1. Lecture 7: Taylor Series Validity, Power Series, Vectors, Dot Products, and Cross Product

2. Part I: Validity of Taylor Series

3. Taylor Series Failure

4. Taylor series remainder term

5. Part II: Power Series

6. Objectives Know what power series are and how to determine the radius of convergence of power series Know how power series can be manipulated within their radius of convergence Corresponding sections of Simmons: 14.2,14.3

7. Power Series

8. Radius of Convergence

9. Manipulating Power Series

10. Uniqueness of Power/Taylor Series

11. Part III: Vectors

12. Objectives Know what vectors are Know how find the magnitude, direction, dot product, and cross product of vectors. Corresponding sections in Simmons: 18.1, 18.2, 18.3

13. Vectors

14. Picture for vectors 01 2 3 4 -2 -3 -4 0 1 2 3 4 -2 -3 -4 56 -5-6 -5 -6 5 6

15. Scalar Multiplication of Vectors and Vector Direction

16. Vector Addition and Subtraction

17. Displacement and Position Vectors

18. Dot Product

19. Properties of the dot product

20. Geometric Picture of the dot product

21. Connection between algebraic and geometric pictures a b c A B C PQ R

22. Condition for Perpendicular Vectors

23. Cross Product

24. Properties of the cross product

25. Geometric Picture of the Cross Product