AKTU B.Tech. AAS103C 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, ECE Stream (Electronics and Communication Engineering). It follows the official syllabus of Differential Calculus and Linear Algebra (course code AAS103C) 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 – 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: Signal strength analysis, Communication system optimization, Frequency response analysis, Amplifier gain optimization, Antenna parameter optimization.
2. Unit 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: Electromagnetism, Wireless Communication, Antenna Theory.
3. Unit 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. Applications: Error detection and correction codes, Loop Current Analysis.
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: Digital signal processing (DSP), wireless communication, antenna array processing, image.
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: Electromagnetism, Wireless Communication, Antenna Theory.

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: AAS103C
• Stream: ECE Stream (Electronics and Communication Engineering)
• Credits: 4
• PDF length: 84 pages
• Format: PDF

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

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