1. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Linearization and Newton’s Method Section 4.5

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 2 Quick Review

3. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 3 What you’ll learn about Linear Approximation Newton’s Method Differentials Estimating Change with Differentials Absolute, Relative, and Percent Change Sensitivity to Change …and why Engineering and science depend on approximation in most practical applications; it is important to understand how approximation techniques work.

4. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 4 Linearization

5. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 5 Example Finding a Linearization

6. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 6 Procedure for Newton’s Method

7. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 7 Procedure for Newton’s Method

8. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 8 Using Newton’s Method

9. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 9 Differentials

10. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 10 Example Finding the Differential dy

11. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 11 Differential Estimate of Change

12. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 12 Estimating Change with Differentials

13. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 4- 13 Example Estimating Change with Differentials

14. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Page 229 (1-7 odd, 11-33 odd) Slide 4- 14