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AKTU Multivariable Calculus and Numerical Methods (AAS203B) Syllabus PDF – B.Tech 1st Year
Multivariable Calculus and Numerical Methods AAS203B
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Official AKTU syllabus of Multivariable Calculus and Numerical Methods (AAS203B) 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 PDFAAS203B · 4 credits · L-T-P 3-1-0
Course Objectives
- Develop the ability to solve ordinary differential equations arising in engineering applications.
- Introduce Laplace Transform techniques for solving differential equations and analyzing engineering systems.
- Build an understanding of sequences and infinite series for convergence analysis in mathematical modelling.
- Develop concepts of complex variable functions, analyticity, and conformal properties for engineering analysis.
- Apply complex integration and residue theory to evaluate integrals and solve 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 : Spring-mass-damper system modeling, Heat conduction in machine components, Mechanical control system modeling. | 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: Transient response analysis of mechanical systems, Modelling of vibration and damping systems, Dynamic response of suspension systems. | 20% |
| 3. | Sequence and Series: Definition of a Sequence, Monotonic Sequence, Convergence and Divergent Sequence, Cauchy Sequence, Necessary Condition for Convergence, Tests of Convergence: Comparison Test, Ratio Test, Raabe’s Test, Logarithmic Test Applications: Convergence analysis of iterative engineering algorithms, Computational fluid dynamics (CFD) simulations, Numerical solutions of engineering equations. | 20% |
| 4. | Complex Variables: Differentiation Functions of Complex Variables, Limit Continuity and Differentiability, Analytic Function, Cauchy- Riemann Equations (Cartesian and Polar Form), Harmonic Function, Milne-Thomson Method for constructing the Analytic Function. Applications : Two-dimensional fluid flow analysis, Stress analysis in elasticity. | 20% |
| 5. | Complex Variables: Integration 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, Evaluation of the Real definite integrals. Applications: Evaluation of contour integrals in fluid mechanics, Frequency response analysis in mechanical vibration and control systems. | 20% |
Course Outcomes
| COs | Course Outcome Statement | KL |
|---|---|---|
| CO1 | Solve higher-order linear differential equations using analytical methods and apply them to mechanical engineering systems. | K3 |
| CO2 | Apply Laplace Transform techniques to solve ordinary differential equations and analyze dynamic engineering systems. | K3 |
| CO3 | Analyze the convergence and divergence of sequences and infinite series using appropriate convergence tests. | K4 |
| CO4 | Solve analytic functions using Cauchy-Riemann equations and construct analytic functions for engineering applications. | K3 |
| CO5 | Solve complex integrals and apply residue theory to solve engineering problems involving complex functions. | 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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