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AKTU Numerical Methods (AAS203D) Syllabus PDF – B.Tech 1st Year
Numerical Methods AAS203D
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Official AKTU syllabus of Numerical Methods (AAS203D) 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.
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Syllabus — Numerical Methods
Download PDFAAS203D · 4 credits · L-T-P 3-1-0
Course Objectives
- Understand advanced mathematical concepts used in engineering and computing.
- Develop analytical and problem-solving skills using differential equations, complex analysis, transforms, and linear algebra.
- Apply mathematical techniques to model and solve real-world problems in computer science and engineering.
- Build a strong foundation for advanced studies in data science, artificial intelligence, machine learning, computer graphics, and cyber security.
Course Content
| Unit | Description | Weightage |
|---|---|---|
| 1. | Differential Equations: Linear differential equation of nth order with constant coefficients, Cauchy- Euler equation, solution of second order linear differential equations with variable coefficient by the method of variation of parameters, change of independent variable, normal form. Applications: Cloud Computing, Computer Networks, Cyber Security | 20% |
| 2. | Complex Analysis: Functions of Complex Variables, Limit Continuity and Differentiability, Analytic Function, Cauchy-Riemann Equations (Cartesian and Polar Form), Harmonic Function, Milne- Thomson Method, Complex integrals, Cauchy- Integral theorem (without proof), Cauchy integral formula (without proof), Taylor’s series and Laurent’s series, Singularities, Residue of a function, Cauchy Residue Theorem, Evaluating the Real definite integrals. Applications: Image Processing and Computer Design, Quantum Computing | 20% |
| 3. | Laplace Transform: Definition of Laplace Transform, Existence Conditions, Linearity Property, Laplace Transform of some standard functions, I and II Shifting theorems (without proof), Change of Scale Property, Laplace transform of derivatives and integrals, Periodic Functions, Unit Step Function, Inverse Laplace Transform, Partial Fraction Method, Convolution theorem (without proof), Application of Laplace transform to solve ordinary differential equation. Applications: Database Systems, Algorithmic Modelling | 20% |
| 4. | Fourier Series& Fourier Transform: Periodic function, even and odd function, Dirichlet’s Condition for the Existence of a Fourier Series, Fourier series expansion of a function in the interval c to c+2l,Change of Interval, Half Range Series: Half range sine and cosine series in the interval -l to l, Parseval’s Identity. Fourier Integral theorem, Fourier transform, Inverse Fourier Transform, Finite Fourier Sin and Cosine transform. Applications: Computer Graphics, Cyber Security, Digital Image Processing, Machine Learning Feature Extraction, Image compression. | 20% |
| 5. | Applied Linear Algebra: Eigen Value Decomposition and Singular Value Decomposition, Matrix factorization, LU Decomposition (Dolittle method), QR Decomposition, Linear transformation, Matrix representation of Linear Transformation, Kernel and Range, Introduction to inner product space, Norm of a vector. Application: 2D & 3D graphics, Neural Networks, Cryptography | 20% |
Course Outcomes
| COs | Course Outcome Statement | KL |
|---|---|---|
| CO1 | Solve higher-order differential equations and apply them to computational models in cloud computing, computer networks, and cyber security. | K3 |
| CO2 | Analyze complex functions and evaluate complex integrals for applications in image processing, computer design, and quantum computing. | K4 |
| CO3 | Apply Laplace transform techniques to solve differential equations arising in database systems and algorithmic modelling. | K3 |
| CO4 | Use Fourier series and Fourier transform techniques for signal processing, image analysis, computer graphics, machine learning, and cyber security. | K3 |
| CO5 | Apply matrix decomposition techniques and linear transformations to computational problems in graphics, neural networks, and cryptography. | 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.
Evaluation Pattern
| Sr. | Details of the Evaluation | Weightage |
|---|---|---|
| 1. | Internal Assessment (CT + Assignment + Quiz + Attendance) | 30% |
| 2. | External Assessment | 70% |
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