## Math 1B: Calculus (Fall 2011)

Description: Second part of the introduction to differential and integral calculus of functions of one variable, with applications. This course is intended for majors in engineering and the physical sciences. Prerequisites: Math 1A. Course control number: 53762. http://persson.berkeley.edu/1B Per-Olof Persson, persson@berkeley.edu, Evans 1089, Phone (510) 642-6947 Office hours: Mon 1:30pm - 3:00pm and Wed 10:00am - 11:30am in Evans 1089 TT 11am-12:30pm, Room 105 Stanley Single Variable Calculus, Early Transcendentals for UC Berkeley, James Stewart, Cengage Learning, ISBN 978-1-424-05500-5 or 1-424-05500-8. Lecture 1: Standard Integrals Lecture 1: Lecture Slides Lecture 2: Trigonometry Review Lecture 3: Lecture Slides Lecture 4: Updated Standard Integrals and Strategy for Integration Lecture 4: Approximate Integration Lecture 8: Sequences (6 slides per page) Math 1B support at the Student Learning Center ASUC Lecture Notes

Announcements: (Dec 14): Final exam results Here are the final exam and the solutions. The average score was 62 out of 100, the standard deviation 21, and the median 64. The approximate grade levels are: A) 81 - 100, B) 61 - 80, C) 41 - 60, D) 21 - 40, F) 0 - 20 (Dec 7): Homework solutions section 17.4 Here are homework solutions for section 17.4. (Dec 1): Final exam The final exam will be held in 2050 VLSB and 2060 VLSB on Wednesday December 14 between 8:00am - 11:00am. Make sure you arrive on time. If your last name begins with the letter A - G, you take the exam in 2060 VLSB. Otherwise, you take the exam in 2050 VLSB. The exam will cover everything we have done, namely, sections 7.1-7.5, 7.7-7.8, 8.1-8.3, 11.1-11.11, 9.1-9.5, 17.1-17.4 of the textbook and homeworks/quizzes 1-11. Bring pens/pencils/eraser and one 2-sided sheet of notes (letter size). No calculator, no book, and no other notes are allowed. Here are some sample final exams from previous 1B courses, with solutions to the problems from the last two exams: Ribet 1997, Sarason 1996, the exam I gave in the Fall 2009, with solutions, and the exam I gave in the Spring 2010, with solutions. (Nov 9): Midterm 2 results Here are Midterm 2 and the solutions. The average score was 19.6 out of 33, the standard deviation 5.6, and the median 20. The approximate grade levels are: A) 27 - 33, B) 20 - 26, C) 13 - 19, D) 6 - 12, F) 0 - 5 (Nov 3): Midterm 2 review sessions SLC: Thursday Nov 3, 7pm-9pm, in room 110 Barrows Hall Zvi Rosen: Sunday Nov 6, 1pm-3pm, in room 126 Barrows Hall Anna Lieb: Sunday Nov 6, 2pm-4pm, in room 2 Evans Hall Heather Lee: Sunday Nov 6, 3:30pm-5:30pm, in room 70 Evans Hall (Nov 1): Midterm 2 Midterm 2 will be held in the regular classroom 105 Stanley on Tuesday November 8 between 11:10am - 12:30pm. Make sure you arrive on time. The exam will cover everything we have done, namely, sections 7.1-7.5, 7.7-7.8, 8.1-8.3, 11.1-11.11, 9.1-9.4 of the textbook and homework/quizzes 1-9. Bring pens/pencils/eraser and one 2-sided sheet of notes (letter size). No calculator, no book, and no other notes are allowed. Here are some sample second midterms from previous 1B courses, the exam I gave in Fall 2009, with solutions, and the exam I gave in Spring 2010, with solutions. Note: 1) These might have covered slightly different material, and might have been 50 minutes long instead of 80 minutes. 2) Different instructors write different exams, so do not draw any conclusions about the exact format of our midterm exam based on these exams. (Oct 6): Midterm 1 results Here are Midterm 1 and the solutions. The average score was 22.0 out of 33, the standard deviation 5.8, and the median 23. The approximate grade levels are: A) 28 - 33, B) 22 - 27, C) 16 - 21, D) 8 - 15, F) 0 - 7 (Sep 29): Midterm 1 review sessions GSIs: Sunday Oct 2, 2pm-4pm, in room 56 Barrows Hall SLC: Sunday Oct 2, 3pm-5pm, in room 102 Moffitt (Sep 23): Midterm 1 Midterm 1 will be held in the regular classroom 105 Stanley on Tuesday October 4 between 11:10am - 12:30pm. Make sure you arrive on time. The exam will cover everything we have done, namely, sections 7.1-7.5, 7.7-7.8, 8.1-8.3, 11.1-11.4 of the textbook and homework/quizzes 1-5. Bring pens/pencils/eraser and one 2-sided sheet of notes (letter size). No calculator, no book, and no other notes are allowed. Here are some sample first midterms from previous 1B courses, the exam I gave in Fall 2009, with solutions, and the exam I gave in Spring 2010, with solutions. Note: 1) These might have covered slightly different material, and might have been 50 minutes long instead of 80 minutes. 2) Different instructors write different exams, so do not draw any conclusions about the exact format of our midterm exam based on these exams.

Homework and Quizzes:
HW/Quiz Date Problems
01 Fri 09/02 7.1: 1,3,7,10,15,17,23,30,33,45,47,65
7.2: 1,3,7,13,17,23,29,35,43,67,69
7.3: 3,5,7,10,15,21,25,31,39
02 Fri 09/09 7.4: 1,5,9,13,15,20,25,29,31,37,43,49,52,57,59
7.5: 17,23,31,41,45,49,57,61,69,81
7.7: 1,6,11,21,22,29,33,45,46
03 Fri 09/16 7.8: 7,13,21,24,34,51,55,59,71
8.1: 7,11,13,16,31,33,37
8.2: 1,5,11,13,25,33
04 Fri 09/23 8.3: 3,9,13,23,29,40,45
11.1: 5,7,9,13,19,23,27,35,43,54,61,66,69,71
05 Fri 09/30 11.2: 9,17,25,29,33,37,41,47,51,55,59,64
11.3: 3,7,11,17,21,27,33,39,41
11.4: 5,11,17,23,25,31,37,38,39,43
06 Fri 10/14 11.5: 3,7,11,13,17,23,32,35
11.6: 3,4,5,9,13,17,21,23,29,32,33
11.7: 5,7,15,18,23,24,27,30,33,36
07 Fri 10/21 11.8: 3,7,10,15,21,23,27,29,37,39
11.9: 5,8,11,13,15,18,25,27,35,37,39
08 Fri 10/28 11.10: 5,6,9,13,19,27,33,35,45,47,53,57,59,63,67
11.11: 5,7,9,13,19,25,29,31,33
9.1: 3,5,7,9,10,11,12
9.2: 1,3,4,5,6,7,9,11,13,21,23
09 Fri 11/04 9.3: 3,7,10,13,15,19,20,21,31,39,41,45,48
9.4: 3,5,7,9,13
10 Fri 11/18 9.5: 1,2,3,4,5,9,13,17,19,23,25,33,35
17.1: 1,5,9,11,17,21,23,25,27,30
11 Fri 12/02 17.2: 3,5,7,9,13,16,21,25,27
17.3: 3,5,9,13,15,17,18
17.4: 3,7,9,11
Syllabus:
Lec Date Topic Other
01 Thu 08/25 7.1: Introduction, Integration by Parts
02 Tue 08/30 7.2: Trigonometric Integrals
7.3: Trigonometric Substitution

03 Thu 09/01 7.4: Integration of Rational Functions by Partial Fractions
04 Tue 09/06 7.5: Strategy for Integration
7.7: Approximate Integration

05 Thu 09/08 7.8: Improper Integrals
06 Tue 09/13 8.1: Arc Length
8.2: Area of a Surface of Revolution

07 Thu 09/15 8.3: Applications to Physics and Engineering
08 Tue 09/20 11.1: Sequences
09 Thu 09/22 11.2: Series
10 Tue 09/27 11.3: The Integral Test and Estimates of Sums
11.4: The Comparison Tests

11 Thu 09/29 Review
12 Tue 10/04 Midterm 1 - In class, 105 Stanley, 11am-12:30pm Midterm 1
13 Thu 10/06 11.5: Alternating Series
14 Tue 10/11 11.6: Absolute Convergence and the Ratio and Root Tests
11.7: Strategy for Testing Series

15 Thu 10/13 11.8: Power Series
16 Tue 10/18 11.9: Representations of Functions as Power Series
17 Thu 10/20 11.10: Taylor and Maclaurin Series
18 Tue 10/25 11.11: Applications of Taylor Polynomials
19 Thu 10/27 9.1: Modeling with Differential Equations
9.2: Direction Fields and Euler's Method

20 Tue 11/01 9.3: Separable Equations
9.4: Models for Population Growth

21 Thu 11/03 Review
22 Tue 11/08 Midterm 2 - In class, 105 Stanley, 11am-12:30pm Midterm 2
23 Thu 11/10 9.5: Linear Equations
24 Tue 11/15 17.1: Second-Order Linear Equations
25 Thu 11/17 17.2: Nonhomogeneous Linear Equations
26 Tue 11/22 17.3: Applications of Second-Order Differential Equations
Thu 11/24 Thanksgiving - No lecture
27 Tue 11/29 17.4: Series Solutions
28 Thu 12/01 Review
Reading/Review/Recitation Week 12/5-12/9 - No lectures
Wed 12/14 Final Exam - Room TBD, 8-11am Final Exam
GSIs and Discussion Sections:
Sec Time Room GSI E-mail Office Office hours
01 MWF 8am - 9am 3 Evans H. Lee mxli@math.berkeley.edu 1085 Evans Tue 4-4:30pm, Wed 5:30-6pm, Thu 1-2pm
02 MWF 4pm - 5pm 45 Evans A. Lieb lieb.anna.m@gmail.com 826 Evans Mon 12-1pm, Thu 4-5pm
03 MWF 9am - 10am 6 Evans H. Lee mxli@math.berkeley.edu 1085 Evans Tue 4-4:30pm, Wed 5:30-6pm, Thu 1-2pm
04 MWF 10am - 11am 3111 Etcheverry Z. Rosen zhrosen@math.berkeley.edu 824 Evans Tue 2:15pm-3:15pm, Wed 2:30pm-3:30pm
05 MWF 11am - 12pm 3111 Etcheverry J. Chen ada@math.berkeley.edu 858 Evans Tue 3:30-4:30pm, Thu 3:30-4:30pm
06 MWF 12pm - 1pm 3111 Etcheverry Z. Rosen zhrosen@math.berkeley.edu 824 Evans Tue 2:15pm-3:15pm, Wed 2:30pm-3:30pm
07 MWF 1pm - 2pm 310 Hearst W. H. Cook whcook@math.berkeley.edu 1008 Evans Mon 3:30-4:30pm, Thu 1:30-2:30pm
08 MWF 2pm - 3pm 285 Cory W. H. Cook whcook@math.berkeley.edu 1008 Evans Mon 3:30-4:30pm, Thu 1:30-2:30pm
09 MWF 3pm - 4pm 35 Evans J. Chen ada@math.berkeley.edu 858 Evans Tue 3:30-4:30pm, Thu 3:30-4:30pm
10 MWF 4pm - 5pm 2 Evans C. Y. Cho chough@math.berkeley.edu 1070 Evans Thu 2-3pm, Fri 3-4pm
12 MWF 5pm - 6pm 45 Evans C. Y. Cho chough@math.berkeley.edu 1070 Evans Thu 2-3pm, Fri 3-4pm
13 M 11am - 12pm
WF 11am - 1pm