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Calculus 1B (001 LEC) Fall 2014


[Announcements] [Textbook] [Grading policy] [Homework] [Exams] [Syllabus] [Resources] [Sections]

Instructor: Alexander Paulin.
e-mail: apaulinberkeley.edu.
Office: 796 Evans Hall.
Office hours : Monday, Wednesday and Friday 2-4pm. Tuesday and Thursday, 1pm-2pm.
Lectures: Mondays, Wednesdays and Fridays, 8am-9am.155 Dwinelle Hall. There will be no lectures on Septmenber 1 or November 28.
Discussion sections: Mondays, Wednesday and Fridays, at various times (see below).
Enrollment: For question about enrollment contact Thomas Brown.

Announcements

  • (9/1) On the week of Thanksgiving the homework submission/quiz will be on Monday as opposed to Wednesday. I will therefore post the homework on monday the previous week.
  • (8/29) I've posted my notes from the first lecture below. Just click on the link directly from the lecture schedule. I'll try to post my notes from each week on Friday evenings.
  • (8/27) There will be no official homework due on September 3. However, as a warm up, I'm giving out a series of exercises (homework 0, I suppose) from the first half of the textbook, i.e. material covered in Calculus 1A. I strongly recommend you do these. It's easy to forget the basics after such a long break and it's a great way to get back in the swing of things.
  • (8/27) Make sure to read the course policy and the detailed syllabus.
  • 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 0 and Solutions 0

    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:

    ScoreGrade
    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:

    ScoreGrade
    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 and solutions.

    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:

    DateTopics 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)

    Discussion sections

    Section TimeRoomInstructore-mailOffice hours
    101MWF 9-10am385 Leconte Shen, Chen
    102MWF 9-10am122 Wheeler Wu, Kumming
    103MWF 9-10am200 Wheeler Xiao, Jianwei
    104MWF 10-11am210 Wheeler Xiao, Jianwei
    105MWF 11-12pm6 Evans Shen, Chen
    106MWF 11-12pm30 Wheeler Hollowood, D
    107MWF 12-1pmB51 Hildebrand Fei, Yang
    108MWF 12-1pm6 Evans Hollowood, D
    109MWF 1-2pm5 Evans Fernando, R
    110MWF 2-3pm75 Evans Fernando, R
    111MWF 3-4pm81 Evans Leake, Jonathan
    112MWF 4-5pm179 Stanley Fei, Yang
    113MWF 4-5pm55 Evans Eng, Emily
    114MWF 5-6pm51 Evans Eng, Emily
    115MWF 1-3pm230C Stephens Rusciano, Alex
    116MWF 2-3pm61 Evans Leake, Jonathan
    117MWF 10-11am5 Evans Wu, Kumming

    Resources

    The Student Learning Center provides support for this class, including study groups, review sessions for exams, and drop-in tutoring.