B.Sc Mathematics Tuition Of Differential Equation
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Course Objectives Of Differential equations Tutorial Classes
The main objectives of this course are to introduce the students to the exciting world of Differential Equations, Mathematical Modelling and their applications.
Course Learning Outcomes:
The course will enable the students to:
- Formulate Differential Equations for various Mathematical models.
- Solve first order non-linear differential equation and linear differential equations of higher order using various techniques.
- Apply these techniques to solve and analyze various mathematical models.
Syllabus Content May vary as per curriculum by university
Course Contents:
Unit 1: Differential Equations and Mathematical Modeling Tuition
Differential equations and mathematical models, Order and degree of a differential equation, Exact differential equations and integrating factors of first order differential equations, Reducible second order differential equations, Application of first order differential equations to equations to acceleration-velocity model, Growth and decay model.
Unit 2: Population Growth Models Tuition
Introduction to compartmental models, Lake pollution model (with case study of Lake Burley Griffin), Drug assimilation into the blood (case of a single cold pill, case of a course of cold pills, case study of alcohol in the bloodstream), Exponential growth of population, Limited growth of population, Limited growth with harvesting.
Unit 3: Second and Higher Order Differential Equations Tuitions
General solution of homogeneous equation of second order, Principle of superposition for a homogeneous equation; Wronskian, its properties and applications, Linear homogeneous and non-homogeneous equations of higher order with constant coefficients, Euler’s equation, Method of undetermined coefficients, Method of variation of parameters, Applications of second order differential equations to mechanical vibrations.
Unit 4: Analysis of Mathematical Models Tuitions
Interacting population models, Epidemic model of influenza and its analysis, Predator-prey model and its analysis, Equilibrium points, Interpretation of the phase plane, Battle model and its analysis.
References:
- Barnes, Belinda & Fulford, Glenn R. (2015). Mathematical Modelling with Case Studies, Using Maple and MATLAB (3rd ed.). CRC Press, Taylor & Francis Group.
- Edwards, C. Henry, Penney, David E., & Calvis, David T. (2015). Differential Equation and Boundary Value Problems: Computing and Modeling (5th ed.). Pearson Education.
- Ross, Shepley L. (2004). Differential Equations (3rd ed.). John Wiley & Sons. India