AKTU B.Tech. AAS203E Calculus and Numerical Method 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 Technology, Handloom & Textile Technology, Carpet & Textile Technology). It follows the official syllabus of Calculus and Numerical Method (course code AAS203E) 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.
• Two AKTU-format model question papers, each followed by complete solutions.

Unit-wise syllabus coverage

1. Unit 1 – 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. Applications: Modeling heat transfer during textile drying and curing processes, Analysis of fiber stretching and yarn tension during spinning.
2. Unit 2 – Laplace Transform: Definition of Laplace Transform, Existence Conditions, Linearity Property, Laplace Transform of some standard functions, I and II Shifting theorems (without proof), Change of Scale Property, Laplace transform of derivatives and integrals, Periodic Functions, Unit Step Function, Inverse Laplace Transform, Partial Fraction Method, Convolution theorem (without proof), Application of Laplace transform to solve ordinary differential equations. Applications: Dynamic analysis of textile machinery and drive systems, Modeling transient heat flow in dyeing and finishing processes.
3. Unit 3 – Complex Analysis: Functions of Complex Variables, Limit, Continuity and Differentiability, Analytic Function, Cauchy–Riemann Equations (Cartesian and Polar Form), Harmonic Function, Milne– Thomson Method, Complex integrals, Cauchy Integral theorem (without proof), Cauchy integral formula (without proof), Taylor’s series and Laurent’s series, Singularities, Residue of a function, Cauchy Residue Theorem, Evaluating the Real definite integrals. Applications: Modeling fluid flow around textile fibers during coating and dye penetration, Analysis of electrostatic fields in electrospinning processes.
4. Unit 4 – Fourier Series and Fourier Transform: Periodic function, even and odd function, Dirichlet’s Condition for the Existence of a Fourier Series, Fourier series expansion of a function in the interval c to c + 2l, Change of Interval, Half Range Series: Half range sine and cosine series in the interval −l to l, Parseval’s Identity, Fourier Integral theorem, Fourier transform, Inverse Fourier Transform, Finite Fourier Sine and Cosine transform. Applications: Fabric defect detection using frequency-domain image processing, Signal analysis in textile quality monitoring systems.
5. Unit 5 – Applied Linear Algebra: Eigen Value Decomposition and Singular Value Decomposition, Matrix factorization, LU Decomposition (Doolittle method), QR Decomposition, Linear transformation, Matrix representation of Linear Transformation, Kernel and Range, Introduction to inner product space, Norm of a vector. Applications: Principal Component Analysis (PCA) for textile quality inspection, Machine learning for textile defect classification using SVD.

Course details

• University: Dr. A.P.J. Abdul Kalam Technical University (AKTU), Lucknow
• Programme: B.Tech. First Year, Semester II
• Subject: Calculus and Numerical Method
• Course code: AAS203E
• Stream: TX Stream
• 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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