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AKTU Differential Calculus and Linear Algebra (AAS103G) Syllabus PDF – B.Tech 1st Year
Differential Calculus and Linear Algebra AAS103G
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Official AKTU syllabus of Differential Calculus and Linear Algebra (AAS103G) 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 — Differential Calculus and Linear Algebra
Download PDFAAS103G · 4 credits · L-T-P 3-1-0
Course Objectives
- Apply differential calculus to analyze and optimize chemical engineering processes.
- Use multiple integrals to solve problems involving area, volume, mass, and energy distribution.
- Apply matrix algebra to solve linear systems and analyze chemical processes.
- Solve differential equations related to reaction kinetics, reactor design, and mass transfer.
- Apply vector calculus to analyze fluid flow and transport phenomena in chemical engineering.
Course Content
| Unit | Description | Weightage |
|---|---|---|
| 1. | Differential Calculus : Introduction of Limits, continuity and differentiability for function of two variables, Partial derivatives, Composite functions, Total derivative, Euler’s Theorem for homogeneous functions, Taylor’s and Maclaurin’s expansion for function of two variables, Jacobians, properties of Jacobian (without proof), Maxima & Minima for a function of up to two variables. Application: Determining reaction rates, mass transfer and diffusion studies, optimization of chemical process. | 20% |
| 2. | Multiple Integrals: Evaluation of double and triple integrals, change of order of integration, Change of variable (double -integral).Beta and Gamma functions, Properties of Beta and Gamma function. Dirichlet’s Integral. Application of double integrals and Triple Integral to find area and volume. Applications: Determining mass and energy distribution, calculation of reactor and storage tank volume. | 20% |
| 3. | Matrix Algebra: Introduction to Matrices, Elementary Transformation, Inverse by E-transformation, Rank of a Matrix by Echelon Form, Solution of system of linear Equations by direct method (Gauss Elimination Method), and Iterative method (Gauss Seidel Method), Eigen Values & Eigen Vectors, Diagonalization, Application: Process simulation and optimization, chemical reaction network analysis. | 20% |
| 4. | 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. Application: Chemical reaction Kinetics, reactor design, mass transfer. | 20% |
| 5. | Vector Calculus: Scalar point function, Vector point function, Gradient of a scalar field, Directional derivatives, Divergence and curl of a vector function and their application to solenoidal and irrotational vectors respectively .Integration of Vectors, Stokes Theorem and Gauss Divergence Theorem(Without Proof). Applications: Fluid flow in pipes and reactors, computational fluid dynamics (CFD). | 20% |
Course Outcomes
| COs | Course Outcome Statement | KL |
|---|---|---|
| CO1 | Apply differential calculus to analyze and optimize chemical engineering processes. | K3 |
| CO2 | Use multiple integrals to solve area, volume, mass, and energy distribution problems. | K3 |
| CO3 | Apply matrix algebra to solve engineering systems and process optimization problems. | K3 |
| CO4 | Solve differential equations related to chemical reactions and reactor analysis. | K3 |
| CO5 | Apply vector calculus to analyze fluid flow and transport phenomena in chemical engineering. | 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.
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