# Mathematics-III (BT-401)

# notes For RGPV Bhopal AICTE Students

## OBJECTIVES

The objective of this course is to fulfill the needs of engineers to understand
applications of Numerical Analysis, Transform Calculus and Statistical techniques in order to
acquire mathematical knowledge and to solving wide range of practical problems appearing
in different sections of science and engineering. More precisely, the objectives are:

To introduce effective mathematical tools for the Numerical Solutions algebraic and
transcendental equations.

To enable young technocrats to acquire mathematical knowledge to understand
Laplace transformation, Inverse Laplace transformation and Fourier Transform which
are used in various branches of engineering.

To acquaint the student with mathematical tools available in Statistics needed in
various field of science and engineering

## Syllabus

**UNIT 1:**

Numerical Methods – 1: (8 hours): Solution of polynomial and transcendental
equations – Bisection method, Newton-Raphson method and Regula-Falsi method. Finite
differences, Relation between operators, Interpolation using Newton’s forward and backward
difference formulae. Interpolation with unequal intervals: Newton’s divided difference and
Lagrange’s formulae.

**UNIT 2**:

Numerical Methods – 2: (6 hours): Numerical Differentiation, Numerical
integration: Trapezoidal rule and Simpson’s 1/3rd and 3/8 rules. Solution of Simultaneous
Linear Algebraic Equations by Gauss’s Elimination, Gauss’s Jordan, Crout’s methods,
Jacobi’s, Gauss-Seidal, and Relaxation method.,

**UNIT 3**:

Numerical Methods – 3: (10 hours): Ordinary differential equations: Taylor’s
series, Euler and modified Euler’s methods. RungeKutta method of fourth order for solving
first and second order equations. Milne’s and Adam’s predicator-corrector methods. Partial
differential equations: Finite difference solution two dimensional Laplace equation and
Poission equation, Implicit and explicit methods for one dimensional heat equation (BenderSchmidt and Crank-Nicholson methods), Finite difference explicit method for wave equation.

**UNIT 4**:

Transform Calculus: (8 hours): Laplace Transform, Properties of Laplace
Transform, Laplace transform of periodic functions. Finding inverse Laplace transform by
different methods, convolution theorem. Evaluation of integrals by Laplace transform,
solving ODEs by Laplace Transform method, Fourier transforms.

**UNIT 5**:

Concept of Probability: (8 hours): Probability Mass function, Probability
Density Function, Discrete Distribution: Binomial, Poisson’s, Continuous Distribution:
Normal Distribution, Exponential Distribution.

## NOTES

**Unit 1****Unit 2****Unit 3****Unit 4****Unit 5**

## Books Recommended

1. P. Kandasamy, K. Thilagavathy, K. Gunavathi, Numerical Methods, S. Chand &
Company, 2nd Edition, Reprint 2012.

2. S.S. Sastry, Introductory methods of numerical analysis, PHI, 4th Edition, 2005.

3. Erwin kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley & Sons,
2006.

4. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 35th Edition, 2010.

5. N.P. Bali and Manish Goyal, A text book of Engineering Mathematics, Laxmi
Publications, Reprint, 2010.

6. Veerarajan T., Engineering Mathematics, Tata McGraw-Hill, New Delhi, 2008.

7. P. G. Hoel, S. C. Port and C. J. Stone, Introduction to Probability Theory, Universal Book
Stall, 2003 (Reprint).

8. S. Ross, A First Course in Probability, 6th Ed., Pearson Education India, 2002.

9. W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, 3rd Ed.,
Wiley, 1968. Statistics