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AKTU Calculus and Linear Algebra (AAS103E) Syllabus PDF – B.Tech 1st Year
Calculus and Linear Algebra AAS103E
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Official AKTU syllabus of Calculus and Linear Algebra (AAS103E) 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 Linear Algebra
Download PDFAAS103E · 4 credits · L-T-P 3-1-0
Course Objectives
- Apply matrix algebra techniques to solve engineering problems related to textile manufacturing, quality control, and CAD applications.
- Use differential calculus to analyze and optimize fibre properties, textile machine performance, and material behavior.
- Apply multiple integrals to compute area, volume, and mass in textile materials and manufacturing processes.
- Understand vector spaces and linear transformations for textile design, quality assessment, and colour analysis.
- Apply vector calculus concepts to analyze airflow, heat transfer, and fluid flow in textile engineering systems.
Course Content
| Unit | Description | Weightage |
|---|---|---|
| 1. | 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, Applications : Quality control, Computer-Aided Textile (CAD), Finite Element Analysis (FEA) | 20% |
| 2. | Differential Calculus: Introduction to 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. Applications: Fibre stress and strain analysis, Textile machine design | 20% |
| 3. | 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: Fabric area and volume calculation, mass calculation | 20% |
| 4. | Vector Spaces: Vector spaces (over the field of real numbers), Subspaces, Spanning set, Linear independence, Basis and Dimension. Linear transformations, Range and Null space, Rank- Nullity theorem, Matrix of a linear transformation. Applications: Fabric structured design, quality control and defect detection, colour analysis and dye matching. | 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: Airflow through fabrics, Computational Fluid Dynamics (CFD), Heat transfer | 20% |
Course Outcomes
| COs | Course Outcome Statement | KL |
|---|---|---|
| CO1 | Apply matrix algebra to solve engineering problems in textile quality control and CAD. | K3 |
| CO2 | Use differential calculus for analysis and optimization in textile engineering. | K3 |
| CO3 | Apply multiple integrals to compute area, volume, and mass in textile applications. | K3 |
| CO4 | Use vector spaces and linear transformations in fabric design and quality analysis. | K3 |
| CO5 | Apply vector calculus to analyze airflow, heat transfer, and fluid flow in textiles. | K3 |
CO–PO Articulation Matrix
Evaluation Pattern
| Sr. | Details of the Evaluation | Weightage |
|---|---|---|
| 1. | Internal Assessment (CT + Assignment + Quiz + Attendance) | 30% |
| 2. | External Assessment | 70% |
Text Books
- 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
- E. Kreyszig, Advance Engineering Mathematics, John Wiley & Sons, 2005.
- 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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