HomeMATHSMATHS M4 (18MAT41)(MODULE 1-MODULE 5) // 4th sem M4-Complex Analysis, Probability and Statistical...

# (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)

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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)
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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)
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## 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)
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## 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)
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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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