This document introduces numerical methods and their importance in computer science and engineering. It explains that numerical methods are used to approximate solutions to mathematical problems that cannot be solved analytically or that are too computationally expensive to solve analytically. It outlines the typical steps involved in using numerical methods which are to formulate a mathematical model, construct an appropriate numerical method, implement the method, and validate the solution. Finally, it provides some examples of how numerical methods are applied in fields like engineering, science, and modeling real-world phenomena.

1. Welcome
Importance of Numerical
Methods in CSE

2. What is Numerical
Methods
Numerical analysis is the study of
algorithms that use numerical
approximation for the problems of
mathematical analysis.
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3. Needs of
Numerical
Methods
 Mathematical models are a central pieces of
science & engineering.
 Some models have closed-form solutions,
therefore they can be solved analytically. Many
models can’t be solved analytical or the analytic
solution is too costly to be practical
 All models can be solved computationally and the
result may not bathe exact answer but it can be
useful.
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4. Steps
involved
to solve
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• Formulation of Mathematical model.
• Construct of an appropriate
numerical methods.
• Implementation of the numerical
method.
• Validation of solution.

5. Why are numerical methods used in engineering
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• Engineers use mathematics modeling
which includes various equation and
data to describe and predict the behavior
of systems.
• Computers are widely used which give
accurate result and are cheap to all.
• Many software packages are available
that can be used to solve the problems.

6. Scientific computing using Numerical
methods
• Design and analysis for numerically
solving mathematical problems in
science and engineering.
• Effects of application and perform
error analysis.
• Modern simulation of engineering
application.
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7. How it applied
Develop a
mathematical
problem with your
skills and the
requirement
1
Come up with a
numerical
algorithm.
2
Implement the
algorithm.
3
Run,dubg,test the
code.
4
Validate the result.
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8. What is the uses of
numerical analysis
in our life?

9. Estimation of
ocean
currents
Modelling of airflow
over airplanes.

10. Shock Wave
Curve fitting of
tabular data

11. Electromagnetic
s
Shuttle tank
separation

12. Thank you