Calculus I (H&SS) 21-111, Fall 2004

Calculus I (H&SS) 21-111
Fall 2004

Announcements:

Important: The final exam will be in Hammerschlag Hall HH B103 & HH B131 on Monday, Dec. 20 at 8:30 am.

Important: Please bring your student ID to the exam as I will check them to make sure all of you take the exam only once. Please try to be at Hammerschlag Hall at least 10 min before the exam (which will start at 8:30 am) so there is time for checking the IDs.

The final exam is scheduled for December 20, 8:30-11:30 in HH B103 & HH B131.
If you cannot make the scheduled exam, there will be an early final on Saturday, December 11, 9-12 am in Porter Hall 100.
Please work through the Review-sheet for the final carefully. If you have any questions feel free to visit me in my office hour or arrange a different time with me if you cannot make the office hour. Answers to the Review for the Final. This might contain mistakes. but the way to solve these problems will be right.
The Grading scheme was slightly changed. Please see the Syllabus for the changes.
If you need help with the course, look here to find out about Peer tutoring, come to my office hours or email me.
Course Description:
Syllabus

Required Text:
Goldstein, Lay, Schneider: Brief Calculus and its Applications (10th Edition) (Pearson Prentice Hall)
Homework:
Homework will be assigned weekly on Wednesdays and posted here. The solutions will be posted a couple of days after the homework was handed in.

Homework 1 Due in recitation on Thursday, September 16.

Homework 2 Due in recitation on Thursday, September 23. Solutions (A.Turlington)

Homework 3 Due in recitation on Thursday, September 30. Solutions page 1, page 2 (G. Nora)

Homework 4 Due in recitation on Thursday, October 7. Solutions page 1 , page 2 (C. Rudloff)

Homework 5 Due in recitation on Thursday, October 14. Solutions (A.Turlington)

Homework 6 Due in recitation on Thursday, October 21. Solutions page 1 ,page 2(G. Nora)

Homework 7 Due in recitation on Thursday, November 4. Solutions page 1 (C. Rudloff)

Homework 8 Due in recitation on Thursday, November 11. Solutions page 1 ,page 2(A. Turlington)

Homework 9 Due in recitation on Thursday, November 18. Solutions page 1 ,page 2(G. Nora)

Homework 10 Due in recitation on Thursday, December 9. Solutions(C.Rudloff)

Diagnostics Test

Course-Test 1 with Solutions

Course-Test 2 solutions

Weekly plan and practice problems

Week 1: Lecture 1: Diagnostic test
Lectures 2/3: According to the diagnostic test, we will go through the basics like adding and multiplying fractions, Exponents and Roots, and Intervals. Then we will learn how to complete a square, and solve equations of different kinds with methods like the quadratic formula.
Extra problems: As there is no book for this part of the course, extra problems will be handed out in class. Please try to find the solutions using methods we learned in class. After the Wednesday lecture you should have methods to solve all the problems up to the questions about intervals. The other questions will use methods we will learn on Friday.
If you missed picking up a copy during class, there will be some extra copies in front of Wean Hall 7124.

Week 2: Lectures 4/5: We will learn ways of changing the form of a polynomial, mostly by looking at different ways of factoring it. Afterwords we will learn about rationalizing the denominator (numerator) of a fraction and how to simplify complex algebraic expressions.
Extra problems: These will be made available on Wednesday in class and do not need to be handed in. You should work the extra problems out nevertheless as mathematics is in a large part practice.
Week 3: Lectures 6/7/8: We will start with Calculus this week . The first lecture will be used to get used to the concept of functions and their graphs, including different ways of representing functions graphically. Afterwords, we will learn about some important functions and how to recognizes them from their graphs. These will include linear functions and quadratic functions, polynomials and rational functions. We will also start to look at the Algebra of functions. The last topic for the week should be Zeros of functions and their meaning.
Extra problemsThese will appear on the homework sheet on this website on Wednesday. If you cannot wait you can work through some of the problems in the book.
Required Reading The required reading for this week are Sections 0.1, 0.2, 0.3 and 0.4 in the text-book.

Week 4: Lectures 9/10/11:This week will start with a short review of solving inequalities. Afterwords we will go back to finding roots of functions. The next topic will be exponent and power functions. Here we will especially concentrate on compound interest. We will then look at geometric and business applications of functions and graphs. The week will end with a first taste of the derivative, namely a discussion of the slope of a straight line. Remember that the Course-Test will take place on Monday the 27th of September.
Review for Course-Test (slightly changed on September 22) As the course-test is coming up next Monday there will be a Review sheet this week. Please do the problems as the questions on the test will be closely related.
If there are any questions about the review sheet, please do not hesitate to ask me or the Ta's. There are solutions on the Review sheet now. If you cannot match the solution on the sheet with your solution, do ask. It is important that you understand these problems.
Required Reading The required reading for this week are Sections 0.5, 0.6 and 1.1 in the text-book.

Week 5: Lecture 12:Course Test
Lecture2 13/14 This week we will learn about tangents to graphs and their connection to derivatives. We will also learn ways to calculate the derivative by using given derivatives, the Secant-Line Calculation and finally the use of limits. We will also learn more about limits and how to calculate with them.
Required Reading The required reading for this week are Sections 1.2, 1.3 and 1.4 in the text-book

Week 6: Lecture 15/16/17:This week we will learn about differentiability and continuity. We will see how continuity is used in real life situations. We will also learn some rules of differentiation, namely rules about constant multiples, the sum rule and the general power rule. Afterwards, we will look at applications of the derivative and the second derivative. We will also look at examples of the second derivative in nature and economics.
Required Reading The required reading for this week is the rest of chapter 1 in the text-book.

Week 7: Lecture 18/19/20: In the beginning of Monday's lecture, we will finish off the chapter 1 in the book. We will learn about approximating the change in a function and the marginal concept in economics. We will then move on to chapter 2 in the book, which is applications of the derivative. We will spend most of this week discussing how we can describe a graph of a function using the derivative. This will include concepts like concavity and asymptotes. We will use this knowledge to sketch graphs more effectively.
Required Reading The required reading for this week are sections 1.8, 2.1 , 2.2 and 2.3.

Week 8: Lecture 21:We will learn more about using the derivative to sketch a graph in this lecture. Then we will move on to optimization.
Lecture 22 will be used for a Review on the material covered in the second Course-Test.
Review for Course-Test.
Solutions in .ps format (including graphs)
Solutions in .pdf format (not including graphs) and graphs as a JPG. Graph 1, Graph 2
Should there be any questions about the Review sheet and the solutions, please see me (office hours Mo 9-10 and Th 12-1) or your TA. As the course-test is coming up next Monday there will be a Review sheet this week. Please do the problems as the questions on the test will be closely related.

Week 9: Lecture 23:Course Test
Lectures 24/25 This weeks lectures will be all about optimization problems. We will look at geometric problems as well as problems from economics.
Required Reading The required reading for this week are Sections 2.5 and 2.6 in the text-book

Week 10: Lecture 26/27/28:This week we will finish speaking about optimization. The last topics we will look at will be problems from business. These will deal with Cost, Revenue, Profit and Demand equations.
Afterwards we will learn more about techniques of differentiation. We will learn and verify Power-rule, Quotient-rule and Chain-rule for Differentiation. We will of course also learn how to use the rules using many examples. If we will have time in the end, we will look at implicit differentiation and related rates, which apply the knowledge we gained about differentiation rules.
Required Reading The required reading for this week are Sections 2.7, 3.1 and 3.2 in the text-book

Week 11: Lectures 29/30/31:Monday's lecture will be about implicit differentiation and related rates.
Next we will speak about exponential functions, their graphs and how to differentiate them. If time allows we will also start looking at logarithmic functions.
Review for Course-Test 3.

Week 12: Lecture 32:Monday's lecture will be about the exponential function again. We will look at how exponential functions are the solutions of the easiest differential equations. We will also have a look at graphs of exponential functions and how to transfer exponential functions with base b to exponential functions with base e. If time permits, we will start defining the natural logarithm as the inverse function of the exponential function.
Lectures 33/34: We will have two review lectures for the test next Monday. The first one will have examples of optimization and related rates and the second one will deal with the other topics. I will try and keep the examples at a level that might appear on the test.
Solutions to Review 3: Here are the written out solutions to Review-sheet 3. Important: Please try to solve the review-questions on your own before reading the solutions. Just reading the solutions won't help you solve the questions on the Test on your own.

Week 13: Lecture 35Course-Test at 3:30 in Porter Hall 100

Week 14: Lectures 36/37/38:On Monday we will talk about logarithmic functions a bit more. We will learn how to differentiate functions including logarithms and we will learn the logarithmic rules.
On Wednesday and Friday we will look at applications for exponential and logarithmic functions. These will include Exponential growth and decay, radiocarbon dating, and compound interest.
I will try to put a review sheet here before Wednesday so you can start preparing for the final early.

Week 15: Lecture 39:This will be the last lecture with new material. We will go through applications of the logarithm, namely the Relative and percentage rate of change and Elasticity of Demand and Price.
Lectures 40/41: In these two lectures we will review relevant material for the final exam.
Saturday, Dec. 11, 9am, Porter Hall 100 For those of you who cannot make the our final exam date on Monday, Dec. 20, this will be the opportunity to take the final early. Please let me know be Wednesday afternoon if you want to take the early final as I need to know the number of people who will take it, so I can prepare enough copies of the final exam.

Homework 1	Due in recitation on Thursday, September 16.
Homework 2	Due in recitation on Thursday, September 23.	Solutions (A.Turlington)
Homework 3	Due in recitation on Thursday, September 30.	Solutions page 1, page 2 (G. Nora)
Homework 4	Due in recitation on Thursday, October 7.	Solutions page 1 , page 2 (C. Rudloff)
Homework 5	Due in recitation on Thursday, October 14.	Solutions (A.Turlington)
Homework 6	Due in recitation on Thursday, October 21.	Solutions page 1 ,page 2(G. Nora)
Homework 7	Due in recitation on Thursday, November 4.	Solutions page 1 (C. Rudloff)
Homework 8	Due in recitation on Thursday, November 11.	Solutions page 1 ,page 2(A. Turlington)
Homework 9	Due in recitation on Thursday, November 18.	Solutions page 1 ,page 2(G. Nora)
Homework 10	Due in recitation on Thursday, December 9.	Solutions(C.Rudloff)

Week 1:	Lecture 1: Diagnostic test Lectures 2/3: According to the diagnostic test, we will go through the basics like adding and multiplying fractions, Exponents and Roots, and Intervals. Then we will learn how to complete a square, and solve equations of different kinds with methods like the quadratic formula. Extra problems: As there is no book for this part of the course, extra problems will be handed out in class. Please try to find the solutions using methods we learned in class. After the Wednesday lecture you should have methods to solve all the problems up to the questions about intervals. The other questions will use methods we will learn on Friday. If you missed picking up a copy during class, there will be some extra copies in front of Wean Hall 7124.
Week 2:	Lectures 4/5: We will learn ways of changing the form of a polynomial, mostly by looking at different ways of factoring it. Afterwords we will learn about rationalizing the denominator (numerator) of a fraction and how to simplify complex algebraic expressions. Extra problems: These will be made available on Wednesday in class and do not need to be handed in. You should work the extra problems out nevertheless as mathematics is in a large part practice.
Week 3:	Lectures 6/7/8: We will start with Calculus this week . The first lecture will be used to get used to the concept of functions and their graphs, including different ways of representing functions graphically. Afterwords, we will learn about some important functions and how to recognizes them from their graphs. These will include linear functions and quadratic functions, polynomials and rational functions. We will also start to look at the Algebra of functions. The last topic for the week should be Zeros of functions and their meaning. Extra problemsThese will appear on the homework sheet on this website on Wednesday. If you cannot wait you can work through some of the problems in the book. Required Reading The required reading for this week are Sections 0.1, 0.2, 0.3 and 0.4 in the text-book.
Week 4:	Lectures 9/10/11:This week will start with a short review of solving inequalities. Afterwords we will go back to finding roots of functions. The next topic will be exponent and power functions. Here we will especially concentrate on compound interest. We will then look at geometric and business applications of functions and graphs. The week will end with a first taste of the derivative, namely a discussion of the slope of a straight line. Remember that the Course-Test will take place on Monday the 27th of September. Review for Course-Test (slightly changed on September 22) As the course-test is coming up next Monday there will be a Review sheet this week. Please do the problems as the questions on the test will be closely related. If there are any questions about the review sheet, please do not hesitate to ask me or the Ta's. There are solutions on the Review sheet now. If you cannot match the solution on the sheet with your solution, do ask. It is important that you understand these problems. Required Reading The required reading for this week are Sections 0.5, 0.6 and 1.1 in the text-book.
Week 5:	Lecture 12:Course Test Lecture2 13/14 This week we will learn about tangents to graphs and their connection to derivatives. We will also learn ways to calculate the derivative by using given derivatives, the Secant-Line Calculation and finally the use of limits. We will also learn more about limits and how to calculate with them. Required Reading The required reading for this week are Sections 1.2, 1.3 and 1.4 in the text-book
Week 6:	Lecture 15/16/17:This week we will learn about differentiability and continuity. We will see how continuity is used in real life situations. We will also learn some rules of differentiation, namely rules about constant multiples, the sum rule and the general power rule. Afterwards, we will look at applications of the derivative and the second derivative. We will also look at examples of the second derivative in nature and economics. Required Reading The required reading for this week is the rest of chapter 1 in the text-book.
Week 7:	Lecture 18/19/20: In the beginning of Monday's lecture, we will finish off the chapter 1 in the book. We will learn about approximating the change in a function and the marginal concept in economics. We will then move on to chapter 2 in the book, which is applications of the derivative. We will spend most of this week discussing how we can describe a graph of a function using the derivative. This will include concepts like concavity and asymptotes. We will use this knowledge to sketch graphs more effectively. Required Reading The required reading for this week are sections 1.8, 2.1 , 2.2 and 2.3.
Week 8:	Lecture 21:We will learn more about using the derivative to sketch a graph in this lecture. Then we will move on to optimization. Lecture 22 will be used for a Review on the material covered in the second Course-Test. Review for Course-Test. Solutions in .ps format (including graphs) Solutions in .pdf format (not including graphs) and graphs as a JPG. Graph 1, Graph 2 Should there be any questions about the Review sheet and the solutions, please see me (office hours Mo 9-10 and Th 12-1) or your TA. As the course-test is coming up next Monday there will be a Review sheet this week. Please do the problems as the questions on the test will be closely related.
Week 9:	Lecture 23:Course Test Lectures 24/25 This weeks lectures will be all about optimization problems. We will look at geometric problems as well as problems from economics. Required Reading The required reading for this week are Sections 2.5 and 2.6 in the text-book
Week 10:	Lecture 26/27/28:This week we will finish speaking about optimization. The last topics we will look at will be problems from business. These will deal with Cost, Revenue, Profit and Demand equations. Afterwards we will learn more about techniques of differentiation. We will learn and verify Power-rule, Quotient-rule and Chain-rule for Differentiation. We will of course also learn how to use the rules using many examples. If we will have time in the end, we will look at implicit differentiation and related rates, which apply the knowledge we gained about differentiation rules. Required Reading The required reading for this week are Sections 2.7, 3.1 and 3.2 in the text-book
Week 11:	Lectures 29/30/31:Monday's lecture will be about implicit differentiation and related rates. Next we will speak about exponential functions, their graphs and how to differentiate them. If time allows we will also start looking at logarithmic functions. Review for Course-Test 3.
Week 12:	Lecture 32:Monday's lecture will be about the exponential function again. We will look at how exponential functions are the solutions of the easiest differential equations. We will also have a look at graphs of exponential functions and how to transfer exponential functions with base b to exponential functions with base e. If time permits, we will start defining the natural logarithm as the inverse function of the exponential function. Lectures 33/34: We will have two review lectures for the test next Monday. The first one will have examples of optimization and related rates and the second one will deal with the other topics. I will try and keep the examples at a level that might appear on the test. Solutions to Review 3: Here are the written out solutions to Review-sheet 3. Important: Please try to solve the review-questions on your own before reading the solutions. Just reading the solutions won't help you solve the questions on the Test on your own.
Week 13:	Lecture 35Course-Test at 3:30 in Porter Hall 100
Week 14:	Lectures 36/37/38:On Monday we will talk about logarithmic functions a bit more. We will learn how to differentiate functions including logarithms and we will learn the logarithmic rules. On Wednesday and Friday we will look at applications for exponential and logarithmic functions. These will include Exponential growth and decay, radiocarbon dating, and compound interest. I will try to put a review sheet here before Wednesday so you can start preparing for the final early.
Week 15:	Lecture 39:This will be the last lecture with new material. We will go through applications of the logarithm, namely the Relative and percentage rate of change and Elasticity of Demand and Price. Lectures 40/41: In these two lectures we will review relevant material for the final exam. Saturday, Dec. 11, 9am, Porter Hall 100 For those of you who cannot make the our final exam date on Monday, Dec. 20, this will be the opportunity to take the final early. Please let me know be Wednesday afternoon if you want to take the early final as I need to know the number of people who will take it, so I can prepare enough copies of the final exam.