Math 150: Multivariable Calculus: MWF:
10-10:50am, room TBD
Below is a quick summary of the most relevant
material, namely the current reading, quizzes, homework, as well as my lecture
notes.
Additional Comments on the lectures:
click here Class Review
sheet:
click here for a course review
sheet (email me to restore images -- caused downloading woes)
Upcoming HW and reading:
click here for a list of homework problems and suggested
problems.
Readings before class: click
here for a bullet point summary to help prepare you for class.
Outline of the course:
a quick summary
Reflections on the the course:
a more extensive
analysis of what was covered
Takeaways for undergraduate classes:
summarizes key points from this and
other undergrad courses
- Review of Calculus I and II:
part I
part II (right click
to download)
- Handout from first day
of class is here First
day lecture:
http://youtu.be/Sabcuhsxekg (February 7, 2014:
Introduction, Pythagoras)
- all of my course
notes (student
notes part 1) (student
notes part 2) (student
notes part 3)
- additional comments from the
lectures,
LaTeX / Mathematica template/videos,
homework problem template.
- Click here for a welcome to the class
- Click here for calculus
review problems and solutions. These are a good way to test your knowledge
of Calc I and II.
-
Click here for many free textbooks from GeorgiaTech (click
here for a free multivariable calculus textbook)
-
The textbook is Edwards and Penney:
Calculus (Early Transcendentals), 7th edition, which was
used in Math 104. You may use either the 7th edition or the 6th;
unfortunately, while the content is essentially the same, the page numbering
and chapter labeling differ, and you are responsible for making sure you do
the right problems (I'll try and make sure the problems are the same, but it
is your responsibility to make sure you do the right ones).
VIDEOS OF LECTURES: Watch before class:
http://web.williams.edu/Mathematics/sjmiller/public_html/150Sp18/articlesvideos.htm
-
Due at Class 28:
Taylor Series Trick, Multivariable Taylor SEries:
https://youtu.be/P5t7eLYRFTI
(slides
here)
-
Due at Class 29:
- Twenty-ninth
day lecture:
http://youtu.be/4OcxtpxuSJw (May 14, 2014:
Special Series, Alternating Series, Pi
formulas, Birthday Problem: Not doing 2018)
- Read
multivariable calculus (Cain and Herod)
and my lecture notes. (You
should have already done this).
-
For Taylor series, see my handout here
(essentially just pages 2 and 3).
- Homework #21: (1) Cain-Herod: Find the limit of the
series \(\sum_{n=1}^\infty \frac{1}{3^n}\). (2) Cain-Herod: Find a value of
\(n\) that will insure that \(1+1/2+1/3+\cdots+1/n > 10^6\). Prove your value
works. (3) Cain-Herod: Question 14: Determine if the series \(\sum_{k=0}^\infty
\frac{1}{2e^k+k}\) converges or diverges. (4) Cain-Herod: Question 15:
Determine if the series \(\sum_{k=0}^\infty \frac{1}{2k+1}\) converges or
diverges. (5) Let \(f(x)=\cos x\), and compute the first eight derivatives of
\(f(x)\) at \(x=0\), and determine the \(n\)-th derivative.
- Due at Class 30: Library Trip
-
Due at Class 31:
Difference Equations
-
Watch: Double Plus Ungood:
https://www.youtube.com/watch?v=Esa2TYwDmwA&t=309s
-
For Taylor series, see my handout here
(essentially just pages 2 and 3).
- Homework #22: Dues Monday May 3: (1) Cain-Herod 10-18: Is the series
\(\left(\sum_{k=0}^n\frac{10^k}{k!}\right)\) convergent or divergent? (2)
Cain-Herod 10-21: Is the following series convergent or divergent? \(\sum_{k=1}^n
\frac{3^k}{5^k(k^4+k+1)}\). (3) Let \(a_n = \frac{1}{(n \ln n)}\) (one divided
by \(n\) times the natural log of \(n\)). Prove that this series diverges. \emph{Hint:
what is the derivative of the natural log of \(x\)? Use \(u\)-substitution.}
(4) Let \(a_n = \frac{1}{ (n\ln^2 n)}\) (one divided by n times the square of
the natural log of \(n\)). Prove that this series converges. \emph{Hint: use
the same method as the previous problem. (5) Give an example of a sequence or
series that you have seen in another class, in something you've read, in
something you've observed in the world, ....
-
Video on logarithms:
https://youtu.be/-SsbkPaB6j8
- Here are some videos you can watch to help review.
- Review: Change of Variables, Odd/Even Functions, Bounding Functions,
Comparison Test: http://youtu.be/8EZQKzoWxEo
- Review:
Mostly series test (one series and we apply all four tests!):
http://youtu.be/HANb4mVLOOc
-
HW: (1) Calculate, to at least 40 decimal places, 100/9801. Do
you notice a pattern? Do you think it will continue forever - why or why not?
(2) Calculate, to at least 40 decimal places, 1000/998999. Do you notice a
pattern? Do you think it will continue forever - why or why not?
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Class 32: Differential Equations and Trafalgar
-
HW (1) Solve the difference equation a(n+1) = 7a(n) - 12a(n-1)
with initial conditions a(0) = 3 and a(1) = 10. (2) Consider the whale problem
from class, but now assume that on every two pairs of 1 year old whales give
birth to one new pair of whales, and every four pairs of 2 year old whales
give birth to one new pair. Prove or disprove: eventually the whales dies out.
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SCHEDULE OF TA REVIEW SESSIONS:
Mon 9-10pm NSB 015 Paul
Tues 9-11pm NSB 019 Paul
Wed 8-9pm Griffin 1 Kunal
Thur 7-8pm Griffin 1 Kunal
Thur 8-9pm Griffin 1 Paul
Sun 7-9pm NSB 113 Kunal
click here for a review sheet
for the course (summarizes main results, definitions, key steps in
the proofs, some examples)
General advice: article
on how to study physics (though much of this applies to any field).