Review for Exam 3
Sections 14.7, 15.1-15.5, 15.7.
50 minutes.
5, 6, problems, similar to homework problems.
No calculators, no notes, no books, no phones.
No green book needed.
Triple integral in cyli
Tangent planes and linear approximations (Sect. 14.6)
Review: Dierentiable functions of two variables.
The tangent plane to the graph of a function.
The linear approximation of a dierentiable function
Review for Exam 2
Tuesday Recitations: Sections 13.1-13.3. 14.1-14.6.
Thursday Recitations: Sections 13.1-13.3. 14.1-14.7.
50 minutes.
From ve 10-minute problems to ten 5-minutes problems.
Problems si
Local and absolute extrema, saddle points (Sect. 14.7)
Review: Local extrema for functions of one variable.
Denition of local extrema.
Characterization of local extrema.
First derivative test.
Second
Double integrals (Sect. 15.1)
Review: Integral of a single variable function.
Double integral on rectangles.
Fubini Theorem on rectangular domains.
Examples.
Review: Integral of a single variable func
Integrals in cylindrical, spherical coordinates (Sect. 15.7)
Integration in cylindrical coordinates.
Review: Polar coordinates in a plane.
Cylindrical coordinates in space.
Triple integral in cylindri
Double integrals on regions (Sect. 15.2)
Review: Fubinis Theorem on rectangular domains.
Fubinis Theorem on non-rectangular domains.
Type I: Domain functions y (x).
Type II: Domain functions x(y ).
Fi
Areas and double integrals. (Sect. 15.3)
Areas of a region on a plane.
Average value of a function.
More examples of double integrals.
Areas of a region on a plane
Denition
The area of a closed, bound
Double integrals in polar coordinates (Sect. 15.4)
Review: Polar coordinates.
Double integrals in disk sections.
Double integrals in arbitrary regions.
Changing Cartesian integrals into polar integral
Review for Exam 2
Sections 13.1-13.3. 14.1-14.6.
50 minutes.
5 problems, similar to homework problems.
No calculators, no notes, no books, no phones.
No green book needed.
Section 14.6
Example
(a) Fin
Triple integrals in Cartesian coordinates (Sect. 15.5)
Triple integrals in rectangular boxes.
Triple integrals in arbitrary domains.
Volume on a region in space.
Triple integrals in rectangular boxes
Triple integrals in Cartesian coordinates (Sect. 15.5)
Review: Triple integrals in arbitrary domains.
Examples: Changing the order of integration.
The average value of a function in a region in space.
Directional derivatives and gradient vectors (Sect. 14.5)
Directional derivative of functions of two variables.
Partial derivatives and directional derivatives.
Directional derivative of functions of