Samantha Dahlberg

## MATH 200 Section 104

### Topics Covered

Friday December 1

• Review 2: Math 200 2016 final exam
• Solution

Wednesday November 29

• Review 1: Comparing different integrations.
• Notes

Monday November 27

• Secondary text number 1 section 15.6: Examples of integration with spherical coordinates.
• Notes
• Picture justifying the calculation for dV in spherical coordinates. click

Friday November 24

• Secondary text number 1 section 15.6: Introduction to spherical coordinates.
• Quiz 5.
• Notes

Wednesday November 22

• Example 2 from Monday's class
• Secondary text number 1 section 15.6: Cylindrical coordinates.
• Notes

Monday November 20

• 13.6: More examples on iterated triple integrals.
• Examples 1 to 4.
• Geogebra illustration for example 1. click
• Geogebra illustration for example 2. click
• Geogebra illustration for example 3. click
• Geogebra illustration for example 4. click

Friday November 17

• 13.6: Setting up the bounds for iterated triple integrals.
• Geogebra illustration for area under the plane in the first octant. click
• Geogebra illustration for last example in class. click
• Notes

Wednesday November 15

• 13.4: Mass and center of mass.
• 13.6: Started discussing triple integrals.
• Notes

Monday November 13

• No classes /li>

Friday November 10

• 13.3: Integrating with polar coordinates.
• Notes
• Quiz 4

Wednesday November 8

• 13.3: Regions and integration with polar coordinates

Monday November 6

• 13.3: Polar coordinates introduction.
• Notes

Friday November 3

• 13.1/13.2: Interpreting integration over regions as a signed volume.
• Notes

Wednesday November 1

• 13.1/13.2: Integration over regions written as iterated integrals written in multiple ways.
• Notes

Monday October 30

• Optimization overview.
• 13.1/13.2: Introduced integration in multiple variables, and what the calculations mean in terms of area and volume.
• Notes

Friday October 27

• Lagrange multiplier examples.
• Notes
• Quiz 3

Wednesday October 25

• 12.8: Part two of finding the distance from a point to a surface. Two solution methods.
• Introduced the ideas behind Lagrange multipliers.
• Notes
• Geogebra example from class of using normal vectors to find distance from a surface to a point. click
• Geogebra example from class of a maximal point on a curve being tangent to a level curve. click

Monday October 23

• 12.8: Finding absolute maxima and minima over a region with boundary. Using contour diagrams to find absolute maxima and minima. Part one of finding the distance from a point to a surface.
• Notes
• Geogebra example from class Finding absolute maxima and minima over a triangular region. click

Friday October 20

• 12.8: Critical points, local maxima and minima and how to classify critical points for multivariable functions.
• Notes

Wednesday October 18

• 12.6 and 12.7: Tangent lines in a certain direction and normal lines.
• Notes

Monday October 16

• 12.5: The last example on chain rule has been posted under examples.
• 12.6: The directional derivative, the formula as a dot product, the gradient and the meaning of the gradient's direction and slope.

Wednesday October 13

• Midterm

Wednesday October 11

• 12.5: We computed chain rule in multiple variables for higher order partial derivatives.

Monday October 9

• No Class: Thanksgiving.

Friday October 6

• 12.4: One example on using the differential to calculate maximum errors.
• 12.5: We introduced the chain rule in multiple variables with a few examples and applications.

Wednesday October 4

• 12.4: Conditions for differentiability, the total differential, the tangent plane equation, linearization and why these last three topics are all the same concept.

Monday October 2

• 12.3: Examples of partial differential equations, examples of calculating partial derivatives given a contour diagram and example of calculating partial derivatives given a table.

Friday September 29

• 12.3: Partial derivatives, how to calculate them with a formula and what do they mean for a surface.

Wednesday September 27

• 12.2: Limits for multivariable functions and continuity for multivariable functions.

Monday September 25

• 12.1: Defined multivariable function and determined domain and range. The focus was on sketching the surface in 3D or using a contour diagram. We also sketched a function in three variables.

Friday September 22

• 10.1: Surfaces of rotation. Emphasis on recognizing a surface of rotation and using that to sketch a picture.
• 12.1: How to draw an equation of a surface. Is is a cylinder, sphere, surface of rotation? If not you can draw z-traces (or y-traces or x-traces).

Wednesday September 20

• 10.5: Many examples including intersection of two lines, intersection of two planes, angle between two planes, a plane defined from three points and the distance from a point to a plane.

Monday September 18

• 10.4: The cross product and its relation to sine, the area of a parallelogram and the volume of the parallelepiped.
• 10.5: Writing the equation of the line as equalities and as a parameterization. The equation of a plane.

Friday September 15

• 10.4: The cross product and its formula as a determinant.
• Quiz 1

Wednesday September 13

• 10.3: A second formula for dot product involving cosine. Dot product and perpendicular vectors. Conditions for parallel vectors. Vectors projected onto other vectors.

Monday September 11

• 10.2: The standard unit vectors and standard unit vector form. Using vectors to solve for the tension in strings holding a weight.
• 10.3: The definition of the dot product and properties of the dot product.

Friday September 8

• Section 10.2: Vectors and how to calculate their magnitude and direction in two and three dimensions. The vector between two points. The component form of a vector. Vector addition and scalar multiplication and how to visualize addition. Unit vectors.

Wednesday September 6

• Section 10.1: Plotting points, line segments, spheres, cylinders, and simple planes. Distance formula and general formula for a sphere.