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
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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
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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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