ENGINEERING MATHEMATICS – III (RAS-401), B.Tech Semester IV
This is a 70-mark, 3-hour theory examination designed to assess a student’s command over complex analysis, numerical methods, Fourier transforms, Z-transforms, curve fitting, probability distributions, and differential equation solving techniques. The paper evaluates conceptual understanding as well as problem-solving abilities.
SECTION A — Short Answer Questions (2 × 7 = 14 Marks)
This section contains seven brief questions to test fundamentals across various mathematical domains.
Topics include:
Cauchy Integral Theorem (Complex Analysis)
Missing value using finite differences (Interpolation Table)
Binomial distribution + mean & standard deviation
Simpson’s 3/8 rule (Numerical Integration)
Average and central difference operators
Condition number (Matrix theory / Numerical stability)
Inverse Z-transform
These questions check definitions, basic formulas, and direct short answers.
SECTION B — Descriptive Questions (7 × 3 = 21 Marks)
Students must attempt any 3 out of 5 questions.
Topics require detailed explanation, derivation, or multi-step solution:
Analyticity of complex functions Least squares method (curve fitting for straight line)
Euler’s method for solving differential equations Fourth-order Runge–Kutta method
Fourier sine transform applications
This section checks problem-solving ability and conceptual clarity in numerical techniques and transforms.
SECTION C — Long Answer Questions (7 marks each)
Each question offers choice (a or b) and requires in-depth solution, derivation, or numerical procedure.
Major topics covered:
Contour integration using Cauchy's theorem and formula
Fourier transform of exponential functions Z-transform of hyperbolic cosine functions
Probability distributions (Poisson / Binomial approximations) Normal distribution applications
Newton–Raphson method Lagrange interpolation
Solving linear equations by Crout’s method Picard’s method for differential equations
This section tests advanced problem-solving, logical steps, numerical calculations, and strong understanding of mathematical tools.
OVERALL PURPOSE OF THE EXAM
This question paper is designed to thoroughly test a student's ability to:
Apply complex analysis (contour integrals, Cauchy theorems)
Solve ODEs using numerical methods (Euler, RK-4, Picard)
Use interpolation and curve fitting
Perform Fourier and Z-transforms
Apply probability distributions to real-world data
Work with numerical linear algebra (Crout’s method)
Perform scientific computations with accuracy and reasoning
It evaluates both theoretical understanding and practical mathematical computation skills, ensuring students are ready for engineering applications.
