practice midterm on Wednesday, in class (just for
practice, not for marks) bring paper!
either mark your own practice midterm or switch with a
fellow student
you will be asked to enter your marks in
16.2 Line Integrals
1. Quote. There is no substitute for hard work.
(Thomas Alva Edison, American inventor, 1847 1931)
2. Problem. Find the work done by the force
F(x, y) = xi + (y + 2)j
in moving an
16.3 The Fundamental Theorem for Line Integrals
1. Quote. There again, that is a fundamental principle: no two situations are alike.
(Lakhdar Brahimi, Algerian Diplomat, 1934 - )
2. Reminder. The Fund
16.6 Parametric Surfaces and Areas
1. Quote. When a blind beetle crawls over the surface of a curved
branch, it doesnt notice that the track it has covered is indeed curved.
I was lucky enough to noti
16.4 Greens Theorem
1. Quote. In the Press, and shortly will be published, by subscription, An
Essay on the Application of Mathematical Analysis to the Theories of
Electricity and Magnetism. By George
16.8 Stokes Theorem
1. Quote. I too feel that I have been thinking too much of late, but in
a dierent way, my head running on divergent series, the discontinuity
of arbitrary constants, . I often thou
13.1 Complex Numbers
1. Quote. Nothing is perfect. Life is messy. Relationships are complex. Outcomes are
uncertain. People are irrational.
(Hugh Mackay, Australian Social Researcher, 1945 )
2. Proble
16.9 The Divergence Theorem
1. Quote. There is an inevitable divergence between the world as it is
and the world as men perceive it.
(James William Fulbright, 1905-1995, was a United States Senator)
13.3 Derivative. Analytic Function
1. Quote. Nothing is built on stone; all is built on sand, but we must build as if the
sand were stone.
(Jorge Francisco Isidoro Luis Borges, Argentine writer, 1899
13.5 Exponential Functions.
1. Fact. In a 1988 poll, readers of the journal Mathematical Intelligencer chose Eulers
equation
ei + 1 = 0
as the single most beautiful equation in all of mathematics.
2.
13.4 Cauchy-Riemann Equations. Laplaces Equation.
1. Quote. What we know is not much. What we do not know is immense.
(Pierre-Simon Laplace, French mathematician and astronomer, 1749-1827)
2. Problem.
13.2 Polar Form of Complex Numbers
1. Quote. The works must be conceived with re in the soul but executed with clinical
coolness.
(Joan Mir i Ferr`, Spanish painter, 1893 - 1983)
o
a
2. Problem. What
13.6 Trigonometric and Hyperbolic Functions. Eulers Formula
1. Quote. The imaginary is what tends to become real.
(Andr Breton, French poet, 1896-1966)
e
2. Problem. What is sin i?
3. Denition. For z
13.7 Logarithm. General Power. Principal Value
1. Quote. The less eort, the faster and more powerful you will be.
(Bruce Lee, Chinese American martial artist, actor, philosopher, and lmmaker, 19401973
16.5 Curl and Divergence
1. Quote. A career is wonderful, but you cant curl up with it on a cold
night.
(Marilyn Monroe, American actress, model, and singer, 1926 1962)
2. Curl. Suppose that the vecto
MATH 254, Summer 2016
Practice Midterm
Question 1: What is the geometric meaning of the gradient of a function?
Question 2: Show that
H
~ F~ = 0 everywhere.
F~ d~l = 0 for any closed loop if
Question
posted on Canvas
MATH 254, Summer 2016
Assignment 3
Due: Tuesday, May 31, at the end of your tutorial
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MATH 254, Summer 2016
Midterm Exam
Friday, June 24, 1:30pm-2:20pm
Show your work to receive full marks. Total marks for this midterm: .
Question 1: (x marks) .
Question 2: (y marks) .
Question 3: .
.
MATH 254, Summer 2016
Midterm Exam
Friday, June 24, 1:30pm-2:20pm
Show your work to receive full marks. Total marks for this midterm: 50.
Question 1: [3 points] Calculate the gradient of the function