What to Study?
What to Study?

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

1 COMMENT

LEAVE A REPLY

Please enter your comment!
Please enter your name here