What to Study?
What to Study?

What to Prepare For Sem 3 Applied Maths:

Mechanical-Sem3 Maths Weightage
Mechanical-Sem3 Maths Weightage
  • 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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