#### welcome

Teacher Information Md. Shorif Hossan (MSH)

Lecturer (Mathematics)

Department Of General Educational Development (GED), FSIT, DIU.

Counseling Time: Anytime

Teachers Room: 505 (AB-4), PC, DIU.

Cell: 01517-814722

E-Mail: shorif.ged0175.c@diu.edu.bd

For more information### Introduction

Today's fast-moving information technology field requires professionals with math skills that will require them to manipulate mathematical concepts and interpret data. Computer Networking and database technologies require knowledge in Ordinary and partial differential equations, and this course will give the students a good working knowledge of these areas.

In mathematics, an

**ordinary differential equation**(**ODE**) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions. The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable.Mathematics III is a branch of applied mathematics concerning mathematical methods and techniques that are typically used in computer engineering and industry. Along with fields like engineering physics and engineering geology, both of which may belong in the wider category engineering science, engineering mathematics is an interdisciplinary subject motivated by engineers' needs both for practical, theoretical and other considerations out with their specialization and to deal with constraints to be effective in their work. Historically, mathematics III consisted mostly of applied analysis, most notably: differential equations; ordinary differential equation, and partial differential equations. The success of modern numerical computer methods and software has led to the emergence of computational mathematics, computational science, and computational engineering, which occasionally use high-performance computing for the simulation of phenomena and the solution of problems in the sciences and engineering. These are often considered interdisciplinary fields but are also of interest to mathematics III. Engineering mathematics in tertiary education typically consists of mathematical methods and model courses.

**Objective/Goals to the course:**A mathematics course has more than one purpose. Students should learn a particular set of mathematical facts and how to apply them; more importantly, such a course should teach students how to think logically and mathematically. To achieve these goals, this text stresses mathematical reasoning and the different ways problems are solved.

Ø Students will be able to apply the concepts and methods described in the syllabus

Ø They will be able to solve problems using the differential equation

Ø They will know a number of applications.

Ø The text and class discussion will introduce the concepts, methods, applications, and logical arguments;

Ø Students will practice them and solve problems on daily assignments, and they will be tested on quizzes, midterms, and the final.

### Outcomes of the course:

On successful completion of this course students will be able to:

- Apply statistical analysis of a variety of experimental and observational studies
- Solve statistical problems using computational tools.
- Derive mathematical models of physical systems.
- Solve differential equations using appropriate methods.
- Present mathematical solutions in a concise and informative manner.
- develop a logical understanding of the subject.
- develop mathematical skills so that students are able to apply mathematical methods & principals in solving problems from Engineering fields.
- identify the pattern of the program outcomes on engineering mathematics subjects.
- explain the concept of a differential equation and Classify the differential equations with respect to their order and linearity.
- solve first-order ordinary differential equations, Convert, separable and homogenous equations to exact differential equations by integrating factors, Solve Bernoulli differential equations.
- find solutions to higher-order linear differential equations.
- classify partial differential equations and transform into canonical form
- solve linear partial differential equations of both first and second order
- apply partial derivative equation techniques to predict the behaviour of certain phenomena.
- apply specific methodologies, techniques and resources to conduct research and produce innovative results in the area of specialisation.
- extract information from partial derivative models in order to interpret reality.
- identify real phenomena as models of partial derivative equations.

### Course Contents:

**Ordinary Differential Equation:**Formation of Differential Equation; First order and a first-degree differential equation, Separation of Variables, Homogenous equation, Equation reducible to homogenous, Exact equation, Linear Equation, Reducible to Linear Equation, Linear Differential Equations with Constant Coefficients, Linear Differential Equation with right-hand side non zero, Variation of parameter, Method of Successive approximation, Reduction of Order, Method of undermined Coefficient, Matrix method, Various types of Application of Differential Equations**Partial Differential Equation:**Formation of Partial Differential equation, Linear and Non-Linear first-order equation, Standard forms, Linear Equation of higher order, Partial Differential Equations With Constant Coefficients, Equation of second order with variable coefficients, Wave & Heat equations, Particular solution with boundary and initial conditions.### Assessment plan:

#### Course Assessment Plan

Assessment Policy:Assessment

Probable Date

Syllabus

Questions

MarkS

Quiz 01

Will be declared in the class.

Class Lecture

Five Short Question

3*5=15

Quiz 02

Will be declared in the class.

Quiz 03

Will be declared in the class.

Assignment

Based on the class lectures

Will be given in class

(5 Marks)

Presentation

After the Midterm exam

The topic will be announced in the class

(8 Marks)

Midterm Exam

According to the date declared by the University

Lecture 01-13

Five out of six questions

5*5=25

Final Exam

According to the date declared by the University

Lecture 14-24

Five out of six questions

5*8=40

Class Attendance

Marks will be distributed equally according to the number of classes attended

(7 Marks)

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

ü Besides, ‘W’ and ‘I’ grade may be awarded as per university rule.

Marks distribution:

The final course grade will be awarded based on the marks distribution shown in the table above. Percentages of marks for the different heads are given below

Attendance

07 %

Class Test

15 %

Assignment

05%

Presentation

08%

Midterm

25%

Final Exam

40 %

Total

100%

**Semester Class Schedule**##### SESSION

##### DURATION

##### COURSE CONTENT

##### Session 1

##### 90 minutes

##### Introductory Class some pre-requisite topics will be discussed

##### Session 2

##### 90 minutes

##### Differential Equations: Basic concepts,

##### Session 3

##### 90 minutes

##### A solution of the first-order and first degree ODE, Separation of variables.

##### Session 4

##### 90 minutes

##### A solution of Homogeneous Equation

##### Session 5

##### 90 minutes

##### Reducible to the homogeneous equation

##### Session 6

##### 90 minutes

##### A solution of 1st order Linear equation with IF factor

##### Session 7

##### 90 minutes

##### Quiz-1 and discussion

##### Session 8

##### 90 minutes

##### A solution of Bernoulli’s equations

##### Session 9

##### 90 minutes

##### A solution of linear model differential equations

##### Session 10

##### 90 minutes

##### Properties of Solutions of general linear equations with constant coefficients

##### Session 11

##### 90 minutes

##### Math Solutions of general linear equations with constant coefficients

##### Session 12

##### 90 minutes

##### Math Solutions of general linear equations with constant coefficients: right side non zero

##### Session 13

##### 90 minutes

##### Quiz 2 and discussion

##### Mid Term Examination

##### Session 14

##### 90 minutes

##### The solution to the initial value problem

##### Session 15

##### 90 minutes

##### Application of linear equations of 1st order

##### Session 16

##### 90 minutes

##### Application of linear equations of 2nd order

##### Session 17

##### 90 minutes

##### Introduction to the PDE

##### Session 18

##### 90 minutes

Formation to the PDE

##### Session 19

##### 90 minutes

##### Quiz 3 and discussion

##### Session 20

##### 90 minutes

##### 1

^{st}order PDE: Lagrange equation##### Session 21

##### 90 minutes

##### PDE with constant coefficient with right-hand side zero

##### Session 22

##### 90 minutes

##### PDE with constant coefficient with right-hand side non zero

##### Session 23

##### 90 minutes

##### Wave and heat equation

##### Session 24

##### 90 minutes

##### Revision of lectures

##### Final Examination