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Unit - 1 Laplace Transform

Module1Laplace Transform

1.1 Laplace transform Existence theorem

1.2 Laplace transforms of derivatives and integrals

1.3 Initial and final value theorems

1.4 Unit step function Dirac delta function

1.5 Laplace transform of a periodic function

1.6 Inverse Laplace transform Convolution theorem

1.7 Application to solve simple linear and simultaneous differential equations

Unit - 2 Integral Transforms

Module2Integral Transform

2.1 Fourier integral Fourier Transform Complex Fourier transform

2.2. Inverse Transforms Convolution Theorems

2.3 Fourier sine and cosine transform

2.4 Applications of Fourier transform to simple onedimensional heat transfer equations Wave equations and Laplace equations

2.5 ZTransform and its application to solve differential equations.

Unit - 3 Formal Logic ,Group, Ring and Field

Module3Formal logic group ring and field

3.1 Introduction to Firstorder logic proposition Algebra of Proposition Logical connectives

3.2. Tautologies Contradictions and contingency

3.3. Logical implication Argument Normal form Rules of inferences

3.4 Semigroup Monoid Group Group

3.5 Cosets Lagrange’s theorem Congruence relation

3.6 Cyclic and permutation groups

3.7 Properties of groups

3.8. Rings and Fields definition examples and standard results only

Unit - 4 Set, Relation, function and Counting Techniques

Module4Set Relation function and Counting Techniques

4.1. Introduction of Sets

4.2. Relation and Function

4.3. Methods of Proof Mathematical Induction Strong Mathematical Induction

4.4. Discrete numeric function generating functions

4.5. Recurrence relations and their solution Pigeonhole principle.

Unit - 5 Lattices and Boolean Algebra

Module5Lattices and Boolean Algebra

5.1. Introduction Partially ordered sets Hasse Diagram

5.2. Maximal and Minimal element Upper and Lower Bounds

5.3 Isomorphic ordered sets

5.4 Lattices Bounded Lattices and Distributive Lattices.

5.5 Duality

5.6 Boolean Algebras as Lattices

5.7 Minimization of Boolean Expressions prime Implicants

5.8 Logic Gates and Circuits

5.9 Truth Table Boolean Functions Karnaugh Maps.

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