This document discusses numerical methods for curve fitting using the least squares method. It introduces curve fitting and covers linear and non-linear least squares methods. Specifically, it describes fitting linear, exponential, and hyperbolic curves to data using the least squares approach and includes examples of applying each method to problems. Quizzes are also provided to test the different curve fitting models.

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