### 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, Eulerâ€™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