Computer Oriented Numerical and Statistical Techniques

Paper Code: 
MCA 423
Credits: 
04
Objective: 

 The course will enable the students to

1         Obtain an intuitive and working understanding of numerical methods for the basic problems of numerical analysis. 

2         Gain experience in the implementation of numerical methods using a computer.

3         Trace error in these methods and need to analyze and predict it.

4         Provide knowledge of various significant and fundamental concepts to inculcate in the students an adequate understanding of the application of Statistical Methods.

 5         Demonstrate the concepts of numerical methods used for different applications

 

 Course Learning Outcomes (CLOs):

 

Learning Outcome (at course level)

Students will be able to:

Learning and teaching strategies

Assessment Strategies

  1. Understanding and Learning of numerical methods for numerical analysis. 
  2. Understanding the implementation of numerical methods using a computer.
  3. Learning of tracing errors in Numerical methods and analyze and predict it.
  4. Learning of application of Statistical methods.
  5. Discuss concepts of numerical methods used for different applications

Approach in teaching:

Interactive Lectures,

Modeling, Discussions, implementing enquiry based learning, student centered approach, Through audio-visual aids

 

Learning activities for the students:

Experiential Learning, Presentations, Discussions, Quizzes and Assignments

 

  • Assignments
  • Written test in classroom
  • Classroom Activity
  • Continuous Assessment
  • SemesterEnd Examination

 

12.00
Unit I: 

Solution of Non Linear equations- Introduction to linear and non linear equations, measures of accuracy, Bisection Method, Iteration Method, Regula-Falsi method, Newton Raphson method, Rate of convergence of iterative methods.

Solutions of system of Linear equations-  Direct Method - Gauss Elimination method  and pivoting, Ill Conditioned system of equations. Iterative method- Gauss Seidal Method.

12.00
Unit II: 

Interpolation and approximation: Finite Differences, Difference tables, Newton’s forward and backward formula, Central Difference Formulae: Gauss forward and backward formula.

Interpolation with unequal intervals: Langrange’s Interpolation, Newton Divided difference formula.

10.00
Unit III: 

Numerical Integration: Trapezoidal rule, Simpson’s rules.

Solution of Differential Equation: Range kutta methods; Predictor-Corrector methods.

13.00
Unit IV: 

Statistical Computation: Frequency charts: Different frequency charts.

Regression Analysis: Curve fitting and Approximation: Method of least squares, fitting of Linear Function, fitting of Nonlinear Function- polynomials, exponential curves.

Linear regression and Nonlinear regression Algorithms; Multiple regression Algorithms

13.00
Unit V: 

Time Service and forecasting: Moving averages; Smoothening of curves: Forecasting models and methods.

Statistical Quality control Methods: Test of significance: Chi-square test, F-Test, T- test, Factor Analysis, ANOVA ,Applications to medicine, psychology etc. 

ESSENTIAL READINGS: 
  1. Salaria, R.S.: Computer Oriented Numerical Methods, Khanna Book Publishing Co. (P.) Ltd., New Delhi. 5th edition 2012
  2. James F. Epperson :An Introduction to Numerical Methods and Analysis Hardcover, 2010
  3. Balaguruswami, E., “Computer Oriented Statistical and Numerical Methods”, Mac. Million, 2000
  4. J.K Sharma, A.M Natarajan, P. Balasubramani and A. Tamilarasi 2013 1st edition : Statitical and Quantitative Methods
REFERENCES: 
  1. Rajaraman, V.,”Computer Programming in C”, Prentice Hall of India, 2004
  2. P. Thangaraj :Computer oriented Numerical Methods PHI learning , Second Edition 2010
Academic Year: 
2019-20
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