Math 1b Reading assignments will be posted by unit Integration Series and Differential Equations If any changes are made once a unit has commenced you will be sent an e mail alerting you to the change All numbers indicate sections from Stewart s Calculus Concepts and Contexts 2nd edition unless it says G in which case it is from supplementary material written by the coursehead which will be made available to you It is password protected you can get the password and login from your teacher Last modified September 26 2004 by RG Reading Assignments for the Integration Unit MWF version Note to students If we followed the order of the textbook we would have to start out with techniques of integration but that would give you the wrong impression about the type of course you are taking In addition some students come into this course knowing some techniques of integration and others do not We would like to have our course start out with an equal playing field and we d like each of you to see something new in the first few classes Therefore we will do start with applications of integration Chapter 6 in the first week of the course include some nonstandard applications from supplementary materials in order to guarantee that you will be able to apply integration whenever you need to in your future career and then get to techniques of integration from Chapter 5 We ll save improper integrals and probability for the end of this unit because i the latter is an application of the former ii improper integrals stretch the definition of the definite integral so it is logical to place it at the end of the unit and iii the language and ideas used are closely related to the ideas of the series unit that follows this one 1 For Monday September 27 Review Section 5 1 Areas and Distances Section 5 2 The Definite Integral Section 5 3 Evaluating Definite Integrals Section 5 4 The Fundamental Theorem of Calculus Section 6 1 More About Areas Reading Sections 5 1 through 5 4 should be review Skim them to remind yourself about Riemann Sums and the Fundamental Theorem of Calculus 6 1 all except Areas Enclosed by Parametric Curves Key areas of focus From 5 1 5 4 What is a Riemann Sum and why do they look the way they do Understand the statements of both forms of the Fundamental Theorem of Calculus Know the interpretation of the definite integral as signed area under a graph In 6 1 Look at the area between curves in Figure 1 You may be accustomed to viewing this as the sum and or difference of signed areas between a curve and the x axis Notice the different way of thinking about this presented in this section Notice that Example 4 is a special case of the general idea that the area under a rate curve is the net change in amount Understand the geometry behind integrating with respect to y as in Example 5 Reading Questions 1 Answer one of the following a What was the most confusing or difficult part of this reading b What questions did this reading bring up for you 2 For Wednesday September 29 Section 6 2 Volumes and Volumes of Revolution Reading All Key areas of focus Understand finding volumes by slicing a solid as one would slice a loaf of bread Then think about the special case of volumes formed as solids of revolution For another take on volumes of revolution you can read G 28 1 pp 856 862 Reading Questions 1 Consider the region bounded below by y 2x above by y 8 and on the left by the y axis Rotate this region about the y axis to get a cone Write an integral that will give you the volume generated and check your answer by using the formula for the volume of a cone 2 Answer one of the following What was the most confusing or difficult part of this reading What questions did this reading bring up for you 3 For Friday October 1 Section G 27 1 Slicing Reading All Key areas of focus Understand what determines how you slice the region or interval under consideration Concentrate on how the integrals are obtained from the approximating Riemann sums rather than looking for formulas Reading Questions 1 G 27 1 1 2 How are the problems in this section related to previous problems of area and volume 3 Answer one of the following What was the most confusing or difficult part of this reading What questions did this reading bring up for you 4 For Monday October 4 Reading Reread G 27 1 and read G 27 2 if useful No pre class reading questions 5 For Wednesday October 6 Sections 6 3 and 6 4 Arc Length and Average Value Reading 6 3 give this only a quick read to get the main gist we ll take a different approach in class We won t be dealing with parameterized curves In 6 4 read all two pages Key areas of focus 6 3 Concentrate on making some sense of formula 2 on p 469 6 4 everything Reading Questions 1 Look at formula 2 on p 469 Let a 1 and b 4 Suppose y c where c is constant What does the formula give for the length of the curve from a to b Does this make sense The formula says that the larger dy dx 2 the larger the arc length Explain why this makes geometric sense 2 6 4 2 Think about this graphically Do you expect the answer to be bigger or smaller than sqrt 2 5 Why 4 Answer one of the following What was the most confusing or difficult part of this reading What questions did this reading bring up for you 6 For Friday October 8 Section 6 5 Applications to Physics and Engineering Reading read pp 476 479 Key areas of focus work as an application of integration Read about hydrostatic pressure moments and centers of mass only if you have an interest in these physics topics Reading Questions 1 6 5 3 Note that the first line allows you to figure out the spring constant for the spring Why is it necessary to write an integral to do this problem 2 Answer one of the following What was the most confusing or difficult part of this reading What questions did this reading bring up for you Monday October 11 Holiday 7 For Wednesday October 13 Section 5 5 Integration by Substitution Reading All Key areas of focus Pay attention to the endpoints of integration when substitution is used on a definite integral Focus also on the subsection on symmetry One can often get a lot of mileage out of it Please don t think of substitution as introducing something extra but rather as unveiling the underlying structure Reading Questions 1 Substitution attempts to undo one of the techniques of differentiation Which one is it 2 5 5 28 3 Answer one of the following What was the most confusing or difficult …