
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, BioTechnology.
Topics to be prepared:
I want to Just Pass: Problems based on:
 Calculate Spearman Rank Correlation Coefficient with Repeated and NonRepeated 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 34 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, BioMedical, BioTechnology, 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 34 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, BioMedical, BioTechnology, 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 Heavyside 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, BioMedical, BioTechnology, Chemical.
Topics to be prepared
I want to Just Pass: Problems based on
 Cartesian form of CauchyRiemann Equations to prove Analytic Function.
 Polar form of CauchyRiemann 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, BioMedical, BioTechnology, 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 wplane for a given curve in zplane.
 Find Image in zplane for a given curve in wplane.
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, BioTechnology.
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, BioTechnology.
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, BioTechnology.
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:
BioTechnology
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 12 constraints; Very Important. One problem on this Topic.
 KuhnTucker conditions with 12 constraints: Very Important. One problem on this Topic.
 Numerical Solution of Partial differential equations using Laplace equation:
Appreciate the recommendation. Will try it out.