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AKTU Calculus and Numerical Methods (AAS203F) Syllabus PDF – B.Tech 1st Year
Calculus and Numerical Methods AAS203F
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Official AKTU syllabus of Calculus and Numerical Methods (AAS203F) 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 Methods
Download PDFAAS203F · 4 credits · L-T-P 3-1-0
Course Objectives
- Understand advanced mathematical techniques such as series solutions, integral transforms, complex analysis, and applied linear algebra for solving engineering problems.
- Apply mathematical methods to model, analyze, and solve problems encountered in biotechnology, biochemical engineering, and life sciences.
- Develop analytical and computational skills for interpreting biological systems, signal processing, and experimental data.
- Utilize mathematical tools for research, simulation, optimization, and multidisciplinary applications in biotechnology.
Course Content
| Unit | Description | Weightage |
|---|---|---|
| 1. | Series Solution & Special Functions: Ordinary and singular point, Series solution about an ordinary point, Solution of equation by Frobenius method to solve second order linear differential equation, formation of Indicial equation, Determination of indicial roots, cases of indicial roots: Distinct roots, equal roots, roots differ by an integer and not differ by an integer. Applications: Modeling enzyme kinetics using differential equations, Population growth and microbial growth models | 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 bioreactors, Pharmacokinetic and pharmacodynamic modeling. | 20% |
| 3. | 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, Fourier Integral theorem, Fourier transform, Inverse Fourier Transform, Finite Fourier Sin and Cosine transform. Applications: ECG and EEG signal analysis, DNA and protein sequence signal processing. | 20% |
| 4. | Numerical Methods I: Zeroes of transcendental and polynomial equations using Bisection method, Regula-falsi method and Newton-Raphson method, Rate of convergence of above methods. Interpolation: Finite differences, Newton’s forward and backward interpolation, Lagrange’s and Newton’s divided difference formula for unequal intervals. Applications: Enzyme Kinetics, Drug Concentration Estimation, Microbial Growth Analysis, Bioprocess Data Analysis | 20% |
| 5. | Numerical Methods II: Solution of system of linear equations, Matrix Decomposition method, Jacobi method, Gauss- Seidel method. Numerical differentiation, Numerical integration, Trapezoidal rule, Simpson’s one third and three-eight rules, Solution of ordinary differential equations by Picard’s and fourth-order Runge-Kutta methods. Applications: Pharmacokinetic Modeling, Population Growth Models, Nutrient Transport, Numerical Solution of Biological ODEs. | 20% |
Course Outcomes
| COs | Course Outcome Statement | KL |
|---|---|---|
| CO1 | Apply series solutions and Frobenius method to solve differential equations arising in biotechnology and biological systems. | K3 |
| CO2 | Use Laplace Transform techniques to solve differential equations encountered in biochemical processes and dynamic biological models. | K3 |
| CO3 | Apply Fourier Series and Fourier Transform techniques for analyzing biological signals and biomedical data. | K3 |
| CO4 | Utilize concepts of complex analysis to solve engineering and biological problems involving fluid flow, transport phenomena, and potential functions. | K3 |
| CO5 | Apply eigenvalue methods, matrix decompositions, and linear transformations to analyze biological datasets, bioinformatics problems, and computational models. | 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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