Unit1
Unit 1: Functions of Complex variable
20%Limit continuity & differentiability, Analytic function & Cauchy- Riemann equations (Cartesian form), Harmonic function, Conjugate function, Milne Thomson method for finding analytic function.
Syllabus
5 units · weightage in %Unit2
Unit 2: Vector Calculus
20%Vector differentiation, Scalar and vector point functions, vector differential operator Del, gradient of a scalar function, normal and directional derivative, divergence and curl of a vector function and their physical interpretation. Line, Surface and Volume integral with illustrative examples, Statements of Green’s, Stake’sand Gauss’s divergence theorem only.
Unit3
Unit 3: Matrices
20%Definition and types matrices, Elementary transformations, Rank of a matrix, Reduction to normal form and triangular form, Inverse of a matrix, Consistency and solution of linear equations, Eigen values, Eigen vectors. Cayley-Hamilton theorem (without proof).
Unit4
Unit 4: Fourier series & Partial differential equation
20%Periodic functions, Fourier series and Dirichlet’s conditions, Fourier series of period 2π. Even and odd function, Half range series , Fourier series of functions having arbitrary period (period 2c), Half range, series ( with period c) , Introduction & formation of partial differentiate equation, solution of Linear partial differentiate equation with constant coefficient.
Unit5
Unit 5: Application of partial differential equation
20%Introduction, Method of separation of variables, problems on One dimensional wave equation, one dimensional heat equation and two-dimensional steady state heat flow equation.
Course Objectives
- Apply the theory of functions of a complex variable, including analytic and harmonic functions, to engineering problems.
- Use vector calculus and integral theorems to analyse field quantities relevant to agricultural engineering systems.
- Apply matrix methods to determine rank, inverse, eigenvalues, and to solve systems of linear equations.
- Construct Fourier series of periodic functions and form and solve partial differential equations.
- Apply partial differential equations to model and solve wave, heat, and steady-state flow problems.
Course Outcomes (COs)
After completion of the course student will be able to:
- CO1Apply the concepts of analytic and harmonic functions and the Cauchy-Riemann equations to construct analytic functions.K3
- CO2Apply vector differentiation and line, surface, and volume integrals, using Green's, Stokes', and Gauss's theorems, to field problems.K3
- CO3Apply matrix methods to find rank, inverse, eigenvalues, and eigenvectors and to solve systems of linear equations.K3
- CO4Construct the Fourier series of periodic and arbitrary-period functions and form linear partial differential equations.K3
- CO5Apply the method of separation of variables to solve one-dimensional wave, one-dimensional heat, and two-dimensional steady-state heat-flow equations.K3
Text Books
- E. Kreyszig, Advance Engineering Mathematics, John Wiley & Sons, 2005.
- 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
- 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, RL Finney, Calculus and Analytical Geometry, Ninth Edition Pearson, 2002.
- James Ward Brown and Ruel V Churchill, Fourier Series and Boundary Value Problems,8th Edition-McGraw-Hill
- D. Poole, Linear Algebra: A Modern Introduction, 2nd Edition, Brooks/ Cole, 2005.
- Veerarajan T., Engineering Mathematics for first year, McGraw-Hill, New Delhi, 2008.
- Charles E Roberts Jr, Ordinary Diffrential Equations, Application, Model and Computing, CRC Press T&F Group.
- Ray Wylie C and Louis C Barret, Advanced Engineering Mathematics, 6th Edition, McGraw-Hill.
- James Ward Brown and Ruel V Churchill, Complex Variable and Applications, 8th Edition, McGraw-Hill.
- P. Sivaramakrishna Das and C. Vijaya kumari, Engineering Mathematics, 1st Edition, Pearson India Education Services Pvt. Ltd.
- Advanced Engineering Mathematics By Chandrika Prasad, Reena Garg Khanna Publishing House, Delhi.
- Laplace Transforms by Schaum’s series, 2005 Edition, Spiegel Publication.
- Dan Hamilton, Calculus 1 - Differentiation and Integration, Hamilton Education Guides 2018.
Official AKTU syllabus
This subject is on page 19, 20, 21, 22, 23 of the original AKTU PDF.