies. In this article, we discuss the Vector Calculus And Complex Functions syllabus.
We intend to provide every topic of the syllabus and content required for academic performance, along with reference books. In this article, MA3452 – Vector Calculus And Complex Functions Syllabus, you will be guided to get an idea of each topic of the syllabus and you can make your preparation strategy, and notes by filtering difficult topics from the different subjects. Then you can concentrate on the topic where you need to focus more. We included all the topics regarding the Aeronautical syllabus. We hope this information is useful to you. Don’t forget to share it with your friends and classmates.
If you want to know more about the syllabus of B.E Computer Science and Engineering connected to an affiliated institution’s under four-year undergraduate degree programme. We provide you with a detailed Year-wise, semester-wise, and Subject-wise syllabus in the following link B.E Aeronautical Engineering Syllabus Anna University, Regulation 2021.
Aim Of Concept:
- To acquaint the student with the concepts of vector calculus, needed for problems in all engineering disciplines.
- To develop an understanding of the standard techniques of complex variable theory so as to enable the student to apply them with confidence, in application areas such as heat conduction, elasticity, fluid dynamics and flow the of electric current.
- To make the student appreciate the purpose of using transforms to create a new domain in which it is easier to handle the problem that is being investigated.
- To make the student acquire sound knowledge of techniques in solving ordinary
- differential equations that model engineering problems.
MA3452- Vector Calculus And Complex Functions Syllabus
Unit I: Vector Calculus
Gradient and directional derivative – Divergence and curl – Vector identities – Irrotational and Solenoidal vector fields – Line integral over a plane curve – Surface integral – Area of a curved surface – Volume integral – Green’s, Gauss divergence and Stoke’s theorems – Verification and application in evaluating line, surface and volume integrals.
Unit II: Analytic Function
Analytic functions – Necessary and sufficient conditions for analyticity in Cartesian and polar coordinates – Properties – Harmonic conjugates – Construction of analytic function – Conformal mapping – Mapping by functions w = z+c, az, 1/z, z² – Bilinear transformation.
Unit III: Complex Integration
Line integral – Cauchy’s integral theorem – Cauchy’s integral formula – Taylor’s and Laurent’s series – Singularities – Residues – Residue theorem – Application of residue theorem for evaluation of real integrals – Use of circular contour and semicircular contour.
Unit IV: Laplace Transforms
Existence conditions – Transforms of elementary functions – Transform of unit step function and unit impulse function – Basic properties – Shifting theorems -Transforms of derivatives and integrals – Initial and final value theorems – Inverse transforms – Convolution theorem – Transform of periodic functions – Application to solution of linear second order ordinary differential equations with constant coefficients.
Unit V: Ordinary Differential Equations
Higher order linear differential equations with constant coefficients – Method of variation of parameters – Homogenous equation of Euler’s and Legendre’s type – System of simultaneous linear differential equations with constant coefficients – Method of undetermined coefficients.
Text Books:
- Erwin Kreyszig,” Advanced Engineering Mathematics “, John Wiley and Sons, 10th Edition, New Delhi, 2016.
- Grewal B.S., “Higher Engineering Mathematics ”, Khanna Publishers, New Delhi, 43rd Edition, 2014.
References:
- Sastry, S.S, “Engineering Mathematics”, Vol. I & II, PHI Learning Pvt. Ltd, 4th Edition, New Delhi, 2014.
- Jain R.K. and Iyengar S.R.K., “ Advanced Engineering Mathematics ”, Narosa Publications, New Delhi, 3rd Edition, 2007.
- Bali N., Goyal M. and Watkins C., “Advanced Engineering Mathematics ”, Firewall Media (An imprint of Lakshmi Publications Pvt., Ltd.,), New Delhi, 7th Edition, 2009.
- Peter V. O’Neil, “Advanced Engineering Mathematics”, Cengage Learning India Pvt., Ltd, New Delhi, 2007.
- Ray Wylie C and Barrett. L.C, “Advanced Engineering Mathematics” Tata McGraw Hill Education Pvt. Ltd, 6th Edition, New Delhi, 2012.
Related Posts On Semester – IV:
- AE3401 – Aerodynamics I
- AE3402 – Air Breathing Propulsion
- AE3491 – Mechanics of Machines
- AE3403 – Aircraft Structures-I
- AE3411 – Aerodynamics Laboratory
- AE3412 – Propulsion Laboratory