MAC 2313/SUM2007/EXAM 2 -- Review
Chap 12
1 Know what a vector function is, how to find their limits and how to determine if they
are continuous. Practice sketching them in both 2 and 3 dimensions. Know how to
identify these curves, be able to match their graphs and equations. Know how to find the
curve of intersection of two surfaces in the form of a vector function
2 Know how to find the derivative of a vector function and the differentiation rules. Be
able to use the derivative for finding the equation of the tangent line to a space curve.
Know what we mean on that a space curve is smooth. Be able to find the unit tangent
vector to a curve. Know how to find the integral of a vector function.
3 Know how to find the arc length of a vector function. Using the unit tangent vector, be
able to find the unit normal vector to a space curve at a given point.
4 Given the vector function describing the position of an object, be able to find the
velocity and the acceleration vector functions and vice versa. Understand how to split up
the acceleration vector into normal and tangential components.
Review Problems recommended to practice on:
12.1 # 3, 10, 14, 24, 28, 60, 72, 74, 76
12.2 # 6, 10, 14, 18, 20, 22, 24, 34, 40, 46, 50, 52, 56, 58, 62, 64, 66
12.3 # 2, 4, 6, 8, 10, 16, 20, 22
12.4 # 6, 12, 24, 26, 32, 36, 40, Example 3
12.5 # 2, 4, 10, 22, 36, 43, Example 3, Example 4, Example 6
Chap 13
1 Understand the three ways of representing two variable functions (algebraic,
numerical and graphical) Be able to find the domain of two and three variable functions.
Know how to graph level curves for them, be able to match graphs of 3 dimensional
surfaces and their contour maps.
2
3
Be able to find limits of two and three variable functions using the Squeeze
theorem or using polar coordinates or continuity. To prove that the limit does not
exist be able to find two different paths through which we obtain different limit
values for the given function.
Know how to find partial derivatives of two and three variable functions
algebraically, numerically and graphically. Be able to describe the meaning of the
partial derivative for application problems.
4
Be able to find the equation of the tangent plane to a surface at a given point. Find
an equation of a normal line to a surface.
5 Know both versions of the chain rule: Case I. z = f (x(t),y(t)) and Case II: z = f
(x(s,t),y(s,t)). Be able to find implicit derivatives for two and three variable functions
6 Know how to find the directional derivative of a two variable function. Understand
the gradient, the meaning of its direction and its length. Be able to estimate the gradient
graphically. Be able to visualize a surface based on the gradient field. Be able to use the
gradient of three variable functions to find the equation of a tangent plane to a surface at
a given point.
Review Problems recommended to practice on:
13.1 # 2, 4, 6, 8, 10, 12, 13, 18, 21, 22, 32, 35, 50, 51, 52, Example 2—4(page 886-888)
13.2 # 6, 8, 9, 10, 12, 13, 18, 20, 22, 24, 32, 34, 36, 44, Example 4-6(page 898-900)
13.3 # 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 30, 32, 34, 36, 40, 52, 58, 60, 62, 74
13.5 # 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 30, 32, 34, 36, 42, 44, 52
13.6 # 8, 10, 12, 14, 16, 18, 22, 26, 28, 32, 42, 50, 56, 58, 60, Example 3—5( page 934-936)
13.7 # 6, 8, 10, 12, 14, 16, 18, 22, 26, 28, 30, 34, 40, 48, 50, Example 3—5(page 946-947)