06MAT41- Engineering Mathematics IV |
PART A |
UNIT I |
Numerical Methods
Numerical solutions of first order and first degree ordinary differential
equations – Taylor’s series method, Modified Euler’s method, Runge – Kutta
method of fourth order, Milne’s and Adams-Bashforth predictor and
corrector methods (All formulae without Proof). |
UNIT II |
Complex Variables
Function of a complex variable, Limit, Continuity Differentiability –
Definitions. Analytic functions, Cauchy – Riemann equations in cartesian
and polar forms, Properties of analytic functions. Conformal Transformation – Definition. Discussion of transformations: W = z2, W = ez, W = z + (I/z),
z 0 Bilinear transformations. |
UNIT III |
Complex Integration
Complex line integrals, Cauchy’s theorem, Cauchy’s integral formula.
Taylor’s and Laurent’s series (Statements only) Singularities, Poles,
Residues, Cauchy’s residue theorem (statement only). |
UNIT IV |
Series solution of Ordinary Differential Equations and Special Functions
Series solution – Frobenius method, Series solution of Bessel’s D.E. leading
to Bessel function of fist kind. Equations reducible to Bessel’s D.E., Series
solution of Legendre’s D.E. leading to Legendre Polynomials. Rodirgue’s
formula. |
PART B |
UNIT V |
Statistical Methods
Curve fitting by the method of least squares: y = a + bx, y = a + bx + cx2,
y = axb y = abx, y = aebx, Correlation and Regression.
Probability: Addition rule, Conditional probability, Multiplication rule,
Baye’s theorem. |
UNIT VI: |
Random Variables (Discrete and Continuous) p.d.f., c.d.f. Binomial, Poisson,
Normal and Exponential distributions. |
UNIT VII |
Sampling, Sampling distribution, Standard error. Testing of hypothesis for
means. Confidence limits for means, Student’s t distribution, Chi-square
distribution as a test of goodness of fit. |
UNIT VIII |
Concept of joint probability – Joint probability distribution, Discrete and
Independent random variables. Expectation, Covariance, Correlation
coefficient.
Probability vectors, Stochastic matrices, Fixed points, Regular stochastic
matrices. Markov chains, Higher transition probabilities. Stationary
distribution of regular Markov chains and absorbing states. |
REFERENCE |
TEXT BOOKS: |
Higher Engineering Mathematics by Dr. B.S. Grewal (36th
Edition Khanna Publishers)
Unit No. |
Chapter No. |
Article Numbers |
Page Nos. |
I |
27 |
27.1, 27.3, 27.5, 27.7, 27.8 |
914, 916 – 922
924, 933 |
II |
20 |
20.1 to 20.10 |
630 – 650 |
III |
20 |
20.12 to 20.14, 20.16 to 20.19 |
652 – 658
661 – 671 |
IV |
16 |
16.1 to 16.6, 16.10, 16.13, 16.14 |
507 – 514,
521 – 523
526 – 529 |
V |
1
23 |
1.12 to 1.14
23.9, 23.10, 23.11, 23.14, 23.16
to 23.18 |
20 – 25
755 – 762, 765
768 – 776
|
VI |
23 |
23.19 to 23.22, 23.26 to 23.30 |
776 – 780
783 – 798 |
VII |
33 |
23.31 to 23.37 |
791 – 816 |
Unit VIII: Text book: Probability by Seymour Lipschutz (Schaums
series) Chapters 5 & 7 |
Reference Books |
1. Higher Engineering Mathematics by B.V. Ramana (Tata-Macgraw
Hill).
2. Advanced Modern Engineering Mathematics by Glyn James
Pearson Education.
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