Research Methodology

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Features of Good Research Design - Experimental Designs ... Research Methodology (Second Revised Edition) - C.R.Kothari; New Age Publishers, 2004.
MMA101 RESEARECH METHODOLOGY (For candidates admitted from 2009 - 2010) Unit I: Introduction, Definition and Design Meaning, Objective, Significance, Approaches, Motivation, Types and Criteria of Good Research - Selection and Definition of Research Problem - Meaning, Need, Concepts and Features of Good Research Design - Experimental Designs Unit II: Sampling, Measurement and Scaling Techniques Sampling Procedure - Implications, Steps, Characteristics and Types of Sampling Design Random Sampling - Measurement in Research - Measurement Techniques - Meaning of Scaling - Scale Classification Basics - Scaling Techniques. Unit III: Collection, Processing and Analysis of Data Observation & Interview Methods of Data Collection - Collection of Data Through Questionnaires and Schedules - Processing Operations - Measures of Central Tendency, Dispersion, asymmetry and relationship - Correlation and Regression. Unit IV: Testing of Hypothesis (Parametric Tests) Central Limit Theorem - Sampling Theory - Concept of Standard Error - Sample Size and its determination - Hypothesis Testing for Means, Proportions, Variance and Correlation Coefficients - Limitations of Tests of Hypothesis. Unit V: Chi-Square Test, ANOCA and ANOCOVA Comparing Variance & Non Parametric Tests Using Chi Square Distribution - Steps Involved in applying Chi Square Test - Yates Correction - One Way and Two Way Analysis of Variance - Coding Method Analysis of Co-Variance. Text Book : Research Methodology (Second Revised Edition) - C.R.Kothari; New Age Publishers, 2004 (Chapters 1 - 11) Reference Books 1. How To Solve It (Second Edition) - G.Polya. 2. How To Get a Research Degree - Elphinstone and Schweitzer 3. Fundamentals of Research Methodology and Statistics - Yogesh Singh

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MMA102 MATHEMATICAL MODELLING (For candidates admitted from 2009 - 2010) Unit I: Modeling Change Topic Modeling Change with Difference Equations Approximating Change with Difference Equations

Solutions to Dynamical Systems

Systems of Difference Equations

1. 2. 1. 2. 3. 4. 5. 1. 2. 3. 4. 5. 1. 2. 3. 4.

Examples A Savings Certificate Mortgaging a Home Growth of a Yeast Culture Growth of a Yeast Culture Revisited Spread of a Contagious Disease Decay of Digoxin in the Blood Stream Heating of a Cooled Object A Savings Certificate Revisited Sewage Treatment Prescription of Digoxin An Investment Annuity Revisited A Checking Account A Car Rental Company The Battle of Trafalgar Competitive Hunter Model Voting Tendencies of the Political Parties

Unit II: Modeling Process & Model Fitting Topic Examples Mathematical Models 1. Vehicular Stopping Distance Modeling Using 1. Kepler’s Third Law Proportionality Modeling Using Geometric 1. Raindrops froma Motionless Cloud 2. Modeling a Bass Fishing Derby Similarity Automobile Gasoline Mileage - Body Weight & Height, Strength & Agility - fitting Models to Data Graphically - Analytic Methods of Model Fitting - applying the Least Squares Criterion - Choosing a Best Model Unit III: Experimental Modeling Examples Topic 1. Harvesting Bluefish Harvesting in the Chesapeake Bay and Other 2. Harvesting Blue Crabs One Term Models High Order Polynomial 1. Elapsed Term of a Tape Recorder Models

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Smoothing : Low Order Polynomials Cubic Spline Models

1. 2. 3. 4. 1.

Elapsed Time of a Tape Recorder Revisited Elapsed Time of a Tape Recorder Revisited Vehicle Stopping Distance Growth of a Yeast Culture Vehicle Stopping Distance Revisited

Unit IV: Graphs of Functions as Models Topic An Arms Race

Examples 1. Civil Defense 2. Mobile Launching Pads 3. Multiple Warheads 4. MIRVs Revisited: Counting Warheads Modeling an arms race in Stages - Managing Non Renewable Resources - Effects of Taxation on the Energy Crisis - A Gasoline Shortage and Taxation

Unit V: Modeling With a Differential Equation Topic Examples Population Growth - Prescribing Drug Dosage - Braking Distance Revisited Graphical Solutions of 1. Drawing a Phase Line and Sketching Solution Curves Autonomous Differential 2. Cooling Soup Equations 3. Logistic Growth Revisited Numerical Approximation 1. Using Euler’s Method Methods 2. A Savings Certificate Revisited Text Book: A First Course in Mathematical Modeling - Giardano, Weir & William, Thompson Asia & China Press (First Published by Brookes & Cole, Thompson’s Learning) References: 1. An Introduction to Mathematical Modeling - Bender 2. Mathematical Modeling (Case Studies and Projects) - Caldwell 3. Bio Mathematics Modeling and Simulation - Mishra

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