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<title>
Test 2 - review
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<h1>Test 2</h1>
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<p class="show">Bring
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<li>calculator
<li>one 8 1/2 X 11 page of notes that you prepare ahead of time.
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<p>There will be two parts of the test. 

<ul><b>Part 1</b> will work like Test 1:
You can bring a page of notes, but you may not consult any other resources / people, and you can't use CoCalc.

<p><b>Part 2</b>. When you turn in the first part, I'll give you the last, Lagrange multipliers problem, and for that part, you may still refer to your notes.  But you can also use CoCalc (or Mathematica if you're more comfortable with that, and have your own copy).  
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<p>Of necessity, the test will be <b>open book</b>.  You may use a calculator (make sure you know how to switch between degrees and radians!). You may consult your notes, my notes, the textbook, use a calculator, but not other people.

<p>The test will be timed.  I'll send out a .pdf of the exam at 11:00 AM (Goshen time).  You may mark it up (Notability) or write your answers on separate pieces of paper, and upload snapshots of them in when finished.

<p>Because the test is timed, you will need to study ahead of time.  Do not expect to be able to learn material you have not yet understood by reading up on it during the test!

<h3  class="show">Topics--Functions of more than one variable</h3>

<h4>Parametric functions</h4>
<p>Be able to parameterize a surface in terms of 2 parameters. 
  Be able to parameterize a path (set of points along a curve) in terms of a single parameter.  For example, if you want to look for a limit as you approach a point along a particular path.  Using the chain rule.

<h4>Limits</h4>
<p>Be able to test for the limits of a function of two variables as you approach a point by various paths.

<h4>Tabular Data</h4>

<p> Understanding how to interpret tabular data for multivariable data. Know how to estimate
partial derivatives from tabular data. Know how to use the methods of
linear approximation (and tangent planes) to estimate values of
functions of two variables from tabular data.

<h4>Contour Maps</h4>

<p>Know the relationship between the 3D graph of a function and the
contour plot of a function. Be able to sketch a contour plot. Know what
a level curve is, what information can be obtained from looking at a
plot of level curves (a contour map). Given a contour map, be able to determine the
sign of first- and second-order partial derivatives.  Given a contour map, be able to estimate values for first-order partial derivatives.


<h4>Derivatives</h4>

<p>Given a function of two variables, be able to compute its
partial derivatives, the gradient, the directional derivative in a
specified direction. Understand the geometrical relationships between the contour
plot of a function and the gradient. Understand the relationship
between directional derivative and the gradient. Clairaut's theorem.


<h4>Maximization/minimization</h4>

<p>Be able to find maximum, minimum, and saddle points. Be able to
find critical points of a function. Be able to interpret a contour
plot in terms of maximum and minimum values of a function. Be able to
set up and do an optimization problem using the technique of Lagrange
multipliers.

<h4>Double Integrals</h4>

<p> Be able to do an integration estimate from a table of values or a
contour plot. Be able to compute double integrals. Be able to
determine limits of integration and change the order of integration.  This includes changing a function of $x$, e.g. $y=f(x)=\frac 12 x^2$ into an equivalent function of $y$, e.g. $x=h(y)=\sqrt{2y}$.



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