**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, e
^{at}, sinh at, cosh at, t^{n}, - 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

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- 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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