( 46 Reviews )

# Introduction to Ordinary Differential Equations

Course Level

Total Hour

Video Tutorials

### 9

1h

#### Conclusion

Ordinary differential equations (ODEs) are a set of mathematical equations that provide a way to describe the behavior of a system that changes over time. They are used in many fields, ranging from engineering to physics and even biology. These equations can be used to describe simple systems or complex ones, depending on the complexity of the problem you’re trying to solve. We will take a look at what ordinary differential equations are, how they work, and some examples of how they can be used in problem-solving.

An ordinary differential equation (ODE) is a differential equation that contains one or more functions of one independent variable and its derivatives. There are several types of Ordinary Differential Equations (ODEs) and it has their own distinct characteristics.  The most general type of ODE is the nonlinear equation. and it can solve using elementary methods. In some cases, it may even be possible to find an exact solution to a nonlinear equation. Differential equations are mathematical models that describe how a system changes over time.

• The advantage is that they can be used to describe complex systems in a concise way.
• The disadvantage is that they can be difficult to solve.

Ordinary differential equations are an important part of mathematics and it helps to solve a wide range of problems. From describing the motion of physical objects to predicting the evolution of populations, ordinary differential equations help us understand and predict phenomena in our world. With their versatile applications and powerful mathematical tools, they will continue to be invaluable in helping us make sense of complex systems in science and engineering.

ODEs can forecast the external environment and have amazing applications. Numerous academic fields, including biology, economics, physics, chemistry, and engineering, employ it. Utilizations for ODEs include:

1. Cooling/Warming Law(Newton)

2. Population Growth and Decay

3. Radio-Active Decay and Carbon Dating

4. Mixture of Two Salt Solutions

5. Series Circuits

6. Survivability with AIDS

7. Draining a tank

8. Economics and Finance

9. Mathematics Police Women

10. Drug Distribution in Human Body

11. A Pursuit Problem

12. Harvesting of Renewable Natural Resources

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How to prepare for studying online

#### What to learn?

Identify the type of a given differential equation and select and apply the appropriate analytical technique for finding the solution of first-order and selected higher-order ordinary differential equations. Evaluate first order differential equations including separable, homogeneous, exact, and linear. Show the existence and uniqueness of solutions. Create and analyze mathematical models using first-order differential equations to solve application problems such as circuits, mixture problems, population modeling, orthogonal trajectories, and slope fields. Solve second-order and higher-order linear differential equations. Determine fundamental solutions and independence using the Wronskian. Solve non-homogeneous equations. Create and analyze mathematical models using higher-order differential equations to solve application problems such as harmonic oscillators and circuits. Solve differential equations using a variation of parameters.

### Audience

• The students who want to learn the ordinary differential equations.

### Protima Dash

1 Courses

Hello, I am Protima Dash. I am working as a Lecturer (Senior Scale) in Mathematics, Department of General Educational Development, Faculty of Science and Information Technology, Daffodil International University, Dhaka,…

### Student Ratings & Reviews

5.0
Total 46 Ratings
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A
4 weeks ago
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MY
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A
4 weeks ago
Nice Class Ma\'am. 4 weeks ago
mathamatics is very well presented
S
4 weeks ago
very impressive
KU
4 weeks ago
good courses are available here
MN
4 weeks ago
It was amazing
MB
4 weeks ago
good
AA
4 weeks ago
It was amazing.
M
4 weeks ago
thank you
R
4 weeks ago
T
4 weeks ago
mind blowing
AI
4 weeks ago
Wonderful
RR
4 weeks ago
good
HI
4 weeks ago
good
WW
4 weeks ago
This course is good for me.
M
4 weeks ago
good
NH
4 weeks ago
EXECELLENT COURSE MAM
AH
4 weeks ago
Outstanding class Ma\'am.
S
4 weeks ago
Good
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