Other university all, Civil Engineering , Mathematics-3 Syllabus

MODULE I

Laplace Transform 
Laplace transform, Existence theorem, Laplace transforms of derivatives and integrals, Initial
and final value theorems, Unit step function, Dirac- delta function, Laplace transform of periodic
function, Inverse Laplace transform, Convolution theorem, Application to solve simple linear
and simultaneous differential equations.

MODULE II
Integral Transforms 
Fourier integral, Fourier Transform , Complex Fourier transform, Inverse Transforms,
Convolution Theorems, Fourier sine and cosine transform, Applications of Fourier transform to simple one dimensional heat transfer equations, wave equations and Laplace equations, Z-
Transform and its application to solve difference equations.

Module- III
Formal Logic ,Group, Ring and Field: Introduction to First order logic, Proposition, Algebra
of Proposition, Logical connectives, Tautologies, contradictions and contingency, Logical
implication, Argument, Normal form, Rules of inferences, semi group, Monoid Group, Group,
Cosets, Lagrange’s theorem , Congruence relation , Cyclic and permutation groups, Properties
of groups, Rings and Fields (definition, examples and standard results only)

Module- IV 
Set, Relation, function and Counting Techniques - Introduction of Sets, Relation and
Function, Methods of Proof, Mathematical Induction, Strong Mathematical Induction, Discrete
numeric function and Generating functions, recurrence relations and their solution , Pigeonhole
principle.

Module- V 
Lattices and Boolean Algebra: Introduction, Partially ordered sets, Hasse Diagram, Maximal
and Minimal element, Upper and Lower bounds, Isomorphic ordered sets, Lattices, Bounded
Lattices and , Distributive Lattices.
Duality, Boolean Algebras as Lattices, Minimization of Boolean Expressions, prime Implicants,
Logic Gates and Circuits, Truth Table, Boolean Functions, Karnaugh Maps.

Text Books
1. E. Kreyszig: Advanced Engineering Mathematics; John Wiley & Sons.
2. R.K. Jain & S.R.K. Iyenger: Adnanced Engineering Mathematics, Narosa Publishing
House.
3. C.L.Liu: Elements of Discrete Mathematics; Tata McGraw- Hill Publishing Company
Limited, New Delhi.

4. S. Lipschutz, M.L. Lipson and Varsha H. Patil: Discrete Mathematics; Tata McGraw-
Hill Publishing Company Limited, New Delhi

5. B. Kolman , Robert C. Busby & S. C. Ross: Discrete Mathematical Structures’ 5
th Edition, Perason Education ( Singapore), Delhi, India.

Reference Books
1. B.S. Grewal: Higher Engineering Mathematics; Khanna Publishers, New Delhi.
2. B.V. Ramana: Higher Engineering Mathematics; Tata McGraw- Hill Publishing
Company Limited, New Delhi.
3. Peter V.O’ Neil. Advanced Engineering Mathematics, Thomas ( Cengage) Learning.
4. Kenneth H. Rosem: Discrete Mathematics its Application, with Combinatorics and Graph
Theory; Tata McGraw- Hill Publishing Company Limited, New Delhi
5. K.D. Joshi: Foundation of Discrete Mathematics; New Age International (P) Limited,
Publisher, New Delhi.