BHARATHIAR UNIVERSITY SYLLABUS OF M.Phil – Applied Mathematics




PAPER I

TEACHING TECHNIQUES IN APPLIED MATHEMATICS

UNIT 1: Methods & Techniques of Teaching
Large Group Techniques: Lecture, Modified lecture, seminar, symposium, panel
discussion, Team Teaching, Project Approach & workshop. Small group techniques:
Group discussion, Simulation, Role playing, Buzz Technique, Brain Stroming, case
discussion and assignment.

Unit II: Educational Computing
Instructional Applications of computer-Computer Assisted Instruction(CAI)-CAI
programmes - Basic Assumptions, Advantages &Limitations of CAI-Role of the Teacher
in CAI - e learning-What is e learning-Levels of e learning -Important features of e
learning-Benefits & pitfills in e learning-Electronic journals-Innovative Instructional
Software-steganography and Educational Applications.

UNIT III: Dimensional analysis and scaling
Dimensional analysis – The program of Applied Mathematics – Dimensional
Methods – The Buckingham Pi theorem – Formulation – Application to a Diffusion Problem –
Proof of the Pi theorem – Scaling – Characteristic Scales – A Chemical Reactor Problem – The
Projectile Problem – Population Models.

UNIT IV: Regular Perturbation Method
The Perturbation Method – Motion in a Nonlinear Resistive Medium – A Non linear
Oscillator – The Poincare-Lindsted Method – Asymptotics.

UNIT V: Singular Perturbation and boundary-layer analysis
Failure of Regular Perturbation – Inner and outer approximations – Algebraic equations
and Balancing – The inner approximation – Matching – Uniform approximations – Worked
example – Boundary Layer Phenomena


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