Section outline

  • General

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    • Teacher Information

      Name: Anip Kumar Paul

      Designation: Lecturer in Mathematics                                                

      Department: GED

      Desk: Room #: 806, ABO4, DSC

      Contact Number: 01780796061

      Email: anip.ged@diu.edu.bd


    • Course Rationale 

      Differential Equations, very important branch of modern mathematics, a technique for determining a function over its entire domain through some of its derivatives at a particular point. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. The term "differential equations" was proposed in 1676 by G. Leibniz. The first studies of these equations were carried out in the late 17th century in the context of certain problems in mechanics and geometry. Ordinary differential equations have important applications in the natural sciences and are extensively employed in mechanics, astronomy, physics, and in many problems of chemistry and biology. The computation of radio-technical circuits or satellite trajectories, studies of the stability of a plane in flight, and explaining the course of chemical reactions are all carried out by studying and solving ordinary differential equations. Differential Equations can describe how populations change, how heat moves, how springs vibrate, how radioactive material decays and much more. They are a very natural way to describe many things in the universe.


    • Course Objectives

      Purpose of this course to indoctrinate the learner about Differential Equations and their solution technique which are extensively employed in our daily life. This study will he assist them to develop differential equations of various essentials problems and increase the capability of giving solution in different cases. From this course, students will learn: 

      ·       Performing derivatives and integrals

      ·       Solving differential equation

      ·       Identify ordinary and partial differential equation

      ·       We can mark out the type and nature of the differential equation

      ·       Demonstrate solution in under physical condition

      ·       We can understand many functions with the rate of change of another function



    • Course Outlines

      CO1

        Set up differential equation of various engineering problem

      CO2

        Solve differential equation in different engineering field

      CO3

        Determine particular solution under physical condition

      CO4

        Solving different partial differential equation

      CO5

        Apply knowledge and skills to solve a problem



    • Grading Policy 


      Grading Policy:

      Marks out of 100

      Letter Grade

      Grade Point

      80 - 100

      A+

      4.00

      75 - 79

      A

      3.75

      70 - 74

      A-

      3.50

      65 - 69

      B+

      3.25

      60 - 64

      B

      3.00

      55 - 59

      B-

      2.75

      50 - 54

      C+

      2.50

      45 - 49

      C

      2.25

      40 – 44

      D

      2.00

      00 - 39

      F

      0.00

       The final course grade will be awarded based on the mark’s distribution shown in the table above. 

      Marks distribution:

      Percentages of marks for the different heads are given below:

      Attendance

      07 %

      Class Test

      15 %

      Assignment

      05 %

      Presentation

      08%

      Mid Term Exam

      25 %

      Final Exam

      40 %

      Total

      100%

       

       

    • Course Delivery Plan

      Brief the course outline and delivery plan in detailed

    • Reference Text Book

      1. Differential Equations by B.D. Sharma

      3.Differential Equations by P. N. Chatterjee

      3. Differential Equations by Md. Abu Yousuf 

      4. Differential Equations by  Shepley L. Ross        Get the book

    • Additional Materials

      Google Classroom Code

      WhatsApp Number: 01780796061

  • Introductory Class


    • Introduction 

      In this class, I will introduce myself and conduct an introductory session with students, also discuss with them how they can be benefited to learn this course.

    • Outcomes 

      In the discussion part, I will cultivate some real life example which can be easily defined by Ordinary and Partial Differential Equations. 

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      Have to do with Forum

  • Lecture 2-3 (Order, Degree & Differential Equation)


    • Introduction

      In this class, we bring up order and degree, also classify a differential equations according to the  order and degree. I introduce how a differential equation can form and represent some example. 

    • Chapter Outcome

      After study this chapter, you able to understand about: 

      §  Order and degree

      §  Linearity and non-linearity of a D.E. (Differential Equation).

      §  Classifications of D.E. according to degree and order.

      §  Formation of D.E. from physical problem.


    • Lecturer Content

      ·       Discuss from lecture slide

      ·       Group work and individual classwork

      ·       Question and answering session

    • Study Materials
                         

        Lecture Note (ppt)                                                        

      Lecture Note (pdf)                                                       

                                                                    

                   


                              

               
             


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      Talk over Forum

  • Lecture 4-5 (Separation of Variable and Reducible to Variable Separable)


    • Introduction

      In this lecture, we introduce first order differential equations of  Separation of Variable and Reducible to Variable Separable type and the method of it's solution. We solve some problem which is related to the variable separation method.  

    • Chapter Outcome

      After study this chapter, you able to understand about: 

      §  Solve ODE in variable separable form

      §  Solve ODE in reducible to variable separable form

      §  Identify variable separable type ODE and reducible to variable separable type ODE

      §  How to reduce an equation to variable separable form 

    • Lecturer Content

      ·       Discuss from lecture note

      ·       Group work and individual classwork

      ·       Question and answering session



    • Study Materials
      Lecture Note (ppt)                                                 
      Lecture Note (pdf) 
      Lecture Note (pdf)                                               
       



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      Discussion session Forum

  • First Quiz

  • Lecturer 6-7 (Homogeneous Equation and reducible to Homogeneous Equation)


    • Introduction

      In this lecture, we introduce first order first degree Homogeneous Equation and reducible to Homogeneous Equation and the method of it's solution. We discuss solution steps and solve some different problem which is related to the Homogeneous Equation method.  


    • Chapter Outcome

      After study this chapter, you able to understand about: 

      §  Identify homogeneous type ODE and reducible to homogeneous type ODE

      §  Solution steps of homogeneous type ODE

      §  Solution steps of reducible to homogeneous type ODE

      §  How to reduce an non-homogeneous equation to homogeneous equation 


    • Lecturer Content

      ·       Discuss from lecture note

      ·       Group work and individual classwork

      ·       Question and answering session



    • Study Materials
      Lecture Note (pdf)                                                                   
      Lecture Note (ppt)
      Lecture Note__2 (ppt)                                                                  



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      Recapitulation session Forum

  • Submit your assignment

  • Lecture 8-9 (Exact Differential Equation and Linear Differential Equation)


    • Introduction

      In this lecture, we introduce first order first degree Exact Differential Equation and Linear Differential Equation and the method of it's solution. We learn how to identify the Exact Differential Equation and Linear Differential Equation. We discuss solution steps and solve some different problem which is related to the exact problem also we learn non-exact condition. 


    • Chapter Outcome

      After study this chapter, you able to understand about: 

      §  Identify exact and non-exact ODE and linear  ODE

      §  Conditions of exactness and linearity of an ODE

      §  Solution steps and assumptions for solving exact and linear  ODE

      §  Find Integrating factor and its necessity 

      §  How to transform a non-exact to exact DE 

    • Lecturer Content

      ·       Discuss from lecture note

      ·       Group work and individual classwork

      ·       Question and answering session



    • Study Materials
      Lecture Note_1 (ppt)
      Lecture Note_2 (ppt)                                                                       
      Lecture Note (pdf)
      Lecture Note_2(pdf)



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      Reflect your idea Forum

  • Lecture 10-11 (Bernoulli's Differential Equation )


    • Introduction

      In this lecture, we introduce for the first time a non-linear Bernoulli type Differential Equation and the method of it's solution. We learn how to identify the Bernoulli’s Equation Equation. We discuss about non-linearity and solution steps, also solve some different non-linear Bernoulli type problem. 


    • Chapter Outcome

      After study this chapter, you able to understand about: 

      §  Know the non-linearity condition for DE

      §   Identify the Bernoulli’s Equation and it's application

      §  Solution steps and assumptions for solving Bernoulli’s Equation

      §  How to transform a non-linear DE to linear DE 

    • Lecturer Content

      ·       Discuss from lecture note

      ·       Group work and individual classwork

      ·       Question and answering session



    • Lecture Note (ppt)                                                     
      Lecture Note (pdf)                                                           		  
      Study Materials




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      Reproduction and discussion session Forum

  • Second Quiz

  • Submit your presentation

  • Instruction for Mid-Term examination

    • Mid-Term Syllabus

      ·       Formation of differential equations.

      ·       Solution of first order differential equations by the method of variable separable and equation reducible to variable separable form

      ·       Homogeneous equation and equation reducible to homogeneous form.

      ·       Exact differential equation.

      ·       Linear differential equation.

      ·       Bernoulli’s type equation.

      ·       Linear differential equation with constant coefficients with right hand side Zero

              Linear differential equation with constant coefficients with right hand side non zero.


      Mid-Term Mark Distribution

      ·       This exam question will be made up of 5 set of questions.

      ·       Each set of questions may include two or three short or descriptive questions.

      ·       Each of the question set contains equal marks (5 marks). Total 25 marks.

      ·       There will no options. You must answer all the questions to get marks.


  • Lecture 12-13 (Partial Differential Equations)


    • Introduction

      In this lecture, we introduce for the first time a Partial Differential Equation and the technique of it's solution. We learn how to identify the Partial Differential Equation. We discuss about partial differentiation and PDE solution steps, also solve some different Partial Differential Equation. 



    • Chapter Outcome

      After study this chapter, you able to understand about: 

      §  Basic idea of Partial DE

      §   Brief  discussion of solution method for a PDE

      §  Solution steps and assumptions for solving PDE

    • Lecturer Content

      ·       Discuss from lecture note

      ·       Group work and individual classwork

      ·       Question and answering session


    • Study Materials
      Lecture Note (pdf)                                                                        
      		  Video Tutorial


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      Afterthought section Forum

  • Instruction for Final examination

    • Final exam Syllabus

      ·       Linear Differential equation with variable coefficients with right hand side zero

      ·       Linear Differential equation with variable coefficients with right hand side non- zero

      ·       Linear equation of second degree: Variation of parameters

      ·       Formation of Partial differential equation.

      ·       Linear Partial differential equations: Lagrange Method

      ·       Non-linear Partial differential equation of order

      ·       Various types of Application of differential equation.


      Final Exam Mark Distribution

      ·       This exam question will be made up of 4 set of questions.

      ·       Each set of questions may include two or three short or descriptive questions.

      ·       Each of the question set contains equal marks (10 marks). Total 40 marks.

      ·       There will no options. You must answer all the questions to get marks.


  • Topic 15