Mathematics 1B - Calculus


Professor Maciej Zworski
895 Evans Hall, 643-7991
zworski@math.berkeley.edu


Office Hours: 1:30-3 PM on Mondays and 3:45-5 on Tuesdays, and by appointment.


Head TA: Daniel Rhea, rhea@math.berkeley.edu, (510) 301-4084. Office hours for first two weeks: 12:20-2:20 Monday, 4-6pm Tuesday, 12:20-2:20 Wednesday, 11:45-1:45 Thursday, 2:20-4:20 Friday, IN MOFFITT UNDERGRADUATE LIBRARY DOWNSTAIRS WITH THE WHITE TABLES.


Class meetings: The main lectures are TuTh 2-3:30 PM in 2050 VALLEY LSB. There are in addition 12 discussion sections meeting MWF:


Section Time (MWF) Location Teaching Assistant
201 8-9 05 EVANS Y.S. Chen
202 8-9 03 EVANS D. Pomereano
204 9-10 04 EVANS Y.S. Chen
205 9-10 06 EVANS D. Pomereano
206 10-11 B0051 HILDEBRAND W. Zheng
207 11-12 07 Evans W. Zheng
208 12-1 81 Evans C. Vinzant
209 12-1 05 EVANS L. Scow
210 1-2 105 LATIMER O. Zeid
211 1-2 51 EVANS C. Vizant
212 2-3 385 LECONTE L. Scow
213 2-3 87 EVANS 0. Zeid


Text: J. Stewart, Calculus (Early Transcendentals), 5th edition.


Overview


Material Number of Lectures
Introduction, Techniques of Integration 8
Sequences and Series 5
Power Series and Approximation of Functions 4
First Order Differential Equations 3
Second Order Linear Differential Equations 6
Review 1
Total 27

Tests


Exam Date Material covered
Midterm # 1 October 11 (in class) Lectures 1-12
Midterm # 2 November 8 (in class) Lectures 13-20
Final Exam December 14, 12:30-3:30 PM All Lectures with 21-28 emphasized

Here is the first Practice Midterm 1

Here is the second Practice Midterm 1

Here is the grading scheme for Midterm 1

Here is the first Practice Midterm 2. And here are the solutions. Try to solve the problems before looking at the solutions. This practice midterm is longer and (probably) harder than the midterm. Corrections to some solutions: In problem 2 a) radius of convergence is 1/2; In problem 3 the remainder is incorrectly labeled at the end. In problem 6 the slopes for y > 1 are positive (contrary to what is drawn). Consequently the solution y = 1 is unstable.

Here is the second Practice Midterm 2. And here are the solutions. Again, try to solve the problems before looking at the solutions. This practice midterm is closer in length (a bit shorter, perhaps) than the midterm.

Here is the grading scheme for Midterm 2

Here is the First Practice Final Exam. And here are the solutions. Try to solve the problems before looking at the solutions. Corrections to some solutions: In problem 1 b) an overall factor of 1/2 is missing; in problem 2 b) y should be in numerator on the right hand side.

Here is the Second Practice Final Exam. And here are the solutions.

Here is the grading scheme for the Final Exam

Special accomodations: Students with disabilities documented through the disabled student's program that require special accomodations for exams should see me as soon as possible.


Grades


Work Percentage of final grade
Homework and Quizzes 20 %
Midterm #1 20 %
Midterm #2 20 %
Final Exam 20 40 %


Grades will be computed in the following way. You will be given a letter grade (+ or - if appropriate) for each item of work above and we will later combine these grades as indicated in the table to obtain the final grade for the course. The TAs will lastly identify borderline cases, for which we will carefully look at the numerical grades on the various tests to determine the grade.

If you do not take Midterm #1, Midterm # 2 will count for 40 % of your grade. If you take Midterm #1 but not Midterm #2, the Final Exam will count for 60 % of your grade. If you take neither Midterm #1 nor Midterm #2, you will fail the course. Consequently, please mark them in your calendars.


Homework and Quizzes: There will be a weekly quiz given each Wednesday in sections. There will be no make-up quizzes, but we will drop the two lowest quiz scores in computing your grade. Homework from main lecture on Tuesday is due on Friday in sections; homework from the main lectures on Thursday is due on Monday in sections. The homework will be graded ``pass/fail''. 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.


ASSIGNMENTS


  Date Topic Homework
1 Aug 29 Introduction, Integration: basic techniques 5.3:2,5,10, 5.4:4,29,32,40,56
2 Aug 30 Methods of Integration I 7.2:2,6,23,27,46,48,55
3 Sept 4 Methods of Integration II 7.3:6,14,29,30,31,32,38
4 Sept 6 Partial Fractions 7.4:1,4,9,12,19,20,25,32,43,49i
5 Sept 11 Strategies for Integration, Using Tables 7.6:1,3,12,24,
6 Sep 13 Approximate Integration 7.7:5,8,15,18
7 Sep 18 Improper Integrals 7.8:3,11,13,21,55,59,61
8 Sep 20 Arc length, Area of Surfaces of revolution 8.1:1,9,13,30,31,34, 8.2:1,3,7,9,25,27
9 Sep 25 Sequences and Limits 11.1:4,6,11,13,18,22,26,49
10 Sep 27 Infinite Series 11.2:2,12,13,15,18,30,27,32,34,41,46,49,50
11 Oct 2 Integral Test, Comparison Test 11.3:1,3,5,8,9,13,15,16,33, 11.4:2,10,11,20,28,32,39,45
12 Oct 4 Alternating Series, Ratio and Root Tests 11.5:2,4,6,14,16,23,25,27 11.6:4,7,8,16,23,25,27
13 Oct 9 Strategies for studying series 11.7:2,5,8,13,14,17,19,28,38
14 Oct 11 Midterm #1 covers Lectures 1-12
15 Oct 16 Power Series 11.8:3,5,8,9,13,14,15,20, 11.8:29,31,33a,34a
16 Oct 18 Taylor Series 11.9:1,3,5,9,13,34,35,39
17 Oct 23 Taylor Series II, Binomial Series 11.10:3,9,14,21,27,37,53,58, 11.11:1,2,7,13,17,19
18 Oct 25 Approximation by Polynomials 11.12:25,26,31
19 Oct 30 Introduction to Differential Equations, Direction Fields 9.1:1,2,3,10,11, 9.2:1,3,4,5,6,10
20 Nov 1 Separable Equations, Exponential and Logistic Growth 9.3:1,3,6,9,11,13,31, 9.4:1,3,7,9, 9.5:3,7
21 Nov 6 Linear Equations 9.6:5,8,15,17,29 This homework is due on Wednesday the 14th
22 Nov 8 Midterm #2 covers Lectures 13-20
23 Nov 13Second Order ODEs 17.1:1,2,6,9,17,19,21,24,25,30,33 This homework is due on Monday the 19th
24 Nov 15 Non-homogeneous Equations 17.2:1,2,3,7,10
25 Nov 20 Non-homogeneous Equations II 17.2:13,14,15,17,21,22
* Nov 22 Thanksgiving  
26 Nov 27 Oscillation and Damping 17.3:1,2,39,10,11,13
27 Nov 29 Series Solutions 17.4:1,2,3,4,5
28 Dec 4 Series Solutions II 17.4:8,9,10,11,12a
29 Dec 6 Review  



M Zworski 2007-08-23