Math 107, Fall 2006: Homework 10, part I
(due Monday December 4 at 1:30pm in Krieger 208)
This is the first of three parts to the homework due on Monday December 4. It is based on
the material covered
Math 107, Fall 2006: Homework 3, part III
(due Monday October 2 at 1:30pm in Krieger 208)
This is the third of three parts to the homework due on Monday October 2. It is based on
the material covered
Math 107, Fall 2006: Homework 4, part II
(due Monday October 9 at 1:30pm in Krieger 208)
This is the second of three parts to the homework due on Monday October 9. It is based on
the material covered
Math 107, Fall 2006: Homework 4, part I
(due Monday October 9 at 1:30pm in Krieger 208)
This is the first of three parts to the homework due on Monday October 9. It is based on
the material covered in
Math 107, Fall 2006: Midterm I Syllabus and Study Guide
The first midterm exam will take place on Tuesday October 10 in Maryland 310 (same room
as normal class). It will be 50 minutes long, starting p
Math 107, Fall 2006: Homework 3, part II
(due Monday October 2 at 1:30pm in Krieger 208)
This is the second of three parts to the homework due on Monday October 2. It is based on
the material covered
Math 107, Fall 2006: Homework 9
(due Monday November 27 at 1:30pm in Krieger 208)
This is the homework due on Monday November 27. It is based on the material covered in
class on November 20-21.
Releva
Math 107, Fall 2006: Homework 4, part III
(due Monday October 9 at 1:30pm in Krieger 208)
This is the third of three parts to the homework due on Monday October 9. It is based on
the material covered
Math 107, Fall 2006: Homework 3, part I
(due Monday October 2 at 1:30pm in Krieger 208)
This is the first of three parts to the homework due on Monday October 2. It is based on
the material covered in
Notes for 15th April finishing 7.4 (Areas) and covering
7.5 (Scalar surface integrals).
1
Recap
1. We did some examples of computing vector line integrals. (Be careful about orientation issues.)
2. We
Notes for 17th Feb (Wednesday) covering 2.5 (Chain
rule) and 2.6 (The Gradient)
February 17, 2016
1
Recap
1. We did properties of the derivative, namely
(a) If f~ and ~g are differentiable then so are
Notes for 18th April finishing 7.5 (Scalar surface
integrals) and covering 7.6 (Vector surface integrals).
1
Recap
1. We defined the area of a parametrised surface (u, v). We calculated it in a few
ex
Notes for 22nd Feb (Wednesday) covering 2.5 (Chain
rule) and 2.6 (The Gradient)
February 19, 2016
1
Recap
1. We finished the topic of gradients by presenting intuition for why it is feasible for
f to
Notes for 29th April doing a review of the new (i.e.
after midterm 2) material.
1. If you need to check whether a given map T : R2 R2 is 1-1, then suppose
T (x1 , y1 ) = T (x2 , y2 ), check whether x1
Notes for 22nd April finishing 8.1(Greens theorem)
and covering 8.2 (Stokes theorem).
1
Recap
~ = F~
1. We gave some examples of the vector surface integral using the trick F~ dA
ndA.
2. We stated an
Notes for 21st Mar finishing 5.2 (Double integrals
done rigorously) and covering 5.3 (The double integral
over more general regions)
1
Recap
RR
1. We defined double integrals
f dA of bounded functions
Name:
Section Number:
110.202 Calculus 3
SPRING 2016
MIDTERM - 1
February 24th, 2016
Instructions: The exam is 6 pages long, including this title page. The number of points each
problem is worth is li
Notes for 13th April finishing 7.2 (Line integrals) and
covering 7.3 (parametrised surfaces).
1
Recap
1. We defined the concept of reparametrisation, and proved reparametrisation invariance of the sca
Notes for 4th Mar (Friday) finishing 3.4 (Lagranges
multipliers) and covering 4.1(Acceleration and
Newtons law) and 4.2 (Arc length)
March 4, 2016
1
Recap
1. Finished Global extrema (with an example).
Notes for 22nd Feb (Wednesday) covering 3.3
(Extrema)
February 25, 2016
1
Goal
One of the reasons to study calculus is to answer questions like How much should I price
this app so that I get the maxim
Notes for 20th April finishing 7.6 (Vector surface
integrals) and covering 8.1(Greens theorem).
1
Recap
1. We did some more examples of the scalar surface integral. Did reparametrisation
invariance of
Practice problems for Midterm 2 (Solutions)
April 6, 2016
Disclaimer: Note that these practice problems are to be treated ONLY as an indication
of the level of difficulty that is to be expected. It is
Notes for 19th Feb (Wednesday) covering 2.5 (Chain
rule) and 2.6 (The Gradient)
February 19, 2016
1
Recap
1. We continued the Chain rule the last time. We in fact, generalised it to vectorvalued funct
Name:
Section Number:
110.202 Calculus 3
SPRING 2016
MIDTERM - 2
April 8th, 2016
Instructions: The exam is 6 pages long, including this title page. The number of points each
problem is worth is listed
Notes for 11th Mar finishing 5.1 (Introduction to
double integrals) and covering 5.2 (Double integrals
done rigorously)
March 11, 2016
1
Recap
1. Defined Divergence (.F~ ), and studied its interpretat
Notes for 25th April finishing 8.4(Gauss theorem).
1
Recap
1. Did some examples of Greens theorem (especially using its curl and divergence
formulations).
2. We stated Stokes theorem, gave examples, a
Notes for 30th Mar covering 6.2 (Change of variables)
1
Recap
1. Did one last example of triple integrals.
2. Wanted to generalise the theory of substitution/change of variables to higher dimensions.
Notes for 23rd Mar finishing 5.3 (The double integral
over more general regions), and covering 5.4 (Change
of order of integration)
1
Recap
1. We did properties of double integrals and a precise state
Practice problems for Midterm 2
March 30, 2016
Disclaimer: Note that these practice problems are to be treated ONLY as an indication
of the level of difficulty that is to be expected. It is definitely
Notes for 28th Mar finishing 5.5 (Triple Integrals), 6.1
(Geometry of maps), and covering 6.2 (Change of
variables)
1
Recap
1. Defined the triple integral over a rectangular box using Riemann sums. St