 # Numerical and Statistical Methods for Computer Engineering (2140706)

## Teaching Scheme (in Hours)

Theory Tutorial Practical Total
3 0 2 5

Subject Credit :  5

Theory
ESE (E)
Theory
PA (M)
Practical
ESE Viva (V)
Practical
PA (I)
Total
0

## Syllabus Content

###### Unit-1:  Unit-1

Mathematical modeling andengineering problem Solving.Approximations and errors. Significant figures, accuracy and 1 precision,Errors, round-off and truncation errors, error propagation.

###### Unit-2:  Unit-2

Roots of Equations: Mathematical background, Bisection, RegulaFalsi, NR method, Secant, Successive approximation method, Budan’s Theorem, Barristow’s method, case studies.

###### Unit-3:  Unit-3

Systems of linear algebraic equations: Mathematical background, Gauss elimination; pitfalls and techniques for improvement, matrix inversion and Gauss-Seidel methods, ill- conditional Equations, Predictor-Corrector methods, case studies.

###### Unit-4:  Unit-4

Curve Fitting: Mathematical background, Least squares linear and polynomial regression, Lagrange interpolating Polynomials. Splineinterpolation, Case studies.

###### Unit-5:  Unit-5

Numerical Integration: Newton-Cotes integration formulas; trapezoidalrule and Simpson’s rules: Interpolation, case studies.

###### Unit-6:  Unit-6

Ordinary differential equations: Euler’s method, Runge-Kutta methods. General methods for boundary value problems, Case studies.

###### Unit-7:  Unit-7

Statistical Methods: Frequency distributions, Data analysis, Expectations and moments, Co- relation and regression, Trend analysis, Seasonal effects, Cyclical Fluctuation, Moving average, MSE, Predictions. Non-parametric statistics. Computer-based resampling techniques. Confidence intervals and statistical significance.

## Reference Books

Sr. Title Author Publication Amazon Link
1 Applied Numerical Methods W/MATLAB S C Chapra and R P Canale McGraw Hill
2 Numerical Methods for Scientific & Engineering Computation M. K. Jain, S.R.K.
3 Introductory Methods of Numerical Analysis S. S. Sastry PHI
4 Numerical Methods J B Dixit Laxmi
5 Numerical Methods in Engineering & Science Dr. B. S. Grewal Khanna
6 Computer Oriented Numerical Methods R. S. Salaria Khanna
7 Miller and Freund's - Probability and Statistics for Engineers Richard A Johnson PHI

## Course Outcome

After learning the course the students should be able to:

• Solve system of linear equations.
• Understand various methods of modeling.
• Apply Mathematical Modeling and for Engineering Problem Solving.
• Solve Mathematical Equations by various methods.
• Find Best Curve fitting for given data.
• Apply Numerical Integration.
• Solve Differential Equations.
• Understand Statistical Methods for Data Analysis and sampling techniques.
• Write programs for various numerical and statistical methods

### BE (CE) ⇒ Semester: 4

Darshan Institute of Engineering & Technology is a leading institute offering undergraduate (B.E.), postgraduate (M.E.) and Diploma programs in engineering.

## Our Contacts

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