• ## Correlation, Regression & Curve Fitting:

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

Engineering Branch which has this chapter in the Syllabus: Computer, Mechanical, Civil, Production, Automobile, Mechatronics, Chemical, Bio-Technology.

Topics to be prepared:

I want to Just Pass: Problems based on:

• Calculate Spearman Rank Correlation Coefficient with Repeated and Non-Repeated Numbers.
• Calculate Karl Pearson Correlation Coefficient.

(Very Important. One problem on Spearman or Pearson Correlation)

• To find Lines of Regression.
• Given regression equations, find means & Correlation Coefficient: Very Important. One problem on this Topic.
• Straight Line Fitting (by Least Square Method)
• Parabolic Curve Fitting (by Least Square Method): Very Important. One problem on this Topic.

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

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

• Proofs based on Correlation and Regression

## Matrices (Eigen Values) & Quadratic Forms

(Note: Very Very Very Easy Chapter. Only a Fool will leave this Chapter. Very Important Chapter as 3-4 problems can be asked. It is a major chapter)

Engineering Branch which has this chapter in the Syllabus:
Chemical and Bio Technology

#### Topics to be prepared

I want to Just Pass: Problems based on

• Finding Eigen Values and Eigen Vectors
• Cayley Hamilton Theorem.
• Diagonalising Matrix, Modal or Transforming Matrix.
• Derogatory Matrix.
• Quadratic Forms using Congruent Transformation
• Quadratic Forms using Orthogonal Transformation
• Finding Rank, Index, Signature and Value Class

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

• Finding Algebraic and Geometric Multiplicity

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

• Theorems and Definitions.

## 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.

## Statistics – Probability Distribution, Expectation of Discrete & Continuous R.V

Engineering Branch which has this chapter in the Syllabus: Chemical and IT

#### Topics to be prepared

I want to Just Pass: Problems based on

• Bayes’ Theorem
• Discrete Probability
• Probability Distribution for Discrete and Continuous Random Variable

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

• Conditional Probability
• Expectation Calculations involving mean and standard deviations (or Variance)

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

• Calculation of Raw and Central Moments
• Interconversion of Raw and Central Moments
• Moment Generating Functions
• Skewness and Kurtosis

## Binomial and Poisson Distribution, Normal  Distribution

Engineering Branch which has this chapter in the Syllabus:
Chemical and Bio Technology

### Topics to be prepared

I want to Just Pass: Problems based on

• Fitting Binomial Distribution.
• Fitting Poisson Distribution.
• Calculation of probabilities using Binomial or Poisson Distribution.
• Calculation of parameters Binomial or Poisson Distribution.
• Calculation of probabilities using Normal Distribution.

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

• Given normal probability to find boundary value.
• Given normal probability to find mean and standard Deviation.
• Finding probabilities using Normal Approximation of Binomial Distribution.

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

• Fitting Normal Distribution.

## Complex Integration

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

Engineering Branch which has this chapter in the Syllabus:

Mechanical, Civil, Production, Automobile, Mechatronics, Bio-Technology.

#### Topics to be prepared

I want to Just Pass: Problems based on

• Complex Integration along line: Very Important. One problem sure in compulsory question on this Topic.
• Complex Integration along circle.
• Dependent / Independent of the Path

## Taylor & Laurent Series

(Note: Only chapter without Trigonometry, Derivatives and Integration

Engineering Branch which has this chapter in the Syllabus:

Mechanical, Civil, Production, Automobile, Mechatronics, Bio-Technology.

#### Topics to be prepared

I want to Just Pass: Problems based on

• Laurent Series: One problem sure in on this Topic.
• Taylor Series.

## Cauchy Integral & Residue Theorem

(Note: A lengthy chapter with very less weightage )

Engineering Branch which has this chapter in the Syllabus:
Mechanical, Civil, Production, Automobile, Mechatronics, Bio-Technology.

Topics to be prepared

I want to Just Pass: Problems based on

• Application of Residue Theorem: Very Important. One problem sure in compulsory question on this Topic.

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

• Problems based on Cauchy Integral Theorems.
• Problems based on Cauchy Integral Formula
• Problems based on Cauchy Residue Theorems.

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

• Proofs of Cauchy Integral Theorems, Cauchy Integral Formula and Cauchy Residue Theorems.

## Optimization – NLPP

Engineering Branch which has this chapter in the Syllabus:
Bio-Technology

#### Topics to be prepared:

I want to Just Pass: Problems based on

• Maximization / Minimization of Objective function
• Lagrange multiplier method for 2 or 3 variables with at 1-2 constraints; Very Important. One problem on this Topic.
• Kuhn-Tucker conditions with 1-2 constraints: Very Important. One problem on this Topic.
• Numerical Solution of Partial differential equations using Laplace equation:

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