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(MODULE 1-MODULE 5) // 4th sem M4-Complex Analysis, Probability and Statistical Methods (18MAT41)(common to all branches)

July 14, 2020

M4-Complex Analysis, Probability and Statistical Methods (18MAT41) notes all modules

(common to all branches-4TH SEM )


MOD1-MOD5 ALL NOTES BELOW

MULTIPLE NOTES FOR EACH MODULE


MODULE 1 NOTES:

CONTENTS OF MODULE 1:

MOD 1-CALCULUS OF COMPLEX FUNCTIONS & CONSTRUCTION OF ANALYTIC FUNCTIONS 

1. Review of a function of a complex variable, limits, continuity, differentiability. 

 2. Analytic functions: Cauchy-Riemann equations in Cartesian and polar forms. Properties and construction of analytic functions and problems. 

 3. Construction of analytic functions: Milne Thompson method-Problems
( RBT Levels: L1 & L2)
 
MOD 1 NOTES BELOW:

NOTE: these are  notes from different authors /publications/ source.


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MODULE 2 NOTES:

CONTENTS OF MODULE 2:

MOD 2-CONFORMAL TRANSFORMATIONS AND COMPLEX INTEGRATION 

1. Conformal transformations: Introduction. Discussion of transformations,  Bi linear transformations- Problems 

2. Line integral of a complex function Cauchy’s theorem and Cauchy’s integral formula and problems

( RBT Levels: L1 & L2) 

MOD 2 NOTES BELOW:

NOTE: these are  notes from different authors /publications/ source.


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MODULE 3 NOTES:

CONTENTS OF MODULE 3:

MOD 3-PROBABILITY DISTRIBUTIONS

1 Random variables (discrete and continuous), probability mass/density functions

2. Binomial, Poisson distributions problems

3. Exponential and Normal distribution  problems

( RBT Levels: L1,L2 & L3) 

MOD 3 NOTES BELOW

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OR






MODULE 4 NOTES:

CONTENTS OF MODULE 4:

MOD 4-CURVE FITTING & STATISTICAL METHODS

1. Curve fitting by the method of least squares- fitting the curves of the form- , & . 2 y ax b y ax y ax bx c

2. Correlation-Karl Pearson’s coefficient of correlation and rank correlation(without repetition) –problems. Regression analysislines of regression –problems

( RBT Levels: L1,L2 & L3) 

MOD 4 NOTES BELOW

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OR



MODULE 5 NOTES:

CONTENTS OF MODULE 5:

MOD 5-JOINT PROBABILITY DISTRIBUTION AND SAMPLING THEORY


1. Joint Probability distribution for two discrete random variables, expectation and covariance. 

2. Introduction to sampling distributions, standard error, Type-I and Type-II errors. 

3. Hypothesis testing of a sampling distribution for single mean, student’s distribution, Chi-square distribution as a test of goodness of fit.  

( RBT Levels: L2, L3 & L4) 


MOD5 NOTES BELOW

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OTHER USEFUL INFORMATION 

Text books:

1. E. Kreyszig: Advanced Engineering Mathematics, John Wiley & Sons, 10th Ed.(Reprint), 2017

. 2. B.S. Grewal: Higher Engineering Mathematics, Khanna Publishers, 44th Ed., 2017.

 3. Srimanta Pal & Subobh C Bhunia: “Engineering Mathematics”, Oxford University Press, 3rd Reprint, 2016.



Reference Books:
1. C.Ray Wylie, Louis C.Barrett : “Advanced Engineering Mathematics", 6th Edition, 2. McGrawHill Book Co., New York, 1995.

 2. S.S.Sastry: “Introductory Methods of Numerical Analysis”, 4 th Edition, PHI, 2010.

 3. B.V.Ramana: "Higher Engineering Mathematics" 11th Edition, Tata McGraw-Hill, 2010

. 4. N.P.Bali and Manish Goyal, “A Text Book of Engineering Mathematics”, Laxmi Publications. Latest edition, 2014

. 5. Chandrika Prasad and Reena Garg ,”Advanced Engineering Mathematics”, Khanna Publishing,2018.


OTHER USEFUL LINKS (3RD-8TH SEM) NOTES

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