Mathematics 1B, Fall 2010

Professor: Vaughan Jones (The other 1B class is taught by Olsson.)

Office hours: Tuesday 5:00-6:00, Wednesday 10:30-11:30, Thursday 10:30-11:30 929 Evans Hall. (For quick questions or to schedule an appointment, ask me after class.)

Email:The class is too big to permit email correspondence. I am delighted to see you at my office hours and have made every attempt to schedule them so that you are able to attend. If you cannot make any of them or if you have a quick question please see me after class. I will not respond to email.

Our class meets in 105 Stanley, 3:30-5pm on Tuesdays and Thursdays. This is the course home page (address If you take this course you are expected to attend lectures, enroll in and attend one of the discussion sections, do the homework each week, and take the two midterms and the final.If for some reason you are prevented from attending a class, it is YOUR responsibility to know what happened in that class, including announcements of mid-term dates, changes in homework etc. I have no control over enrollment, so please do not ask me about getting into this class. If you have questions about enrollment send them to Barbara Peavy ( Enrollment in discussion sections is also usually handled by telebears. You MUST attend the discussion section you are registered for. If you wish to add or drop this course after telebears ends, here is the form and instructions.

For the times, places, and instructors of the discussion sections click here. WARNING: the places and times of discussion sections are sometimes changed at the last minute.

Catalogue Description: Mathematics 1B

Course Format: Three hours of lecture and two hours of discussion per week.

Prerequisites: Math 1A

Credit option: Students will receive 2 units of credit for 1B after taking 16A.

Description: This sequence is intended for majors in engineering and the physical sciences.Continuation of 1A. Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations.


Stewart, Single Variable Calculus (Custom Edition for UCB) ISBN: 978-1-424-05500-5

We will cover the material not in 1A, in other words chapters 7, 8, 9, 11, 17. This is probably th e same textbook that you used for 1A. Warning: there are dozens of different and incompatible editio ns of Stewart's book, and several different "Berkeley special editions": check the ISBN to make sure you are getting the right edition.

The ASUC textbook store sells the textbook and they may buy it back for half price.


My goal is to teach the course material as clearly as possible. The biggest success for me would be to be able to assign an A grade to every student. According to past experience this is unlikely.

From time to time I will add material or do examples that are not in the book in order to enhance understanding. When that occurs I will be careful to present a clear written account on the blackboard. Otherwise your main source of a clear written account is the textbook. Lectures are used to explain the content of the textbook, not reproduce it on the blackboard.

It is my expectation that every student attend every class. It may happen that something prevents you from attending a class. In this case it is YOUR RESPONSIBILITY to find out exactly what was covered in that class and any announcements made.


There will be a quiz given each week in the discussion sections. There will be no make-up quizzes.

The grading will be:

homework and quizzes 20%, midterms 15% each, final 50%.

The final grade is not based on a curve or on previously fixed marks for certain grades. Instead the grades for the course will be based on my judgment of how well the class is doing, and will be higher if everyone is working hard at the homework and doing well on the exams. Grades will be assigned after consultation with the other instructor of MATH1B.

Almost all of the questions in the midterms or finals will be similar to randomly selected homework questions from the book, possibly with the constants in the questions changed. So if you understand how to do all the homework questions you will be able to do almost all of the questions on the exams.

I only change grades for exams or quizzes if there is a clear error on the part of the grader, such as adding up marks incorrectly or forgetting to grade a question. I will not increase grades just because someone needs a higher grade to graduate or get into some program.

The final homework and quiz grade will be computed from the grades for the 10 best homeworks and quizzes, so it does not matter much if you forget one or two. If you miss the first midterm with a documented medical excuse, your score for the second midterm will be doubled. If you miss the second with a documented medical excuse then your score for the final will be weighted accordingly. If you miss both midterms or the final then you are in trouble. There will be no makeup exams or quizzes.


You may bring one (ordinary sized) sheet of paper to the exams, with writing on one side for the midterms and both sides allowed for the final. Apart from this one sheet, the exams are "closed book". In particular you may not bring textbooks or notebooks or calculators.

The dates for the midterms have not yet been set but will be announced at least two weeks before they take place. The midterms occur during regular class hours in the regular lecture room.

The second midterm will be on the material covered since the first midterm.

The final is on Friday 17 December from 7 to 10 pm. It is not held in the lecture room and is not at the normal lecture time. It will cover the whole course with an emphasis on the material covered after the second midterm.


Homework is due by the beginning of the first discussion section of the week after it is assigned. Late homework will not be accepted. The grade for homework will be based just on the number of questions attempted, as Berkeley does not at the moment have money to pay for homework grading. Collaboration on homework is fine, but if you hand in similar homework to your collaborator you should clearly state so and say who you are working with, in order to avoid unfortunate misunderstandings. Be aware that you will be taking the exams ON YOUR OWN. If you collaborate on homework there is a risk that you do not fully understand the solutions. At the very least you should write the final version of your answer on your own.

The homework assigned is intended to be minimal. If you are still finding the questions difficult after completion of the homework assignment you should do some of the unassigned exercises.

Incomplete grades

Incomplete "I" grades are almost never given. The only justification is a documented serious medical problem or genuine personal/family emergency. Even then you are required to be doing work at a passing level. Falling behind in the course or problems with workload on other courses are not acceptable reasons.

Special arrangements.

If you are a student with a disability registered by the Disabled Student Services (DSS) on UCB campus and if you require special arrangements during exams, you must provide me with the DSS document and you must contact me via office hours at least 10 days prior to each exam, explaining your circumstances and what special arrangements are requested. If you do not contact me 10 days in advance then I will not have time to make arrangements and you will have to take the exam along with everyone else and under the regular conditions provided for the class.

Reading and Homework Assignment

Most questions have answers in the back of the book, and many (the ones in red in the book) have hints on one of the CDs. Homework and reading will be assigned (on this page) at the beginning of each week. Homework is due at the first discussion section of the following week. Various other course announcements, such as dates of mid-terms, will also appear on this page.

Week 1 Due first section of week beginning 30 August .

  • Reading: 7.1-7.2
  • Homework: 7.1: 1, 5, 7, 13, 17, 25, 29, 31, 33,45.

    Week 2 Due first section of week beginning 6 September. Reading: 7.2-7.3

  • Homework: 7.2: 1,3,7,9, 11, 13,15,23,27,33,41,45,49,68. 7.3: 1,3,7,9, 11, 13,17,23,29,35,43.

    Week 2 Due first section of week beginning 13 September. Reading: 7.4-7.5 especially pages 487-488.

  • Homework: 7.4: 1,3,7,9, 11, 13,15,27,33,43,45,57,59. 7.5: 1,3,7,9, 11, 13,17,23,35,43,61,81.

  • First mid term will be in class time on Thursday October 7. It will cover all the material up to and including the previous Thursday, i.e. September 30.

    Week 3 Due first section of week beginning 20 September. Reading: 7.7-7.8.

  • Homework: 7.7: 1,2,5,19,21,33,37,45. 7.8: 1,3,5,7,11,21,25,39,41,49,53,55,77.

  • Week 4.

    As noted in class the exercises from 7.8 are not due till next week.

  • The notion of limit is right up there as one of the most important concepts in all of Mathematics. We have already used it without careful definition in numerical integration and improper integrals. It's time we confronted it. Thus we shall continue now with chapter 11 on sequences and series. Reading for this week is thus 11.1 and 11.2.

  • Homework (due week beginning 27 September)
  • Do exercises from 7.8 as above.
  • 11.1:1,3,11,17,23,31,35,39,55,57,58,63,67,81.
  • Homework (due week beginning 4 October)
  • Reading 11.2,11.3,11.4,11.5
  • 11.2:1,2,5,11,17,23,31,35,39,45,51,55,76.
  • 11.3:1,2,3,7,12,21,27,31,33,42.

    For now totally unfathomable reasons I have lost my html file twice so this homework may differ slightly from ones previously assigned. Make sure you do one of the assigned ones.

  • I am unable to be at my office hours on Wednesday 29 and Thursday 30 September, but will be there on Tuesday 5 October.

  • sample first midterm.

  • Homework (due week beginning 11 October)
  • Reading 11.5,11.6
  • 11.4:1,2,5,11,17,27,31,33,37,39,41,42,45.
  • 11.5:1,3,11,13,15,25,35.
  • 11.6:1,3,5,15,19,23,29,31,37.

  • Homework (due week beginning 18 October)
  • Reading 11.7,11.8,11.9
  • 11.7:1,3,15,33,19,37,31.
  • 11.8:1,2,3,13,19,25,33,35,41,42.
  • 11.9:1,2,3,7,11,13,15,23,27.

  • Homework (due week beginning 25 October)
  • Reading 11.9,11.10,11.11
  • 11.9:33,35.
  • 11.10:1,2,3,5,13,15,25,27,31,33,35,45,47,55,57,59,63,65,71.

  • The second midterm will be on Thursday November 18. The exact material to be covered in the midterm will be announced in class.

  • Homework (due week beginning 1 November )
  • Reading 9.1,9.2,9.3
  • 11.11:25,26,31.
  • 9.1:1,3,6,11.
  • 9.2:1,3,11,25.
  • 9.31,3,9,11,15,19,21,41,43.

  • Homework (due week beginning 8 November )
  • Reading 9.4,9.5,8.1,8.2.
  • Read the download below on Runge Kutta methods, and do the exercises therein.
  • 9.4:3.
  • 9.5:1,3,5,11,15,19,25,29.
  • 8.11,3,9,11,15,35.

  • Homework (due week beginning 15 November )
  • 8.21,3,7,9,13,15,27 (a,b).

  • Homework (due week beginning 22 November )
  • 17.11,3,7,9,17,21,27,25,31,33.34 .

  • The second midterm will be on Thursday November 18. The exact material to be covered in the midterm is: all the work we have done in class on series, differential equations, length of curves and area of surfaces of revolution. Sections of the book not covered in class will not be examined.

  • Homework (due week beginning 29 November )
  • 17.21,3,7,13,17,21,25,27.

  • Homework (due week beginning 6 December )
  • 17.31,3,11,13.
  • 17.41,3,8,9.

  • CHANGE OF OFFICE HOURS: I have to be away on Wednesday (8 December) and may not get back in time for my regular office hours on Thursday morning. So I will hold a long office hour on Thursday during what would normally be class time, 3:30-5, and beyond. You should let me know if you want to come after 5:30 on Thursday. Note once again that I will be away the entire week before the final exam.

  • The final. We have 1 Pimentel for the final on Friday December 17 at 7pm. That's a room large enough to seat the entire class with a gap of exactly one seat between people. So when you come to the exam make sure you leave exactly one space between you and your neighbour. If not you will be reseated. 7pm is awfully late for an exam to start so I will do my best to make it short. The exam will cover the entire course with an emphasis on the work covered since the second midterm. It will closely resemble the sample final and of course, as for the midterms there will be questions taken straight from lecture.

  • The week of 6-10 December: I will hold a lecture in class time on Tuesday as usual but we will have no lecture on Thursday. In Tuesday's lecture there will be no new material so I will go over what you probably found hardest in the course, namely convergence of series. If there are other topics you want me to cover please let me know the previous week.

  • I will be away in Washington the entire week leading up to the exam. If you have any questions you should get them sorted out the week 6-10 December. If you are seeking accomodations you have until Tuesday 7 December to request them.

  • sample final

  • sample second midterm.

  • Runge-Kutta methods .

    Particular solution for the LCR circuit

  • Sample exams from many classes

  • Tartaglia's poem. Cubic

    Here is a link to an exam archive:

  • Exam archive.

    Links related to the course: