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
FFunction 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 Calculus of Variations
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 Difference Equations and Z-transforms
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
23
23.31 to 23.37
791 – 816
Unit – VIII: Text book: Probability by Seymour Lipschutz (Schaum’s
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.
*Note.
1. One question is to be set from each unit.
2. To answer Five questions choosing atleast Two questions from each part.