AKTU B.Tech. AAS103E Calculus and Linear Algebra Solved Question Bank

This EduQuest solved question bank supports exam preparation for Dr. A.P.J. Abdul Kalam Technical University (AKTU) B.Tech. First Year, TX Stream (Textile Engineering). It follows the official syllabus of Calculus and Linear Algebra (course code AAS103E) unit by unit.

What is included

• Quick revision sheet of key formulae at the start of every unit.
• 12 short answer questions (2 marks) per unit with exam-ready answers.
• 12 long answer questions (7 marks) per unit with complete step-by-step solutions, diagrams and numericals.
• MOST IMPORTANT and IMPORTANT tags with a summary list for each unit.
• AKTU-format model question papers with complete solutions.

Unit-wise syllabus coverage

1. Unit 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).
2. Unit 2 – 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. Applications: Fibre stress and strain analysis, Textile machine design.
3. Unit 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.
4. Unit 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.
5. Unit 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.

Course details

• University: Dr. A.P.J. Abdul Kalam Technical University (AKTU), Lucknow
• Programme: B.Tech. First Year
• Subject: Calculus and Linear Algebra
• Course code: AAS103E
• Stream: TX Stream (Textile Engineering)
• Credits: 4
• PDF length: 85 pages
• Format: PDF

Use this question bank along with the official syllabus, your class notes and the prescribed text books.

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