AKTU B.Tech. AAS103B Differential 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, ME Stream (Mechanical Engineering). It follows the official syllabus of Differential Calculus and Linear Algebra (course code AAS103B) 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: Machine Design, Finite Element Analysis, Dynamics of Mechanical Systems.
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: Optimization and Machine Design, Fluid Mechanics, Control Systems, Stress and Strain Analysis.
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: Area of Irregular Surfaces, Volume of Solids, Fluid Mechanics, Heat Transfer.
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: Force & Moment Analysis, Mechanics of Machines, Mechanical Vibrations, CAD.
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: Fluid flow analysis, Aerodynamics, Drone navigation systems.

Course details

• University: Dr. A.P.J. Abdul Kalam Technical University (AKTU), Lucknow
• Programme: B.Tech. First Year
• Subject: Differential Calculus and Linear Algebra
• Course code: AAS103B
• Stream: ME Stream (Mechanical 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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