RESEARCH METHODOLOGY AND SPECIAL SKILLS

Paper Code: 
MAT141
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Unit I: 
I
12.00
Research: Meaning, Definition, Methodology, Research process, Rationale for research Criterion of good research.
Types of Research: Fundamental or basic, Applied, Descriptive, Analytical, Quantitative, Qualitative, Conceptual, Experimental, Case study, Research approaches.
Research Design: Meaning, Concepts, Need and types of research design; Library, laboratory and field research; Advantages of designing a research, research methods and its types.
Research problem and developing research proposal: Selection of research area and topic, Statement of the research problem and its scope, Steps involved in developing a research proposal.
Literature Study: Reviewing related literature, Referencing, Abstracting, Bibliography, Evaluation of the published research work.
Defining concepts, Objectives, Basic assumptions, Limitations and delimitations of the problem, Statement of hypothesis. 
Unit II: 
II
12.00
Variables: Independent and dependent variables, Qualitative and quantitative variables, Discrete and continuous variables, Confounding variables, Methods of controlling variables.
 
Sampling: Meaning, Characteristics of a good sample design, steps in sampling design, types, advantages.
 
Techniques of Data Collection: Primary data; Questionnaire, Schedules, Interview, Observation and Rating scale.
 
Reliability, Validity, Objectivity of a test, Suitability and adequacy of data.
 
Processing and Analysis of Data: Editing, Coding, Classification and tabulation of data, Elements of Data analysis, Role of statistics in data analysis, Statistical tables, Report writing: Types, Format.
Unit III: 
III
12.00
Probability: Basic aspects, Probability of combination of events, probability of random variables, Distribution of random variable.
Statistical Methods: Measures of Central tendency: Mean, Median, Mode, Arithmetic, Geometric and Harmonic mean. 
Measures of Dispersion: Range, Mean Deviation, Variance, Standard Deviation, Coefficient of variation.
Regression and Correlation: Least square method for fitting a regression line, Curvilinear regression, Correlation methods, Correlation coefficient.
Test of Significance: t-test, Chi-test, ANOVA, f-test Hypothesis. 
 
Unit IV: 
IV
12.00
Common distribution functions: Binomial probability distribution, Poisson distribution and normal distribution.
Errors in Calculations: Approximate numbers and significant figures, Rounding of numbers, Absolute and relative errors, Relation between relative error and significant figures, General formula for errors, Application of error formulas to fundamental operations of arithmetic, The impossibility of obtaining results more accurate than the data used; Accuracy of results computed from a formula or complex expression, Tabulated functions and series approximation. 
 
Unit V: 
V
12.00
Solution of algebraic and transcendental equations: Bisection method, Regula-Falsi method, Newton-Raphson method, Rate of convergence of Newton’s method.
Newton’s forward and backward formulae of differences, Lagrange’s interpolation formula, Stirling’s interpolation formula. Numerical differentiation.
Numerical integration: Newton-Cote’s formulae, Trapezoidal rule, Simpson’s 1/3rd rule, Simpson’s 3/8th rule and their error estimation.
Numerical Solution of ordinary differential equations: Euler’s Methods, Picard’s Methods and Runga- Kutta Method.
References: 
  1. Agrawal, B.L., Basic statistics, New Delhi: New Age publishers.
  2. Ahuja Ram, Research Methods, Jaipur: Rawat Publication, 2006.
  3. Jain M.K., and Iyengar, Numerical methods problems and solutions, New Age International   Ltd.
  4. Kothari, C.R. Research Methodology: Methods and Techniques, Bangalore, Wiley Eastern, 1989.
  5. Rosander, A.C., Elements of Probability and Principles of Statistics, Calcutta: East West Press, 1965.
  6. Bose, Pradip Kumar, Research Methodology, New Delhi:ICSSR, 1995
  7. Burns, Robert B. Introduction to Research Methods, New Delhi; Sage Publications, 2000.
  8. Curtis F. Gerald and Patrick O. Wheatly, Applied Numerical Analysis, Pearson, 2006.
  9. Hamming Richard, Numerical Methods for Scientists and Engineers, Courier Corporation, 1973.
  10. Kharab and Guenther, An Introduction to Numerical Methods: A-MATLAB Approach. 
  11. Sarvavanavel, P., Research Methodology, Allahabad; Kitab Mahal, 2003.
  12. Shanlla K.R. Research Methodology, New Delhi: National Publishing House, 2002.
  13. Weatherburu, C.E.A. A First Course in Mathematical Statistics, Cambridge, 1946
  14. Yule, G.V. and Kendall, M.G., An Introduction to the theory of Statistics.
  15. Scarborough J.B., Numerical Mathematical Analysis, New Delhi: Oxford & IBH Pub. Co., 1971.
 
Academic Year: 
2020-2021
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