Calculus I

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Assignments

There will be two types of assignments for this course: solving problems from your textbook and writing assignments (essays) based on material covered in class.

Problems from Textbook
Chapter 2: Section 2.1: # 1, 3, 4, 5, 6, 7, 8, 11, 14, 16 Section 2.2: # 1, 3, 5, 7, 11, 13, 15, 19, 20, 22, 30, 32, 34 Section 2.3: # 1, 3, 8, 9, 10, 14, 16, 22, 24, 26 Section 2.4: # 5, 8, 11, 15, 22, 24, 31, 33, 38, 39 Section 2.5: # 2, 6, 7, 9, 12, 15, 19 Section 2.6: # 2 - 6, 12, 14, 18, 18, 20, 22 Section 2.7: # 2, 6, 8, 10, 11 Chapter 3: Section 3.1: # 5, 6, 9, 10, 21, 22, 25, 27, 40, 42 - 44, 59 Section 3.2: # 5, 6, 12, 16, 24, 25, 28, 35, 38, 40, 43, 44 Section 3.3: # 2, 4, 11, 20, 28, 29, 32, 41, 42, 47	Chapter 3 (Cont.) Section 3.4: # 2, 12, 20, 24, 26, 41, 44, 53, 55, 56, 58, 63 Section 3.5: # 4, 5, 11, 18, 20, 25, 27, 37, 46, 47, 48 Section 3.6: # 3, 4, 8, 18, 20, 22, 25, 32, 41, 45, 47 Section 3.7: # 2, 9, 10, 11, 21, 27 Section 3.9: # 2, 4, 10, 11, 15 Section 3.10: # 2, 4, 6, 13, 14, 19 Chapter 4: Section 4.1: # 2, 4, 9, 10, 18, 19, 24,25, 26, 32, 34, 36, 40, 42 Section 4.3: # 2, 4, 12, 15, 25, 31, 32 Section 4.5: # 2, 5,6, 14, 16 Section 4.7: # 8-10, 13-15, 18, 22, 26, 30, 31	Chapter 5: Section 5.1: # 2-4, 6-8, 11, 14 Section 5.2: # 1, 2, 8, 13, 16, 20, 23, 24, 27, 30 Section 5.3: # 6, 8, 9, 14, 18, 20, 23, 24, 31 Section 5.4: # 1, 5, 6, 9, 11, 12, 14, 15 Chapter 6: Section 6.1: # 1, 4, 6, 10, 11, 15, 17, 18, 23 Section 6.2: # 6, 12, 16, 28, 32, 37, 46, 53, 55, 67, 72, 77, 81, 83 Section 6.3: # 2, 4, 7, 12-14, 19, 23 Section 6.4: # 2, 4, 6, 8, 11, 18, 19, 22, 23 Section 6.5: # 2, 4, 6 Chapter 7: Section 7.1: Even #s 4-40, Even #s 49-68, 43, 44, 70, 75 Section 7.2: # Even #s 2 - 54

Writing Assignments:

1. Discuss the existence/non-existence of the limit of a function at a point. Give examples to illustrate your point. Extend your discussion to limits at infinity. Give examples to illustrate functions that have limits at infinity and those that do not. Where possible, make generalizations. As you write, please remember to use complete sentences and check your spelling.
Due date: 3/25/02. Length: 2-3 pages.

2. Discuss the three conditions that must be met for a function to be continuous at a point. Give examples of functions that fail one, two, and/or all three conditions, as well as examples of functions that meet all three conditions. When giving examples of discontinuous functions, explain in detail which conditions fail. Illustrate your work with graphs. Additionally, discuss how you would determine that a function is continuous on a closed interval. Support your discussion with an example.
Due date: 4/10/02. Length: 3-4 pages.

3. Revisit the "Derivatives and Applications" forum on Blackboard and write a report on what you heard. If you read any statements that could be improved on, do so in your report.
Due date: 5/20/02. Length: 3 - 4 pages.

Final Project

We have discussed many interesting calculus topics in class, and in some cases, we have tried to give some of the underlying history. As I am sure you have come to appreciate, the mathematics we study today has been influenced by many cultures around the world: Africans, Arabs, Asians, Babylonians, Greeks, Mayans, to name a few.

Choose a concept you have studied in any mathematics course and that you find interesting, and write at least an eight (8) page report discussing its development and how it has been used to solve real-life problems.

Before you embark on this project, visit the library and some of the links on this site, and write a synopsis of your chosen topic. Make an appointment to see me to discuss how to refine your ideas so that the project will be manageable.

Here are some suggested topics that have already been proposed by your classmates:

1. Who should get the most credit for calculus: Newton or Leibniz?

2. Applications of some calculus concepts in economics.

3. The derivative of a function and some related applications.

4. Zero in the world of the Mayans.