(SEM IV) THEORY EXAMINATION 2022-23 MATHEMATICS III

SECTION A — What This Section Covers

Section A contains 10 short 2-mark questions that test the student’s basic understanding of Laplace transform, Z-transform, Fourier integrals, group theory, permutations, relations, lattices, Boolean algebra, and simple set theory problems.

This section checks fundamental concepts like unit step Laplace transform, existence conditions of Laplace transform, Z-transform computations, Fourier integral representation, classification of even/odd permutation, Lagrange’s theorem in group theory, simple set operations, differentiability of piecewise functions, lattice properties, and Boolean absorption laws.

It ensures the student understands foundational definitions, formulas, and reasoning principles before proceeding to long-answer questions.

SECTION B — What This Section Covers

Section B consists of any three descriptive 10-mark questions involving applications of transforms, logic, and recurrence relations.

It includes problems on inverse Laplace transform using convolution, solving the heat equation using Fourier transform, checking validity of a logical argument, solving recurrence relations, and converting Boolean expressions into DNF and CNF.

This section evaluates the ability to perform transform techniques, apply mathematical logic rules, solve difference equations, and rewrite Boolean expressions in standard forms.

SECTION C — What This Section Covers

Section C requires attempting one part from each question (3 to 7), covering higher-order applications of Laplace transforms, Z-transforms, Fourier transforms, group theory, logic, mathematical induction, and relations.

Topics include solving differential equations using Laplace transform, finding Laplace of piecewise functions, applying Fourier transforms to specific functions, solving difference equations using Z-transform, proving rational numbers form an abelian group, identifying tautology/contradiction/contingency, proving statements using mathematical induction, testing equivalence or partial order relations, constructing Hasse diagrams for posets, and designing switching circuits from Boolean expressions.

This section tests deeper understanding and application of advanced transform methods, abstract algebra, discrete mathematics, relations and logic systems, and circuit representation.