Calculus 1B (001 LEC) Fall 2014

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Textbook

The textbook for this course is: Stewart, Single Variable Calculus: Early Transcendentals for UC Berkeley, 7th edition (ISBN: 978-0538498678, Cengage).

This is a custom edition containing chapters 1-9, 11 and 17 of Stewart's "Calculus: Early Transcendentals", 7th edition. The regular edition is also fine, it just contains extra chapters covered in math 53. The 6th edition is also acceptable, but you will need to watch for differences in the numbering of assigned homework problems. In chronological order, we'll cover the material in chapters 7, 8, 11, 9 and 17.

Grading and course policy

Weekly homework and quizzes 20%; two midterms 20% each; final exam 40%. The lowest midterm can be dropped and replaced by the final exam grade. There will be no make-up exams. This grading policy allows you to miss one midterm, but check your schedule to make sure you have no conflict for the final exam.

Make sure to read the detailed course policy for important information.

Homework

Homework assignments are due each Wednesday in section; they will be posted here. The first homework will be due on September 10. For more detailed information see the course policy.

Homework 1 and Solutions 1

Homework 2 and Solutions 2

Homework 3 and Solutions 3

Homework 4 and Solutions 4

Homework 5 and Solutions 5

Homework 6 and Solutions 6

Homework 7 and Solutions 7

Homework 8 and Solutions 8

Homework 9 and Solutions 9

Homework 10 and Solutions 10

Homework 11 and Solutions 11

Exams

There will be two midterms, the first on Monday September 29 and the second on Friday October 31, both from 8am to 9am in the usual lecture room. The final exam will be on Monday December 15 (7-10pm).

Practice First Midterm: Good Solutions and Bad Solutions

Here is the first midterm, together with solutions. A rough breakdown of the letter grades for the first midterm is as follows:

Score	Grade
85-100	A
65-84	B
45-64	C
35-44	D

The mean score was 71 and the median was 73. Keep in mind that these letter grades are estimates only - only the numbers are used to compute your final grade.

Practice Second Midterm and solutions.

Here is the second midterm, together with solutions.A rough breakdown of the letter grades for the second midterm is as follows:

Score	Grade
81-100	A
61-80	B
41-60	C
30-40	D

The mean score was 64 and the median was 65. Keep in mind that these letter grades are estimates only - only the numbers are used to compute your final grade.

Practice Final Exam

Here is a link to many past exams. Of these, the ones I recommend trying first are Ribet97, Sarason96 and Reshetikhin03. Remember though, when you look at these older exams the instructor may have focussed on different things and so they may be quite different from mine.

Syllabus

In Math 1A or elsewhere, you studied functions of a single variable, limits, and continuity. You learned about derivatives, which describe how functions change, and which can be used to help find maxima and minima of functions. You also learned about integrals which describe the aggregate behavior of a function over an interval, such as the area under a curve or the average of a varying quantity. The derivative and the integral are tied together in the fundamental theorem of calculus, one version of which relates the integral of the derivative of a function over an interval to the values of the function at the endpoints of the interval.

In this course we will continue the study of calculus in three parts as follows:

• The first part of the course is about techniques of integration (sections 7.1 to 7.8 of the book). As you should already know, differentiation is relatively straightforward: if you know the derivatives of elementary functions, and rules such as the product rule and the chain rule, then you can differentiate just about any function you will ever come across. Integration, on the other hand, is hard. Sometimes it is even impossible to integrate a given function explicitly in terms of known functions. We will introduce a collection of useful tricks with which you can integrate many functions. The hard part is to figure out which trick(s) to use in a given situation. For integrals which we cannot evaluate explicitly, we will learn how to find good approximations to the answer.
• The second part of the course is about sequences and series (chapter 11 of the book). This can be regarded as the general theory of approximating things. This part of the course is subtle and involves new ways of thinking. It may be a lot harder than the first part, especially if you have seen some of the first part before.
• The third part of the course is an introduction to ordinary differential equations (chapters 9 and 17 of the book). Here one tries to understand a function, given an equation involving the function and its derivatives. ("Ordinary" means that we consider functions of a single variable. Functions of several variables enter into "partial" differential equations, which you can learn about in a more advanced course.) The theory of differential equations is perhaps the most interesting part of calculus, is the subject of much present-day research, and has many real-world applications. Our study of differential equations will make use of most of the calculus we have done so far.

Here is the lecture schedule for the course:

Date	Topics	Book
Fri 8/29	Introduction and Reminders	§ 1,2,3,5
Mon 9/2	NO CLASS (Labor Day)
Wed 9/3	Integration by parts	§ 7.1
Fri 9/5	Trigonometric integrals	§ 7.2
Mon 9/8	Trigonometric substitution	§ 7.3
Wed 9/10	Integration of rational functions	§ 7.4
Fri 9/12	Strategies for integration	§ 7.5
Mon 9/15	Approximate integration	§ 7.7
Wed 9/17	Improper integrals	§ 7.8
Fri 9/19	Arc Length	§ 8.1
Mon 9/22	Area of a surface of revolution	§ 8.2
Wed 9/24	Review of error bounds (see 9/15)
Fri 9/26	Review of comparison test (see 9/17)
Mon 9/29	MIDTERM 1
Wed 10/1	Review of Midterm 1 / Sequences	§ 11.1
Fri 10/3	Sequences	§ 11.1
Mon 10/6	Series	§ 11.2
Wed 10/8	The integral test and estimates of sums	§ 11.3
Fri 10/10	The comparison tests	§ 11.4
Mon10/13	Alternating series	§ 11.5
Wed 10/15	Absolute convergence and the ratio and root tests	§ 11.6
Fri 10/17	Strategy for testing series	§ 11.7
Mon10/20	Power Series	§ 11.8
Wed 10/22	Representations of functions as power series	§ 11.9
Fri 10/24	Taylor and Maclaurin series	§ 11.10
Mon10/27	Taylor and Maclaurin series continued	§ 11.10
Wed 10/29	Review
Fri 10/31	MIDTERM 2
Mon 11/3	Modelling with differential equations	§ 9.1
Wed 11/5	Direction fields and Euler's method	§ 9.2
Fri 11/7	Separable equations	§ 9.3
Mon11/10	Models for population growth	§ 9.4
Wed 11/12	linear equations	§ 9.5
Fri 11/14	Predator-prey systems	§ 9.6
Mon11/17	Second-order homogeneous linear equations	§ 17.1
Wed 11/19	Introduction to the complex numbers	Appendix H
Fri 11/21	Second-order homogeneous linear equations continued	§ 17.1
Mon11/24	nonhomogeneous second-order differential equations	§ 17.2
Wed 11/26	No Class
Fri 11/28	NO CLASS (Thanksgiving)
Mon 12/1	nonhomogeneous second-order differential equations continued	§ 17.2
Wed 12/3	Series solutions	§ 17.4
Fri 12/5	Series solutions continued	§ 17.4
Mon 12/8	Review	§ 7, 8
Wed 12/10	Review	§ 11
Fri 12/12	Review	§ 9,17
Mon 12/15	FINAL EXAM (7-10pm)

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