B.E. (All Branches) – Semester IV – Engineering Mathematics – IV

Subject Teachers:
Civil : Mr.Praveen H Patil
Mech : Mr.Eshwar.T
CSE/ISE : Dr.Savitramma G
EEE/ECE : Dr.Savitramma G

PART-A

Chapter-1:Numerical Methods-1

Lecture-1 Numerical solution of ODE’s of First order and first degree by Picard’s Method

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Lecture-2 Taylor’s Series Method

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Lecture-3 Problems on Taylor’s Series Method

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Lecture-4 Modified Euler’s Method

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Lecture-5 Runge-Kutta Method of Fourth Order

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Lecture-6 Predictor and Corrector Methods

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Lecture-7 Adams-Bashforth Method

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Unit-2 :Numerical Methods-2

Lecture-8 Picard’s Method

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Lecture-9 Runge-Kutta Method of 4th Order

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Lecture-10 Numerical Solution of Second Order ODEs by Picard’s & Runge-Kutta Methods

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Lecture-11 Problems on Picard’s & Runge-Kutta Methods

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Lecture-12 Milne’s Method

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Lecture-13 Problems on Milne’s Predictor & Corrector Method

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Unit 3 :Complex Variables-1

Lecture-14 Basic concept of Complex Analysis

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Lecture-15 Cauchy-Riemann equations in the Cartesian form & Polar form

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Lecture-16 Problems on Analytic functions-Type-1

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Lecture-17:Problems on Analytic Functions Type-II.

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Lecture-18 Harmonic function & Harmonic conjugate

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Lecture-19 Applications to flow problems

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Unit -4 Complex Variables-2

Lecture-20 Conformal Transformations

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Lecture-21 Bilinear Transformation

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Lecture-22 Discussion of Confomal Transformations

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Lecture-23 Complex Integration

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Lecture-24 Cauchy’s Theorem

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Lecture-25 Cauchy’s Integral Formula

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Lecture-26 Problems on Cauchy’s Integral Formula

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PART-B

unit 5 : Special Functions

Lecture 27 :Bessel’s Differential Equation

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Lecture 28:Series solution of Bessel’s Differential equation leading to Bessels functions

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Lecture-29 : Properties of Bessel functions

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Lecture 30:Recurrence Relations

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Lecture 31:Recurrence Relations(Cont…)

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Lecture 32: Orthogonal Property of Bessel functions

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Lecture 33:Legendre Polynomials &Rodrigue’s formula

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Unit 6:Probability Theory -1

Lecture 34: Introduction to Probability Theory

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Lecture 35: Probability Theorems

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Lecture 36: Problems on Probability Theorems

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Lecture 37:Axioms of Probability

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Lecture 38: Baye’s Theorem on Conditional Probability

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Lecture 39: Problems on Baye’s Theorem

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Unit-7 :Probability Theory-2

Lecture 40: Random Variables

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Lecture 41: Bernoulli’s Theorem

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Lecture 42: Problems on Binomial Distribution

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Lecture 43:Poisson Distribution

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Lecture 44:probability density function

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Lecture 45 :Exponential Distribution

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Lecture 46 :Normal Distribution

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Unit 8 :Sampling Theory

Lecture 47:Random Sampling

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Lecture 48:Testing Hypothesis

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Lecture 49:Significance Level

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Lecture 50:Student’s t-distribution

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Lecture 51:Chi-square distribution

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Lecture 52:Test of Significance of difference of properties

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Lecture 53:Chi-square test as a test of goodness of fit

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Part A

Chapter No. Chapter Name Lecture Notes
1 Numerical Methods-1  Click Here
2 Numerical Methods-2   Click here
3 Complex Variables -1   Click here
4 Complex Variables-2   Click here

Part B

Chpater No. Chapter Name Lecture Notes
5 Special Functions  Click here
6  Probability Theory-1  Click here
7 Probability Theory-2  Click here
8 Sampling Theory  Click here