curve fitting in numerical methods

1. Numerical Methods For Engineers
Lecture 7: Curve Fitting
By
MD Irfan Ali
Thermal & Aerospace Program
School of Mechanical Chemical & Materials
Engineering
1

2. Contents
1) Introduction
2) Least Square Method
3) Linear Curve Fitting using least square method
4) Non-Linear Curve Fitting using least square method

3. Introduction

4. Least Square Method

5. Least Square Method

6. Least Square Method

7. Least Square Method

8. Least Square Method

9. Linear Least Square Method

10. Problem on Linear Least Square Method
Solution:

11. Non-Linear Least Square Method (Exponential Form)

12. Problem on Least Square Method (Exponential Form)
Solution:

13. Non-Linear Least Square Method (Hyperbolic Form)

14. Problem on Least Square Method (Hyperbolic Form)
Solution:

15. Quiz: Choose the best answer
The exponential fit is of the form:
a) 𝑦 = 𝑎𝑥 + 𝑏
b) 𝑦 = 𝑎𝑒𝑏𝑥
c) 𝑦 = 𝑎 +
𝑏
𝑥
d) None of the above
Ans.: b

16. Quiz: Choose the best answer
The Linear fit is of the form:
a) 𝑦 = 𝑎𝑥 + 𝑏
b) 𝑦 = 𝑎𝑒𝑏𝑥
c) 𝑦 = 𝑎 +
𝑏
𝑥
d) None of the above
Ans.: a

17. Quiz: Choose the best answer
The Hyperbolic fit is of the form:
a) 𝑦 = 𝑎𝑥 + 𝑏
b) 𝑦 = 𝑎𝑒𝑏𝑥
c) 𝑦 = 𝑎 +
𝑏
𝑥
d) None of the above
Ans.: c

18. Summary
In this chapter we covered the following topics:
1) Introduction to curve fitting
2) Least Square Method
3) Linear Curve Fitting using least square method
4) Non-Linear Curve Fitting (Exponential and Hyperbolic) using least square
method