What to Study?
What to Study?
  • 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
One problem Surely asked)

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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