Scientific Programming using Excel for Beginners: Newton's Method

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This document describes using Newton's method to find the root of a function. It begins with an introduction to the problem and objective, which is to approximate the root of a function using Newton's method. It then provides details on how Newton's method works through iterative approximations. The document walks through an example problem step-by-step to find the root of a cubic equation. It concludes by demonstrating how to program Newton's method using VBA code in Excel, with exercises to define a function to estimate the root over multiple iterations using a loop.

Education

Scientific Programming Using Excel
for Beginners: Newton's Method
by
RIZAuddin bin Saian
Faculty of Computer & Mathematical Sciences
Universiti Teknologi MARA (Perlis)
Venue: Lab 1, UiTM Perlis
5 February 2016 (Friday)
3pm

Scientific Programming Using Excel for Beginners: Newton's Method
Problem
• We want to find the root for .
 xfy 
 xfy 
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Scientific Programming Using Excel for Beginners: Newton's Method
Objective
• To approximate the root for
using Newton’s method (Newton-Raphson
method)
– Perform Newton’s method by hand.
– Write a VBA code to perform the Newton’s
method.
 xfy 
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Scientific Programming Using Excel for Beginners: Newton's Method
Newton’s Method
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Scientific Programming Using Excel for Beginners: Newton's Method
Equation of tangent line
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Scientific Programming Using Excel for Beginners: Newton's Method
Initial Guess of x
Actual root
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X
X
x0
(Initial guess)
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Scientific Programming Using Excel for Beginners: Newton's Method
Iteration 1
X
Tangent line at x0 = -1
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xx 
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Actual root
(Initial guess)
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Scientific Programming Using Excel for Beginners: Newton's Method
Iteration 2
x1
Tangent line at x1
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Scientific Programming Using Excel for Beginners: Newton's Method
Example: Find the root.
Actual root
X
x0 = -1
X
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  13
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Scientific Programming Using Excel for Beginners: Newton's Method
Initial guess of x
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Scientific Programming Using Excel for Beginners: Newton's Method
Iteration 1
i x xn+1
0 - 1 -1.5
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Scientific Programming Using Excel for Beginners: Newton's Method
Iteration 2
i x xn+1
0 - 1 -1.5
1 -1.5 -1.347826087
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Scientific Programming Using Excel for Beginners: Newton's Method
Iteration 3
i x xn+1
0 - 1 -1.5
1 -1.5 -1.347826087
2 -1.347826087 -1.325200399
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Scientific Programming Using Excel for Beginners: Newton's Method
Iteration 4
i x xn+1
0 - 1 -1.5
1 -1.5 -1.347826087
2 -1.347826087 -1.325200399
3 -1.325200399 -1.324718174
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Scientific Programming Using Excel for Beginners: Newton's Method
Iteration 5
i x xn+1
0 - 1 -1.5
1 -1.5 -1.347826087
2 -1.347826087 -1.325200399
3 -1.325200399 -1.324718174
4 -1.324718174 -1.324717957
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Scientific Programming Using Excel for Beginners: Newton's Method
Iteration 6
i x xn+1
0 - 1 -1.5
1 -1.5 -1.347826087
2 -1.347826087 -1.325200399
3 -1.325200399 -1.324718174
4 -1.324718174 -1.324717957
5 -1.324717957 -1.324717957
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Scientific Programming Using Excel for Beginners: Newton's Method
Visual Basic for Application (VBA)
Press Alt key and hold. Then, press F11 together to open the VBA Editor.
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Scientific Programming Using Excel for Beginners: Newton's Method
Add new Module
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Scientific Programming Using Excel for Beginners: Newton's Method
Define a function
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Scientific Programming Using Excel for Beginners: Newton's Method
Exercise 1
• Define function Newton with parameter “x”
and return the estimation value for the root of
with x0=-1.  13
 xxxf
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Scientific Programming Using Excel for Beginners: Newton's Method
Loop
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Scientific Programming Using Excel for Beginners: Newton's Method
Exercise 2
• Modify the Newton function in Ex. 1 to use
loop to calculate the root using 4 iterations.
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THANK YOU
www.rizauddin.com
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The recent surge in pro-Palestine student activism has prompted significant responses from universities, ranging from negotiations and divestment commitments to increased transparency about investments in companies supporting the war on Gaza. This activism has led to the cessation of student encampments but also highlighted the substantial sacrifices made by students, including academic disruptions and personal risks. The primary drivers of these protests are poor university administration, lack of transparency, and inadequate communication between officials and students. This study examines the profound emotional, psychological, and professional impacts on students engaged in pro-Palestine protests, focusing on Generation Z's (Gen-Z) activism dynamics. This paper explores the significant sacrifices made by these students and even the professors supporting the pro-Palestine movement, with a focus on recent global movements. Through an in-depth analysis of printed and electronic media, the study examines the impacts of these sacrifices on the academic and personal lives of those involved. The paper highlights examples from various universities, demonstrating student activism's long-term and short-term effects, including disciplinary actions, social backlash, and career implications. The researchers also explore the broader implications of student sacrifices. The findings reveal that these sacrifices are driven by a profound commitment to justice and human rights, and are influenced by the increasing availability of information, peer interactions, and personal convictions. The study also discusses the broader implications of this activism, comparing it to historical precedents and assessing its potential to influence policy and public opinion. The emotional and psychological toll on student activists is significant, but their sense of purpose and community support mitigates some of these challenges. However, the researchers call for acknowledging the broader Impact of these sacrifices on the future global movement of FreePalestine.

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Chapter wise All Notes of First year Basic Civil Engineering Syllabus Chapter-1 Introduction to objective, scope and outcome the subject Chapter 2 Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country. Chapter 3 Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements. Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station. Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps. Chapter 4 Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation Chapter 5 Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures. Chapter 6 Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems. Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect Text Books: 1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers. 2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers. 3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House. 4. BCP, Surveying volume 1

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Scientific Programming using Excel for Beginners: Newton's Method

1. Scientific Programming Using Excel for Beginners: Newton's Method by RIZAuddin bin Saian Faculty of Computer & Mathematical Sciences Universiti Teknologi MARA (Perlis) Venue: Lab 1, UiTM Perlis 5 February 2016 (Friday) 3pm

2. Scientific Programming Using Excel for Beginners: Newton's Method Problem • We want to find the root for .  xfy   xfy  5/2/2016 2 http://www.rizauddin.com

3. Scientific Programming Using Excel for Beginners: Newton's Method Objective • To approximate the root for using Newton’s method (Newton-Raphson method) – Perform Newton’s method by hand. – Write a VBA code to perform the Newton’s method.  xfy  5/2/2016 3 http://www.rizauddin.com

4. Scientific Programming Using Excel for Beginners: Newton's Method Newton’s Method    n n nn xf xf xx ' 1  5/2/2016 4 http://www.rizauddin.com

5. Scientific Programming Using Excel for Beginners: Newton's Method Equation of tangent line                      n n nn n n nn nnnn n nnnnn xf xf xx xf xf xx xxxfxf xxf xxxfxfxf ' ' '0 interceptat the0 ' 1 1 1 1 11           5/2/2016 5 http://www.rizauddin.com

6. Scientific Programming Using Excel for Beginners: Newton's Method Initial Guess of x Actual root  xfy  X X x0 (Initial guess) 5/2/2016 6 http://www.rizauddin.com

7. Scientific Programming Using Excel for Beginners: Newton's Method Iteration 1 X Tangent line at x0 = -1    0 0 01 ' xf xf xx  X  xfy  x0x1 Actual root (Initial guess) 5/2/2016 7 http://www.rizauddin.com

8. Scientific Programming Using Excel for Beginners: Newton's Method Iteration 2 x1 Tangent line at x1    1 1 12 ' xf xf xx  X X  xfy  x0 Actual root (Initial guess) 5/2/2016 8 http://www.rizauddin.com

9. Scientific Programming Using Excel for Beginners: Newton's Method Example: Find the root. Actual root X x0 = -1 X 5/2/2016 9 http://www.rizauddin.com   13  xxxf

10. Scientific Programming Using Excel for Beginners: Newton's Method Initial guess of x   13  xxxf    13' 1 2 3   xxf xxxf 1 ,ofguessInitial 0 x x     13 1 ' 2 3 1     x xx x xf xf xxn The estimated root, 5/2/2016 10 http://www.rizauddin.com

11. Scientific Programming Using Excel for Beginners: Newton's Method Iteration 1 i x xn+1 0 - 1 -1.5 5/2/2016 11 http://www.rizauddin.com

12. Scientific Programming Using Excel for Beginners: Newton's Method Iteration 2 i x xn+1 0 - 1 -1.5 1 -1.5 -1.347826087 5/2/2016 12 http://www.rizauddin.com

13. Scientific Programming Using Excel for Beginners: Newton's Method Iteration 3 i x xn+1 0 - 1 -1.5 1 -1.5 -1.347826087 2 -1.347826087 -1.325200399 5/2/2016 13 http://www.rizauddin.com

14. Scientific Programming Using Excel for Beginners: Newton's Method Iteration 4 i x xn+1 0 - 1 -1.5 1 -1.5 -1.347826087 2 -1.347826087 -1.325200399 3 -1.325200399 -1.324718174 5/2/2016 14 http://www.rizauddin.com

15. Scientific Programming Using Excel for Beginners: Newton's Method Iteration 5 i x xn+1 0 - 1 -1.5 1 -1.5 -1.347826087 2 -1.347826087 -1.325200399 3 -1.325200399 -1.324718174 4 -1.324718174 -1.324717957 5/2/2016 15 http://www.rizauddin.com

16. Scientific Programming Using Excel for Beginners: Newton's Method Iteration 6 i x xn+1 0 - 1 -1.5 1 -1.5 -1.347826087 2 -1.347826087 -1.325200399 3 -1.325200399 -1.324718174 4 -1.324718174 -1.324717957 5 -1.324717957 -1.324717957 5/2/2016 16 http://www.rizauddin.com

17. Scientific Programming Using Excel for Beginners: Newton's Method Iteration 6 i x xn+1 0 - 1 -1.5 1 -1.5 -1.347826087 2 -1.347826087 -1.325200399 3 -1.325200399 -1.324718174 4 -1.324718174 -1.324717957 5 -1.324717957 -1.324717957 STOP! 5/2/2016 17 http://www.rizauddin.com

18. Scientific Programming Using Excel for Beginners: Newton's Method Visual Basic for Application (VBA) Press Alt key and hold. Then, press F11 together to open the VBA Editor. 5/2/2016 18 http://www.rizauddin.com

19. Scientific Programming Using Excel for Beginners: Newton's Method Add new Module 5/2/2016 19 http://www.rizauddin.com

20. Scientific Programming Using Excel for Beginners: Newton's Method Define a function 5/2/2016 20 http://www.rizauddin.com

21. Scientific Programming Using Excel for Beginners: Newton's Method Exercise 1 • Define function Newton with parameter “x” and return the estimation value for the root of with x0=-1.  13  xxxf 5/2/2016 21 http://www.rizauddin.com

22. Scientific Programming Using Excel for Beginners: Newton's Method Exercise 1 • Define function Newton with parameter “x” and return the estimation value for the root of with x0=-1.  13  xxxf 5/2/2016 22 http://www.rizauddin.com

23. Scientific Programming Using Excel for Beginners: Newton's Method Loop 5/2/2016 23 http://www.rizauddin.com

24. Scientific Programming Using Excel for Beginners: Newton's Method Exercise 2 • Modify the Newton function in Ex. 1 to use loop to calculate the root using 4 iterations. 5/2/2016 24 http://www.rizauddin.com

25. Scientific Programming Using Excel for Beginners: Newton's Method Exercise 2 • Modify the Newton function in Ex. 1 to use loop to calculate the root using 4 iterations. 5/2/2016 25 http://www.rizauddin.com

26. THANK YOU www.rizauddin.com 5/2/2016 26 http://www.rizauddin.com

Scientific Programming using Excel for Beginners: Newton's Method

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