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AKTU Calculus and Numerical Method (AAS203E) Syllabus PDF – B.Tech 1st Year
Calculus and Numerical Method AAS203E
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Official AKTU syllabus of Calculus and Numerical Method (AAS203E) 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 Numerical Method
Download PDFAAS203E · 4 credits · L-T-P 3-1-0
Course Objectives
- Develop the ability to formulate and solve differential equations arising in engineering and scientific applications.
- Understand and apply Laplace transforms for solving differential equations and analyzing engineering systems.
- Acquire knowledge of complex variable theory and apply complex analysis techniques to engineering problems.
- Learn Fourier series and Fourier transforms for the analysis of periodic and non-periodic phenomena in engineering.
- Develop an understanding of advanced linear algebra concepts and their applications in computational and engineering problems.
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: Modeling heat transfer during textile drying and curing processes, Analysis of fiber stretching and yarn tension during spinning. | 20% |
| 2. | 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: Dynamic analysis of textile machinery and drive systems, Modeling transient heat flow in dyeing and finishing processes. | 20% |
| 3. | 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: Modeling fluid flow around textile fibers during coating and dye penetration, Analysis of electrostatic fields in electrospinning processes. | 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: Fabric defect detection using frequency-domain image processing, Signal analysis in textile quality monitoring systems. | 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: Principal Component Analysis (PCA) for textile quality inspection, Machine learning for textile defect classification using SVD. | 20% |
Course Outcomes
| COs | Course Outcome Statement | KL |
|---|---|---|
| CO1 | Solve higher-order linear differential equations using analytical methods and apply them to engineering problems. | K3 |
| CO2 | Apply Laplace transform techniques to solve ordinary differential equations and analyze dynamic engineering systems. | K3 |
| CO3 | Solve complex functions, evaluate contour integrals, determine residues, and solve engineering problems using complex variable techniques. | K3 |
| CO4 | Apply Fourier series and Fourier transform methods to analyze periodic and transient engineering signals and processes. | K3 |
| CO5 | Apply matrix decompositions, linear transformations, and vector space concepts to solve computational and engineering problems. | K3 |
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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