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AKTU Multivariable Calculus and Numerical Methods (AAS203G) Syllabus PDF – B.Tech 1st Year
Multivariable Calculus and Numerical Methods AAS203G
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Official AKTU syllabus of Multivariable Calculus and Numerical Methods (AAS203G) 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 — Multivariable Calculus and Numerical Methods
Download PDFAAS203G · 4 credits · L-T-P 3-1-0
Course Objectives
- Develop the mathematical foundation required to solve engineering problems using differential equations, special functions, integral transforms, complex variables, and linear algebra.
- Apply advanced mathematical techniques to model, analyze, and optimize chemical engineering processes such as transport phenomena, reaction engineering, process control, and separation processes.
- Interpret mathematical models arising in chemical engineering and use appropriate analytical methods for engineering decision-making.
- Enhance analytical thinking, computational skills, and problem-solving ability for multidisciplinary engineering applications and higher studies.
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: Radial heat conduction in cylindrical and spherical reactors, Diffusion in porous catalyst particles. | 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 stirred tank reactors (CSTR), Process control and transfer function analysis | 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, Parseval’s Identity, Fourier Integral theorem, Fourier transform, Inverse Fourier Transform, Finite Fourier Sin and Cosine transform. Applications: Heat conduction in solids, Mass diffusion analysis. | 20% |
| 4. | 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: Potential flow around pipes and reactors, Two-dimensional heat conduction. | 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. Applications: Material balance calculations, Process simulation and optimization. | 20% |
Course Outcomes
| COs | Course Outcome Statement | KL |
|---|---|---|
| CO1 | Apply series solution and Frobenius method to obtain solutions of differential equations encountered in chemical engineering models. | K3 |
| CO2 | Use Laplace transform techniques to solve ordinary differential equations arising in process dynamics and control systems. | K3 |
| CO3 | Apply Fourier series and Fourier transform methods for analysis of heat transfer, diffusion, and signal processing problems in chemical engineering. | K3 |
| CO4 | Analyze complex-valued functions and apply residue calculus to solve engineering problems involving fluid flow, heat transfer, and electrochemical systems. | K4 |
| CO5 | Apply matrix decomposition techniques and linear transformations for solving systems of equations, process modeling, and computational problems in chemical engineering. | 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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