AKTU B.Tech. AAS203A Differential Calculus and Numerical Methods 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, CE Stream (Civil Engineering, Environmental Engineering). It follows the official syllabus of Differential Calculus and Numerical Methods (course code AAS203A) 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: Structural vibration analysis of buildings and bridges, Deflection analysis of beams and columns.
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 structures subjected to earthquake loading, Vibration analysis of bridges and tall buildings.
3. Unit 3 – 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: Convergence analysis in finite element methods (FEM), Numerical solutions for structural analysis.
4. Unit 4 – Complex Variable: Differentiation: Functions of Complex Variables, Limit, Continuity and Differentiability, Analytic Function, Cauchy–Riemann Equations (Cartesian and Polar Form), Harmonic Function, Milne– Thomson Method for constructing the Analytic Function. Applications: Two-dimensional seepage flow through soils, Potential flow around bridge piers and hydraulic structures.
5. Unit 5 – Complex Variable: Integration: 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: Stress concentration analysis around tunnels, openings, and cracks, Evaluation of contour integrals in elasticity problems.

Course details

• University: Dr. A.P.J. Abdul Kalam Technical University (AKTU), Lucknow
• Programme: B.Tech. First Year, Semester II
• Subject: Differential Calculus and Numerical Methods
• Course code: AAS203A
• Stream: CE Stream
• Credits: 3
• PDF length: 81 pages
• Format: PDF

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

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