AKTU B.Tech. AAS203C Calculus, Laplace Transform and Numerical Techniques 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, EE Stream and ECE Stream (Electrical, Electrical & Electronics, Electrical & Computer; Electronics, Electronics & Communication, VLSI Design, Electronics & Instrumentation, Instrumentation & Control, Electronics & Computer). It follows the official syllabus of Calculus, Laplace Transform and Numerical Techniques (course code AAS203C) 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 – Series Solution and Special Functions: Ordinary and singular point, Series solution about an ordinary point, Solution of equation by Frobenius method to solve second order linear differential equations, formation of Indicial equation, Determination of indicial roots, cases of indicial roots: Distinct roots, equal roots, roots differ by an integer and not differ by an integer. Applications: Fluid mechanics, quantum mechanical wave equation, Heat transfer, Solving electromagnetic field equation.
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: Transfer Function Determination, Circuit Equations, Step Response.
3. Unit 3 – 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: Computer Graphics, Cyber Security, Digital Image Processing, Machine Learning Feature Extraction, Image compression.
4. Unit 4 – 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: Network Theory, Electromagnetic Waves, Transmission line.
5. Unit 5 – Sequence and Series: Definition of a Sequence, Monotonic Sequence, Convergence and Divergent Sequence, Cauchy Sequence, Necessary Condition for Convergence, Tests of Convergence: Comparison Test, Ratio Test, Raabe’s Test, Logarithmic Test. Applications: Discrete Time Signal Representation.

Course details

• University: Dr. A.P.J. Abdul Kalam Technical University (AKTU), Lucknow
• Programme: B.Tech. First Year, Semester II
• Subject: Calculus, Laplace Transform and Numerical Techniques
• Course code: AAS203C
• Stream: EE Stream and ECE Stream
• Credits: 4
• PDF length: 83 pages
• Format: PDF

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

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