Lec. 4 Sept. 20: Meaning of a function being continuous at a point
x=a. Functions which are and are not continuous. Intermediate
value theorem. Discussion of horizontal
and vertical asymptotes and their relation to limiting values of
a function.
Lec. 5 Sept. 22: The slope of a tangent line as a limit. Finding
the equation of a tangent line. Instantaneous velocity as an instantaneous
rate of change. Definition
of the deriviative of f(x) at a point a. Interpretation of the derivative
as an instantaneous rate of change.
Lec. 6 Sept. 27: Derivatives as functions. Definition of a differentiable function. Functions which are and are not differentiable. Differentiability implies continuity.
Lec. 7 Sept. 29: Rules for differentiation. Powers, sum rule, product and quotient rules.
Lec. 8 Oct. 4: Rules revisited, derivative of exponential function.
Angular variables, trigonometric functions, derivative of sin x and
cos x. Derivatives of other trig functions.
Begin discussion of chain rule.
Lec. 9 Oct. 6: Review problems for Exam I. The chain rule.
Lec. 10 Oct. 11: Implicit differentiation. Derivatives of inverse trig functions.
Lec. 11 Oct. 18: Higher derivatives, differerntiating the log function, logaritmic differentiation. Differentiation of x to function of x.
Lec. 12 Oct. 20: Related rates, linear approximations and differentials.
Lec 13. Oct. 25: The differential as a linear approximation. Maximum
and minimum of a function, absolute (global) or local (relative). Local
extrema occur at critical points.
Finding the absolute maximum and minimum of a closed interval [a,b].
Lec. 14 Oct. 27: Mean value theorem. Use of f' and f'' in graphing.
Lec. 15 Nov. 1: Graphing continued. L'Hospital's rule.
Lec. 16 Nov. 3: More graphing and L'Hospital's rule.
Lec. 17 Nov. 8: Optimization problems: methods and examples.
Lec. 18 Nov. 10: Optimization in economics, Newton's method.
Lec. 19 Nov. 15: Review problems for Exam II.
Lec. 20 Nov. 22: Antiderivatives. The calculation of area .
Lec. 21 Nov. 24: Upper and lower approximatgions to area. The area
as a limit. Distance as an area calculation.
Definition of the definite integral.
Lec. 22 Nov. 29: Properties of the definite integral. Begin discussion of the fundamental theorem of the calculus.
Lec. 23 Dec. 1: More on the fundamental theorem. Applications and uses.
Lec 24 Dec. 6: Indefinite integrals and total change. Substitution.
Lec. 25 Dec. 8: More on substitution. The log function as an integral.
Lec. 26 Dec. 13: Review.
Lec.4 Sept. 20: Read sect. 2.5. Main idea is to understand
what it means for a function to be continuous at a point a, and over an
interval, and how to recognize
when a function is or is not continuous at a point. Read about the
intermediate value theorem and see why it is necessary that the function
be continuous for this theorem to be true. Read sect.
2.6. The main goal here is to understand what the limits are, what
the notation is for limits involving x approaching +
or - infinity, but mainly how the limits can be computed.
Problems: Sect. 2.5: 3,5,9,11,19, 43. Sect. 2.6: 3,7,15,19.
Lec. 5 Sept. 22: Read sects. 2.7 and 2.8. Problems: Sect. 2.7:
3,5, 7,9,13,17. Sect. 2.8: 4,7,15,21 (replace x by something involving
a and h).
QUIZ NEXT MONDAY, in recitation, on material through Sect.
2.4.
Lec. 6 Sept. 27: Read Sect. 2.9. Problems: Sect. 2.9: 7,11,19,21,23,25,27,29,39
Lec. 7 Sept. 29: Read Sects. 3.1 and 3.2: Sect. 3.1: 5,7,15,19,27,32,39. Sect. 3.2: 3,7,11.
NOTE: Because of coming exam on Oct. 13, there will be a QUIZ NEXT
MONDAY, Oct. 4, covering sections 2.5 through 3.2. You should
be able to compute a derivative of simple
functions using the definition of the derviative as a limit a h
tends to zero. You should be able to find the tanget line to a curve. For
more complicated
functions, be able to use rules for powers, sum, product, and quotient
to find the derivative.
ANNOUNCEMENTS: Anyone who has not registered for a recitation should
do so immediately! See Vikki Johnson in room 703 WWH.
TUTORING is now available through the math department. Schedules will be
available in class Sept. 29, and can be picked up outside room 705 WWH.
Lec. 8 Oct. 4: Skip section 3.3 and read 3.4, start 3.5. Problems: Sect. 3.4:5,7,9,13,15,19,23,29,35,43.
IN-CLASS EXAM Wednesday Oct. 13, covering material through Section
3.5. Some review problems
will be suggested in class Oct. 6. The exam will be CLOSED
BOOK. However you will be allowed one 5x8 inch index card (front and back)
of notes, as well as
your calculator.
Lec. 9 Oct. 6: Finish reading section 3.5. Problems: Sect. 3.5: 1,3,5,7,11,21,27,33,37,39.See ANSWERS to the review problems given in class.
Lec. 10 Oct. 11: Read sects. 3.6 and 3.7. Problems: Sect. 3.6: 1,3,7,13,15,23,27,36,53. Sect. 3.7: 1,9,19.
Lec. 11 Oct. 18: Read sects. 3.7 and 3.8 . Problems: Sect.
3.7: 23, 35, 51. Sect. 3.8: 3,5,9,1,13,17,23,35,47. Note: Exam
I will be returned Monday in recitation,
along with an answer sheet. Exams not picked up in recitation will
be available in class on Wednesday, Oct. 20.
QUIZ NEXT MONDAY covering 3.5,3.6,3.7,3.8.
Lec. 12 Oct. 20: SKIP SECTION 3.9. Read 3.10, 3.11. Problems: Sect.
3.10: 1,3,7,9,17,29. Sect. 3.11: 5,7,17,31,36,42.
QUIZ NEXT MONDAY covering 3.5,3.6,3.7,3.8.
Lec. 13 Oct. 25: Finish 3.11 and read 4.1. Problems: Sect. 4.1: 1,3,7,11,17,33,49,55,57,61,77.
Lec. 14 Oct. 27: Read 4.2, 4.3. Problems: Sect. 4.2: 1,3,5,11,19. Sect. 4.3: 3, 8,11,14,21,25.
Lec. 15 Nov. 1: Read 4.4,4.5: Problems: Sect. 4.3: 45. Sect. 4.4: 5,7,9,15,21,27,33,37,43,50.
Lec. 16 Nov. 3: Finish reading section 4.5. Wewill skip section 4.6
but students with graphing calculators may want to read through it anyway.
Problems: Sect. 4.5: 11,13,19,29,33.
QUIZ #4 NEXT MONDAY Nov. 8, covering sections 3.10-4.5.
Lec. 17 Nov. 8: Read 4.7. Problems: Sect. 4.7: 3,7,12,15,21,29,49.
Lec. 18 Nov. 10: Read 4.8, 4.9. Problems: Sect. 4.8: 3, 5,13,17,23. Sect. 4.9:5,9,11,28
See REVIEW PROBLEMS for Exam II.
See the TeX file for these problems Review Problems in TeX format .
Lec. 19 Nov. 15: Review for Exam II. Use the review exercises at
the end of each chapter. Concentrate on implicit differentiation,
the log function,
logarithmic differentiation, finding relative and absolute max and
min of a function, related rates, linear approximation and differentials,
Rolle's theorem and the
mean value theorem, optimization problems, and Newton's method.
Over the weekend read Sect. 4.10.
Lec. 20 Nov. 22: Read 4.10, 5.1. Problems: Sect. 4.10: 3,11,17,19,23, 35,61,63,71,75. Sect. 5.1: 3,
Lec. 21 Nov. 24: Finish 5.1, read 5.2. Problems: Sect. 5.1: 5, 13, 20. Sect. 5.2: 1, 5,15,17,19
QUIZ #5 next Monday, Nov. 29 covering sections 4.7, 4.9, and 4.10.
Lec. 22 Nov. 29: Finish 5.2. Begin 5.3. Problems: Sect. 5.2: 21,25,31,33,35,43,47,51.
QUIZ #6 next Monday, Dec. 6, covering 4.10, 5.1,5.2,5.3.
Lec. 23 Dec. 1: Finish Sect. 5.3. Problems from Sect. 5.3: 3,5,9,11,17,27,31,35,47,49.
Lec. 24 Dec. 6: Read 5.4, begin 5.5. Problems: Sect. 5.4:3,5,9,13,17,21,31,35,41,57,58.
See review problems for final exam.
(I will go over these problems on Dec. 13.)
Lec. 25 Dec. 8: Finish 5.5. Read 5.6. The main point from this section
is to understand how the logarithm can be defined as
an area under a curve. Problems: Sect. 5.5: 1,3,5,6,9,19,25,27,31,41,47,55,65,69.
THE FINAL EXAM is scheduled for 12-1:50 on Tuesday, December 21,
IN ROOMS 713 MAIN and 714 MAIN. We will fill
both rooms as seating is in every other seat. You will be allowed
a calculator and three 5"X 8" index cards of notes during the exam.
An EARLY FINAL EXAM for students holding tickets for travel before
Dec. 21 will be
given Wednesday, Dec. 15, 12:30-2:20, in Room 1314 WWH. You
must have contacted me in advance by e-mail to arrange this.
You will be allowed a calculator and three 5"X 8" index cards of
notes during the exam.
Additional office hours after Dec. 13 (Room 717 WWH):
Tuesday, Dec. 14: 10-11:30am
Thursday, Dec, 16: 10-11:30 am
Monday, Dec. 20: 10-11:30 am