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# Book Details # Engineering Mathematics – IV

 Course Code : 10MAT41 Author : uLektz University : Visvesvaraya Technological University, Karnataka (VTU) Regulation : 2010 Categories : General Engineering Format : ePUB3 (DRM Protected) Type : eBook

FREE

Description :Engineering Mathematics – IV of 10MAT41 covers the latest syllabus prescribed by Visvesvaraya Technological University, Karnataka (VTU) for regulation 2010. Author: uLektz, Published by uLektz Learning Solutions Private Limited.

Note : No printed book. Only ebook. Access eBook using uLektz apps for Android, iOS and Windows Desktop PC.

##### Topics
###### UNIT-I: NUMERICAL METHODS - 1

1.1 Numerical solution of ordinary differential equations of first order and first degree; Picard’s method,Taylor’s series method,Modified Euler’s method,Runge-kutta method of fourth-order.

1.2 Milne’s and Adams-Bashforth predictor and corrector methods (No derivations of formulae).

###### UNIT-II: NUMERICAL METHODS – 2

2.1 Numerical solution of simultaneous first order ordinary differential equations: Picard’s method,Runge-Kutta method of fourth-order.

2.2 Numerical solution of second order ordinary differential equations: Picard’s method,Runge-Kutta method and Milne’s method.

###### UNIT-III: Complex variables – 1

3.1 Function of a complex variable;Analytic function-Cauchy- Riemann equations in cartesian and polar forms.Properties of analytic functions.

3.2 Application to flow problems : Complex potential, velocity potential, equipotential lines, stream functions, stream lines.

###### UNIT-IV: Complex variables – 2

4.1 Conformal Transformations: Bilinear Transformations, Discussion of Transformations: w = z², w = ez , w = z + (a² / z) .

4.2 Complex line integrals-Cauchy’s theorem and Cauchy’s integral formula.

###### UNIT-V: SPECIAL FUNCTIONS

5.1 Solution of Laplace equation in cylindrical and spherical systems leading Bessel’s and Legendre’s differential equations-Series solution of Bessel’s differential equation leading to Bessel function of first kind; Orthogonal property of Bessel functions.

5.2 Series solution of Legendre’s differential equation leading to Legendre polynomials, Rodrigue’s formula.

###### UNIT-VI: PROBABILITY THEORY - 1

6.1 Probability of an event,Empherical and axiomatic definition-Probability associated with set theory,Addition law

6.2 Conditional probability,Multiplication law,Baye’s theorem.

###### UNIT-VII: PROBABILITY THEORY- 2

7.1 Random variables (discrete and continuous),Probability density function,Cumulative density function.

7.2 Probability distributions -Binomial and Poisson distributions; Exponential and normal Distributions.

###### UNIT-VIII: SAMPLING THEORY

8.1 Sampling,Sampling distributions,Standard error

8.2 Test of hypothesis for means-Confidence limits for means

8.3 Student’s t-distribution;Chi -Square distribution as a test of goodness of fit.

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