Visvesvaraya Technological University, Karnataka, Mechanical Engineering Semester 4, Engineering Mathematics - IV Syllabus

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Unit - 1 Numerical Methods

1.1 Numerical solutions of first order and first degree ordinary differential equations – Taylor’s series method

1.2 Modified Euler’s method

1.3 Runge – Kutta method of fourth order

1.4 Milne’s and Adams Bashforth predictor and corrector methods All formulae without Proof

Unit - 2 Complex Variables

2.1 Function of a complex variable Limit Continuity Differentiability – Definitions

2.2 Analytic functions

2.3 Cauchy – Riemann equations in cartesian and polar forms

2.4 Properties of analytic functions

2.5 Conformal Transformation – Definition

2.6 Discussion of transformations

2.7 Bilinear transformations

Unit - 3 Complex Integration

3.1 Complex line integrals

3.2 Cauchy’s theorem Cauchy’s integral formula

3.3 Taylor’s and Laurent’s series Statements only

3.4 Singularities Poles Residues Cauchy’s residue theorem statement only

Unit - 4 Series Solution Of Ordinary Differential Equations And Special Functions

4.1. Series solution – Frobenius method

4.2. Series solution of Bessel’s D.E Leading to Bessel function of fist kind

4.3. Equations reducible to Bessel’s D.E

4.4. Series solution of Legendre’s D.E Leading to Legendre Polynomials. Rodirgue’s formula

Unit - 5 Statistical Methods

5.1 Curve fitting by the method of least squares

5.2 Correlation and Regression

5.3 Probability Addition rule Conditional probability

5.4 Multiplication rule Baye’s theorem

Unit - 6 Random Variables

6.1 Random Variables Discrete and Continuous p.d.f. c.d.f.

6.2 Binomial Poisson Normal and Exponential distributions

Unit - 7 Sampling

7.1 Sampling Sampling distribution Standard error

7.2 Testing of hypothesis for means Confidence limits for means

7.3 Student’s t distribution

7.4 Chisquare distribution as a test of goodness of fit.

Unit - 8 Concept Of Joint Probability

8.1 Concept of joint probability – Joint probability distribution Discrete and Independent random variables

8.2 Expectation Covariance Correlation coefficient

8.3 Probability vectors Stochastic matrices Fixed points Regular stochastic matrices

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