(SEM IV) THEORY EXAMINATION 2018-19 ENGINEERING MATHEMATICS III

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.