Holy Cross Mathematics and Computer Science
MATH 135 -- Calculus 1, section 1, Fall 2019
Note: I will make every attempt to keep the information on this page current.
Any changes after the start of the semester will also be announced in class.
Syllabus and Schedule
- Course syllabus
- Course schedule; Note: the
plan for classes on 12/9, 12/11, 12/13 has now changed (see below).
Information and Announcements
- Information about calculus courses and textbook
- Quick Start Guide for WebAssign.
Our section's WebAssign class key: holycross 8442 7556 (note the "holycross" is all lower-case
letters, with no space)
- Exam Week Office Hours
- Monday, 12/16 -- 10am - 12noon
- Tuesday, 12/17 -- 1pm - 3pm
- Wednesday, 12/18 -- 8am - 10am
- Thursday, 12/19 -- 2pm - 4pm
- The Final Exam is coming up at 8:00am on Saturday, December 21, in our regular classroom.
- More information about the final
- The final exam from Fall 2016, and solutions. (Note that we did not cover the topic of question 8 this
year; there will not be a question of that type -- i.e. no ``related rates'' problem.) I'll post solutions for
these problems a couple of days before the final if you want to try these and check your work.
- Review sheets and other materials for the midterms:
- Revised plan for last week of semester: Because of the results of Exam 3, I want to spend
the remaining class days reviewing for the Final Exam rather than starting into any new material.
- Problem Set 9 has been revised to a review assignment on material from Chapters 3 and 4 (see below).
Sorry for inconvenience if any one started on the previously posted problems.
There is no WebAssign part for this one.
Solutions
Examples, Class Notes, Etc.
Assignments
- Information and Guidelines on problem sets.
- Problem Set 1, due: Friday, September 13.
- Part A -- in WebAssign
- Part B -- Write up solutions by hand on paper and submit at the start of class:
- Section 1.2/48, 54 (Note: The problem is asking you to do the following
two calculations: (1) Let the coordinates of P be (x,y).
Express the distances d1 and d2 in terms of x,y,
set them equal and use algebra to show that the equation y = x2 is a consequence.
Then, (2) show that if y = x2, then d1 = d2 is a consequence.
The first part shows that the locus of points where the two distances are equal is contained in the parabola; the second part shows that the parabola is contained in the locus of points where the distances are equal. Hence
that locus is equal to the parabola. The point (0,1/4) is called the focus of the parabola.
The line y = -1/4 is called the directrix.);
- Section 1.3/40;
- Section 1.4/40, 60 (Note: The Law of Cosines is the equation
c2 = a2 + b2 - 2 a b cos(θ). You are to derive
this, assuming the Pythagorean theorem holds in the right triangles in the figure.)
- Problem Set 2, due: Friday, September 20.
- Part A -- in WebAssign
- Part B -- Write up solutions by hand on paper and submit at the start of class:
- Section 1.6/36.
- Section 2.1/24, 30
- Section 2.2/58 (use a graphing calculator, copy the part of the graph for
-1 < x < 1 by hand, then explain your estimate for the value
of the limit).
- Problem Set 3, due: Friday, October 4
- Part A -- in WebAssign
- Part B -- Write up solutions by hand on paper and submit at the start of class:
- Section 2.4/64, 66 (be sure to include clear solid dots indicating the
values of the functions at the x-values in question.
- Section 2.5/56.
- Section 2.6/42 (Hint: Put in extra factors that cancel, but that let you apply
Theorem 2 on page 90), 50
- Problem Set 4, due: Friday, October 11
- Part A -- in WebAssign
- Part B -- Write up solutions by hand on paper and submit at the start of class:
- Section 2.7/32. Also, explain why the formula in the Hint is valid.
- Section 2.8/18, 20.
- Section 3.1/48.
- Problem Set 5, due: Friday, October 25
- Part A -- in WebAssign
- Part B -- Write up solutions by hand on paper and submit at the start of class.
As always, you must show all work necessary to justify your answers. Please write
up your solutions neatly!
- Section 3.2/66, 92.
- Section 3.3/38, 45. Call 3.3/45 from the book part (a). Also do
these three added parts:
- (b) Use your first answer
and the product rule to compute the derivative of e4x.
- (c) Do the same for e8x using your answer from (b).
- (d) Based on your
answers to (a-c), what would you guess about a general rule for the derivative of
eax if a is a constant?
- Problem Set 6, due: Friday, November 8
- Part A -- in WebAssign
- Part B -- Write up solutions by hand on paper and submit at the start of class.
As always, you must show all work necessary to justify your answers. Please write
up your solutions neatly!
- Section 3.6/52 (Note: the distance will be greater than zero; that is the
reason for the absolute value)
- Section 3.7/88,90
- Section 3.8/54
- Problem Set 7, due: Friday, November 15
- Part A -- in WebAssign
- Part B -- Write up solutions by hand on paper and submit at the start of class.
As always, you must show all work necessary to justify your answers. Please write
up your solutions neatly!
- Section 3.8/40
- Section 3.9/78
- Section 4.2/24, 88 (Note: 88 is asking for two separate graphs in the two parts!)
- Problem Set 8, due: Friday, November 22
- Part A -- in WebAssign
- Part B -- Write up solutions by hand on paper and submit at the start of class.
As always, you must show all work necessary to justify your answers. Please write
up your solutions neatly!
- Section 4.3/68
- Section 4.4/22,24
- Section 4.5/54
- Section 4.6/54 with added directions: Do not just plot the graphs on a graphing
calculator and match based on the calculator plots. Explain why you are making your
choice in each case. You must give a complete reason--for instance, explain the signs
of the one-sided limits as x approaches a vertical asymptote, or the state the
limit as x goes to infinity.
- Problem Set 9, due: Friday, December 13
- No Webassign part A this week.
- Part B -- Write up solutions by hand on paper and submit at the start of class.
As always, you must show all work necessary to justify your answers. Please write
up your solutions neatly!
- Chapter 3 Review Exercises (pages 189 - 192): 31 - 69 odds, 103. (For full credit, you must
show all work to derive your answer, not just the final answer. Note there are answers for
these odd-numbered problems in the back.)
- Chapter 4 Review Exercises (pages 256 - 258): 40 (read the question carefully!), 46, 57 (the
first sign is f'; the second is f'', 61, 63, Extra Credit: 68.
Related Links
- Biographical information on Isaac
Newton
- Biographical information on Gottfried
Leibniz
- Note: The Greek phrase appearing next to the heading of this page is one traditional rendering of
the reported inscription over the entrance to Plato's Academy in Athens
(founded about 387 BCE).
It means (roughly)
Let no one ignorant of geometry enter. This is a reflection of the foundational
role of geometry in Plato's ideas about knowledge and education.
Downloading Information
The links for assignments and other handouts shown above with the
notation (.pdf) lead
to documents in PDF format. To read and print these, you will need to have
Adobe Acrobat Reader installed on your computer. This is available at no
cost from Adobe.
To
my personal homepage
To the Math homepage
To the Holy Cross homepage
Last modified: December 21, 2019