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AKTU Calculus and Linear Algebra (AAS203H) Syllabus PDF – B.Tech 1st Year
Calculus and Linear Algebra AAS203H
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Official AKTU syllabus of Calculus and Linear Algebra (AAS203H) for B.Tech 1st Year – 4 credits, L-T-P 3-1-0. Read the unit-wise course content, course outcomes, evaluation pattern and recommended books online, or download the PDF.
Syllabus — Calculus and Linear Algebra
Download PDFAAS203H · 4 credits · L-T-P 3-1-0
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 Content
| Unit | Description | Weightage |
|---|---|---|
| 1. | Functions of Complex variable: Limit continuity & differentiability, Analytic function & Cauchy- Riemann equations (Cartesian form), Harmonic function, Conjugate function, Milne Thomson method for finding analytic function. | 20% |
| 2. | Vector Calculus: 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. | 20% |
| 3. | Matrices: 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). | 20% |
| 4. | Fourier series & Partial differential equation: 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. | 20% |
| 5. | Application of partial differential equation: Introduction, Method of separation of variables, problems on One dimensional wave equation, one dimensional heat equation and two-dimensional steady state heat flow equation. | 20% |
Course Outcomes
| COs | Course Outcome Statement | KL |
|---|---|---|
| CO1 | Apply the concepts of analytic and harmonic functions and the Cauchy-Riemann equations to construct analytic functions. | K3 |
| CO2 | Apply vector differentiation and line, surface, and volume integrals, using Green's, Stokes', and Gauss's theorems, to field problems. | K3 |
| CO3 | Apply matrix methods to find rank, inverse, eigenvalues, and eigenvectors and to solve systems of linear equations. | K3 |
| CO4 | Construct the Fourier series of periodic and arbitrary-period functions and form linear partial differential equations. | K3 |
| CO5 | Apply the method of separation of variables to solve one-dimensional wave, one-dimensional heat, and two-dimensional steady-state heat-flow equations. | K3 |
| CO5 | 3 | 2 | 3 | 2 | 3 | – | 2 |
Evaluation Pattern
| Sr. | Details of the Evaluation | Weightage |
|---|---|---|
| 1. | Internal Assessment (CT + Assignment + Quiz + Attendance) | 30% |
| 2. | External Assessment | 70% |
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.
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