Course Content:

  • Trigonometric and inverse trigonometric functions and indeterminate forms (Sec 5.6, 5.7, 5.8, 5 lectures)
  • Techniques of Integration (Secs 6.1 – 6.3, 6.5 – 6.6, 8 lectures)
  • Applications of integration (Secs 7.1 – 7.4, 7.6 – 7.7, 10 lectures)
  • Sequences and infinite series (Secs 8.1 – 8.8, 14 lectures)
  • Polar coordinates (Secs 9.3 – 9.4: Polar Coordinates, 3 lectures)

InstructorLarry Goldstein, larry at usc dot edu, KAP 406D, 213 740 2405. Office Hours: Monday 10-11, Friday 1-2:30
Lecture:  ZHS 163, MWF 9:00-9:50, 39531D

Text: Essential Calculus, Stewart

Teaching Assistant: Hongying Zhao, hongyinz at usc dot edu. Office Hours: 10-11AM Tuesday and Thursday, and 2-3PM Wednesday in the Math Center

Previous Math 126 Final Exams
See the registration calendar for important (drop) dates.
An inverse tangent formula for π

Please check this page regularly for updates and changes.

Exams, Grading and Course Policy

Attendance is not taken in class, but students who come regularly to class do vastly better than students who do not.

There will be a weekly quiz in your discussion section every Tuesday starting in week 2, except in weeks in which midterms are given. Students who complete all their homework assignments with full understanding should have no difficulty on the quizzes. The quiz may be composed of questions covering past as well as current material. Your lowest two quiz scores will be dropped, hence there will be no make up quizzes given for any reason. Missing more than two quizzes is a sign of less than sufficient involvment in the course, and such students should consider dropping the course and taking it in a semester in which they can devote their full attention.

Exams will be administered only on the dates that follow, so students need to check the exam dates below at the start of the semester and make sure those are cleared on their calendars. There will be no make-up exams for any reason. If you miss one midterm exam due to some unforeseen emergency, upon furnishing appropriate proof of your situation your final course grade will be computed based on your scores on the remainder of your completed work.

Students are kindly asked to turn their cell phones and computers off during class and put those away, along with any outside reading materials.

  • Quizzes: 20%
  • Computer Assignments: 10%, Discussion will meet in KAP Calculus Lab KAP 265 on Thursday October 16th and Thursday November 13th.
  • Midterm 1: 20%: Friday, October 10th. Will cover all material up to and including Section 7.3.
  • Percentiles: 25th 68, Median 78, 75th  120, high score 180 of 200
  • Midterm 2: 20%, Friday, November 7th. Will cover all assigned material between Sections 7.4 and 8.3 inclusive. The exam may include questions from previous years final exams. The exam will be closed book, no notes or calculator allowed.
  • Percentiles: 25th 65, Median 80, 75th  170, high score 198 of 200
  • Common Final Exam: 30%, Saturday, December 13th, 2-4 p.m. ZHS 252

Calculators and other electronic devices, books and lecture notes will not be allowed.
You may use one self-prepared handwritten formula sheet, letter size paper, both sides.
You should also bring your USC identification card.


Quiz Coverage: The Quiz may include problems on any previously covered material:

  • Sept 2:   5.6 to problem 28
  • Sept 9:   5.6 to 5.8
  • Sept 16: 6.1
  • Sept 23: 6.2 to 6.3
  • Sept 30: 6.5, 6.6 and 7.1
  • Oct 14 : 7.2-7.4
  • Oct 21:  7.6
  • Oct 28:  7.7 and 8.1
  • Nov 11: 8.2 to 8.3
  • Nov 18: 8.4 to 8.5
  • Dec 2:   8.6 and 8.7

5.6: 4, 6, 10, 14, 20, 28, 30, 35, 38, 41, 43, 45 and #5(i) from F’04 (Ignore the limits of integration and solve as if it were an indefinite integral.)
5.7: 5, 10, 15, 17, 19(a,b,c,d), 25,34,45,47,51
5.8: 41,42,43,45,50,56 and #6 from F’ 03, #1 from S’ 04, #4 from F’ 04, #3 from F’ 05, #1 from F’ 07
6.1: 3,5,12, 15,25,27,33,2 (Parts i and iii only) from F’ 05, 1 (Parts a and c only) from S’ 06, 2 (Parts a and b only) from S’ 09
6.2: 1,6,13,18,19,28,37,42,47,56,65,66
6.3: 1,4,5,7,10,15,21,23,29,34 35,39,41,43,44, 2 from F’ 05,2ab S’ 07,1b S’ 06
6.5: 2,5,10,15,20,25,28,36,39
6.6: 1,5,7,20,27,29,41,42,48,49,50, 4 on F’05, 2 on S’06, 3 on S’07
7.1: 1,3,5,9,13,28,32,33
7.2: 1,4,8,12,16,17,28,32,33,38,47,50,51
7.3: 2,5,7,8,9,11,19,30,33,34,40,43. F’ 07, #4, S’06 #3
7.4: 2,3,7,12,16,18,26,27,32,34 (set up the equation),35 (set up the integral)
7.6: 5,9,12,16,18,21,22,23,24,31,34,43,48,53
7.7: 1,7,9,11,15,21,28,31,34,36,39,45,47,50, #7 from F’ 08
8.1: 3,4,9,12,14,23,29,31,32,34,37,41,43,45,46,53
8.2: 9,11,14,17,24,25,26,29,35,38,41,44,47,50,56,57,60, #6 S’09
8.3: 1,3,8,10,13,17,19,21,22,27,29,31,3,41,43,45,46,47
8.4 :5,8,9,14,17,18,23,29,31,35,39,42,44,45,46
8.5: 3,5,11,16,20, 22,23,27,35,36
8.6: 1,2,6,9,11,15,18,28,32,35,39,40,41
8.7: 5,8,13,15,20,23,29,32,40,44,50,54,55,59,61,66,67,68,70a
8.8: 9ab, 12ab,14ab,20,25,26,29,30
9.3: 7,10,13,20,21,25,28,38,41,46,47,50,51,56
9.4: 2,3,6,10,17,21,30,33,36

Mathematica assignments: Please enter your name in the Mathematica Notebook at the top, in the form of a Mathematica comment (* Your Name *). Also use commenting to separate out the different problems in the assignment, as in entering (*Problem 1*) before starting the first problem. Enter additional comments that explain your computations. You may hand in a paper printout, or, save some paper and email your .nb file, or a pdf of it, to Shadow.

Computer assignment #1: November 6nd.

Computer assignment #2: December 2nd.

Course Journal

Monday, August 25th.       Introduction to second semester calculus, course coverage and policies
Wednesday, August 27th. Trigonometric functions, their inverses and derivatives
Friday, August 29th.         Trigonometric functions, their inverses, application. Introduction to Hyperbolic functions
Wednesday, Sept. 3rd.      Hyperbolic functions, inverses and their derivatives. L’Hopital’s rule
Friday, Sept. 5th.               L’Hopital’s rule
Monday, Sept. 8th.            Integration by parts
Wednesday, Sept 10th.      Integration by parts, Trigonometric integrals
Friday, Sept 12th.              Trigonometric substitutions, Partial Fractions
Monday, Sept 16th.           Partial Fractions
Wednesday, Sept 18th.      Numerical Integration
Friday, Sept 20th.              Numerical Integration, Improper Integrals
Monday, Sept 22th.           Improper Integrals
Wednesday, Sept 24th.      Improper Integrals
Friday, Sept 26th.              Areas between curves
Monday, Sept 29th.           Volumes
Wednesday, Oct 1st.          Volumes, disc and shell method
Friday, Oct 3rd.                  Volumes
Monday, Oct 6th.               Arclength, work
Wednesday, Oct 8th.          Work
Friday, Oct 10th.                Midterm I
Monday, Oct 13th.             Hydrostatic pressure
Wednesday, Oct 15th.        Hydrostatic pressure, center of mass
Friday, Oct 17th.                Center of mass, first order separable differential equations
Monday, Oct 20th.             First order separable differential equations, sequences
Wednesday, Oct 22nd.       Mixing problems, sequences
Friday, Oct 24th.                Direction fields, sequences
Monday, Oct 27th.             Sequences, Series
Wednesday, Oct 29th.        Series, Integral and Comparison tests
Friday, Oct 31st.                 Series, Integral and Comparison tests
Monday, Nov 3rd.              Series, book stacking, limit comparison test, alternating series
Wednesday, Nov 5th.         Alternating series, absolute and conditional convergence
Monday, Nov 10th.            Absolute and conditional convergence, ratio test
Wednesday, Nov 12th.       Root test. Power series
Friday, Nov 14th.                Power series, compostion, derivatives and integrals
Monday, Nov 17th.             Power series, log and arctan expansions, Bessel function differential equation
Wednesday, Nov 19th.        Power series, Taylor and Maclaurin series, Taylor’s theorem
Friday, Nov 21st.                Taylor and Maclaurin series, remainder
Monday, Nov 24th.             Taylor and Maclaurin series, Binomal series
Wednesday, Nov 26th.        Binomial Series
Friday, November 28th.       Binomial Series, Applications
Monday, December 1st.       Multiplication and division of series, Applications of series, integration, taking limits, and in physics
Wednesday, December 2nd. Polar coordinates, graphing polar function, derivatives
Friday, December 5th.          Polar coordinates, derivatives, areas