## Laplace Transform I

Engineering Branch which has this chapter in the Syllabus:

Electronics, Electrical, EXTC, Instrumentation, Computer, IT, Mechanical, Civil, Production, Automobile, Mechatronics, Bio-Medical, Bio-Technology, Chemical.

Topics to be prepared

I want to Just Pass: Problems based on:

• Definition of Laplace Transform: This type of problems involves integrations.
• Formula based: Here students needs to use Laplace Transform of sin at, cos at, eat, sinh at, cosh at, tn,
• First Shifting Property
• Multiplication by ‘t’ Property
• Division by ‘t’ Property
• Laplace of Integration
• Evaluation of Definite Integrals using Laplace Transform
• Combination of Properties of Laplace Transform

I want to get good Marks: (As above and plus)

• Laplace of Derivatives
• Second Shifting Property
• Change of Scale Property
• Error function, sin , cos

I want to Score Maximum: (As above and plus)

• Theorems on properties of Laplace Transform
• Periodic Function

## Laplace Inverse

(Note: Very Important Chapter as 3-4 problems can be asked. It is a major chapter)

Engineering Branch which has this chapter in the Syllabus:

Electronics, Electrical, EXTC, Instrumentation, Computer, IT, Mechanical, Civil, Production, Automobile, Mechatronics, Bio-Medical, Bio-Technology, Chemical.

Topics to be prepared

I want to Just Pass: Problems based on

• Partial Fractions: With Linear factors, quadratic factors etc. and their combination.
• Completing the square Method
• Convolution Theorem: Very Important. One problem sure on this Topic
• Division by s
• Application to Differential Equations: Very Important. One problem sure on this Topic. Solution of ordinary differential equations of first order and second order with boundary condition using Laplace transform

I want to get good Marks: (As above and plus)

• Multiplication by ‘s’
• Laplace of Heavy-side Functions and Laplace inverse

I want to Score Maximum: (As above and plus)

• Theorems on properties of Laplace Inverse
• Dirac Delta Function

## Complex Variable

(Note: Sometimes One Compulsory Question is asked from this Chapter)

Engineering Branch which has this chapter in the Syllabus:

Electronics, Electrical, EXTC, Instrumentation, Computer, IT, Civil, Production, Automobile, Mechatronics, Bio-Medical, Bio-Technology, Chemical.

Topics to be prepared

I want to Just Pass: Problems based on

• Cartesian form of Cauchy-Riemann Equations to prove Analytic Function.
• Polar form of Cauchy-Riemann Equations to prove Analytic Function.
• Find Constants if the given functions is Analytic.
• Harmonic Function;
• Milne Thompson method
• Given ‘u’ find f (z) & v: Very Important.
• Given ‘v’ find f (z) & u: Very Important.
• Given ‘u ± v’ find f (z): Very Important.
• Orthogonal Trajectory: Very Important.

I want to get good Marks: (As above and plus)

• Theorems of Complex Variable

I want to Score Maximum: (As above and plus)

• Angle between Curves in polar forms
• Checking Analyticity using Limits.
• Prove that problems

## Conformal Mapping

(Note: An Easy Chapter. One problem asked in compulsory question)

Engineering Branch which has this chapter in the Syllabus:

Electronics, Electrical, EXTC, Instrumentation, Computer, IT, Civil, Production, Automobile, Mechatronics, Bio-Medical, Bio-Technology, Chemical.

Topics to be prepared

I want to Just Pass: Problems based on

• Bilinear Transformation: Very Important.
• To find Invariant or Fixed points.

I want to get good Marks: (As above and plus)

• Find Image in w-plane for a given curve in z-plane.
• Find Image in z-plane for a given curve in w-plane.

## Set Theory & Pigeon-Hole Principle

(Note: School Level Chapter. Very Easy Chapter. Only a Fool will leave this Chapter)

Engineering Branch which has this chapter in the Syllabus: IT

Topics to be prepared

#### I want to Just Pass: Problems based on

• Venn Diagrams
• Cartesian Products
• Counting principle, Cardinality and Countability (Countable and Uncountable sets)
• Pigeonhole Principle: Very Important. One problem on this Topic.

#### I want to get good Marks: (As above and plus)

• Definition of Sets and different types, Operations on Sets

#### I want to Score Maximum: (As above and plus)

• Proofs of some general identities on sets.

## Relation & Functions

(Note: An easy Chapter)

Engineering Branch which has this chapter in the Syllabus: IT

#### Topics to be prepared

I want to Just Pass: Problems based on

• Composition of Functions. One problem on this Topic.
• Pictorial representation of relation using Digraph
• Equivalence Relations.
• Symmetric and Reflexive Closure.
• Transitive Closure using Warshall Technique. Very Important.

I want to get good Marks: (As above and plus)

• Definitions of types of Relations and Functions.
• Properties of relation.
• Partial Ordering Relation, POSETS.

I want to Score Maximum: (As above and plus)

• Domain and Range of a relation.
• Recursively Defined Functions.

## Permutations, Combinations & Probability

(Note: Totally New Chapter)

Engineering Branch which has this chapter in the Syllabus: IT

#### Topics to be prepared

I want to Just Pass: Problems based on

• Bayes’ Theorem
• Discrete Probability

I want to get good Marks: (As above and plus)

• Conditional Probability

I want to Score Maximum: (As above and plus)

• Find Permutations and Combinations
• Algorithms for generation of Permutations and Combinations
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