# What to Prepare For Sem 3 Applied Maths:

• ## 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

## 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

## Fourier Series

(Note: Simple Chapter as all the problems can be done by the same method. Very Important Chapter as 3-4 problems can be asked. It is a major chapter.Sometimes Compulsory Question is asked from this Chapter)

Engineering Branch which has this chapter in the Syllabus:

Electronics, Electrical, EXTC, Instrumentation, Computer, Mechanical, Civil, Production, Automobile, Mechatronics, Bio-Medical.

Topics to be prepared

I want to Just Pass: Problems based on Fourier Series of

• Algebraic and Exponential functions in single Range
• Algebraic and Exponential functions in multiple Range
• Even & Odd Functions: Very Important. One problem sure on this Topic.
• Half Range Series: Very Important. One problem sure on this Topic.

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

• Deductions from Fourier Series
• Parseval’s Identity
• Fourier Series of Trigonometric functions

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

• Dirichilet’s Conditions.
• Euler’s Formulae

## Complex form of Fourier Series &  Orthogonal & Orthonormal Functions

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

Engineering Branch which has this chapter in the Syllabus:

Electronics, Electrical, EXTC, Instrumentation, Computer,

Topics to be prepared

I want to Just Pass: Problems based on

• Orthogonal & Orthonormal Functions: Very Important. One problem sure in compulsory question on this Topic.

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

• Complex (or Exponential) form of Fourier Series:

## 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.

## 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.

## Partial Differential Equations & Appln

(Note: One part Very Easy Second Part Difficult. It is a Major Chapter)

Engineering Branch which has this chapter in the Syllabus:

Mechanical, Civil, Production, Automobile, Mechatronics

Topics to be prepared

I want to Just Pass: Problems based on

• Numerical Solution of Partial differential equations using Bender-Schmidt Explicit Method: Very Important. One problem on this Topic.
• Numerical Solution of Partial differential equations using simplified Crank- Nicolson implicit method: Very Important. One problem on this Topic.
• Numerical Solution of Partial differential equations using Laplace equation:

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

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

• Classification of partial differential equations of second order Heat equation, Wave equation
• Method of Separation of variables
• Solution of one dimensional heat conduction equation and steady state configuration for heat flow,
• Solution of one dimensional transverse vibrations of an elastic string,
• Laplace equation in rectangular region.
• Use of Fourier series and applications of Laplace transform in solving these equations.
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