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Topic outline
- General
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General
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 |
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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%
|
|
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
- Introductory Class
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.
- Lecture 2-3 (Order, Degree & Differential Equation)
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:
§ 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
- Lecture 4-5 (Separation of Variable and Reducible to Variable Separable)
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
- First Quiz
- Lecturer 6-7 (Homogeneous Equation and reducible to Homogeneous Equation)
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
- Submit your assignment
- Lecture 8-9 (Exact Differential Equation and Linear Differential Equation)
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
- Lecture 10-11 (Bernoulli's Differential Equation )
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
- Second Quiz
- Submit your presentation
- Instruction for Mid-Term examination
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)
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
- Third Quiz
- Instruction for Final examination
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