# MATH20 Z2

## Spring 2014 Edition

### Lecture summaries, notices and other resources for Fundamentals of Calculus II

#### Resources:

Course syllabus.
MyMathLab, and some registration instructions.
You can use the computer labs in Votey or Perkins if they are available.
Some helpful information regarding the textbook (courtesy of Joe Kudrle).

#### Final exam practice:

Final exam practice questions are here, and the solutions are here.
(Note: The critical point in 2(a)(i) should be (x,y) = (11/4,-2), and please let me know if there are other typos)

#### Quiz Solutions:

Midterm 1
Midterm 2
Quiz 1
Quiz 2
Quiz 3
Quiz 4
Quiz 5
Quiz 6
Quiz 7
Quiz 8 (final solution should be (x,y)=(3,-2) not (3,2))
Quiz 9 (my sketch of the region R is wrong, but doesn't change the final answer...)
Quiz 10
Quiz 11 (take home, due Monday 4/28) [solutions]

#### Lectures:

4/30: Revision, practice exam. Worked solutions are above. See you on Friday for the final!
4/28: Sections 12.1 & 12.2 - geometric sequences, sum of geomestric sequences and annuities.
4/23: Section 11.3 - uniform, exponential and normal distributions. These are the most common distributions, being useful for modelling all kinds of phenomena, including sports.
4/21: Section 11.2 - expected value, variance, standard deviation, median of a continuous distribution. These are all the usual measures of "center" and "spread" of a distribution.
4/16: Section 11.1 - continuous probability distributions, continuous random variables. Cumulative density functions. Things like earthquake statistics are pretty interesting, and has led to some spectacular failures of prediction. Nate Silver has written some interesting stuff on this, and plenty of other topics in statistics.
4/14: Section 10.4 - applications of differential equations. Logistic growth is a very useful application of first order linear equations, and predator-prey models like Lotka-Volterra can be solved by separation of variables, and are highly enjoyable.
4/9: Finished talking about zombie growth. Section 10.2 - first-order linear differential equations. Integrating factors and the like.
4/7: Went over some of the questions from Midterm II. Section 10.1 - elementary and separable differential equations. Talked a little bit about zombie population growth, which happens to be well documented in the literature.
4/2: Finished Section 9.6 - double integrals. Finding the volume underneath a surface, double integrals over non-rectangular regions, and changing the limits of integration for difficult integrals.
3/26: Started section 9.6 - double integrals, up to Fubini's theorem. This will be all that will be on Midterm II next Monday.
3/24: Section 9.4 - Lagrange multipliers. General method plus a few examples, including utility maximization.
3/19: Finished Section 9.2 - partial derivatives with a quick discussion of Newton's law of gravity. Covered Section 9.3 - maxima and minima. Introduced the discriminant, local max/min, saddle points, did a couple of examples. Set Quiz 7 as a take-home quiz as a result.
3/17: Section 9.2 - partial derivatives. Definitions, meaning, first and second derivatives. Climbed a virtual Mt. Mansfield USING MATH
3/12: Talked a little bit about robots, dinosaurs and how they ran. Finished off Section 9.1 - multivariate functions, and went home early to avoid the blizzard!
3/10: Went over some questions from Midterm 1. Started Section 9.1 - functions of several variables. Covered definitions of multivariate functions and their domain and range. Definition of and graphing planes, as well as some plots of other surfaces such as hyperbolic paraboloids and hyperboloids. I know I promised you dinosaurs -- we will get to them on Wednesday!
2/24: Topics for Wednesday's midterm exam. Covered all of 8.4 - improper integrals, instead. A bit of discussion about continuously compounded interest from Section 8.3 (which we will otherwise skip for now).
2/22: Finished off Section 8.2 - volumes of solids of rotation. Calculated the volumes of footballs, icecream cones, and the Earth.
2/12: Finished off Section 8.1 - integration by parts. Covered the second half of Section 8.2, ie., the average of a function.
2/10: Went over the solutions to Quiz 3. Started Section 8.1 - integration by parts, including column integration. Solutions to the exercises from the end of class are here.
2/5: Finished Section 7.5 with a few worked examples calculating the area between curves. Talked about a fun application of this from economics of Lorenz curves and the Gini index, which shows how income inequality is increasing.
2/3: Finished off Section 7.4 by talking about calculating areas, and began Section 7.5 - the area between curves. Will do more examples of this on Wednesday.
1/29: Here is a spreadsheet which should help you with HW 7.6. After getting distracted by trigonometry and hedonometer we talked integration rules and integration by substitution from Section 7.4. Quiz 2 on definite integrals and numerical integration.
1/27: Section 7.6 - numerical integration. Trapezoidal rule and Simpson's rule. Started Section 7.4 - the fundamental theorem of calculus. (Will cover substitution and area in Wednesday's lecture.)
1/22: Section 7.3 - area and the definite integral. HW online, due Monday 1/27. Next lecture will skip ahead to Section 7.6 - numerical integration.
1/15: Watched a movie and showed we can math as hard as Jake Gyllenhaal. Finished Section 7.1, covered the essence of Section 7.2 - integration by substitution (but we'll do some more examples in the next lecture).
1/13: Introduction. Started Section 7.1 - definition of the antiderivative, and rules for polynomials, exponential and trig functions.

NOTICES:
• Bonus office hours tomorrow! 1-4pm. If I'm not in my office in Farrell Hall, I'll be downstairs in the Decision Theater, just come and find me there.
• All remaining HWs are available, and are all due Friday 5/9 after classes finish. Enjoy!
• Practice exam questions are at left. This also shows which topics are in the final -- if it isn't in the practice questions, it isn't on the final!

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