# Math 100, WT1 2016, Sections 102/104

The main website for all sections of Math 100 is here.

If you need to get ahold of me, the best way is through email: elyse@math.ubc.ca.
My office is in the Mathematics Building (behind the Koerner library), room 229F.

The syllabus for this section is here.
A list of things you're supposed to be doing for this class is here.

## Office Hours

Wednesdays, 3:30-4:30
Thursdays, 10-12
Fridays, 10-11

Office hours before the final: Wednesday, Thursday, and Friday (December 7-9), 2-5pm, Hennings 201
Wednesday will be a chance to sit a full-length mock exam. I'll have printouts of the 2015 exam; you bring paper (and another old exam if you've already done 2015)
Tuesday and Thursday: come with questions! :)

Hand-written solutions to the 2015 final.
(Remember the other finals have solutions on the wiki.)

## Slides

Sections Topics Dates File
Introduction Sept 7 (MWF), Sept 8 (TR) Introduction.pdf
Chapter 1 1.1-1.6 Limits and Velocity Sept 7 - 19 (MWF), Sept 8 - 15 (TR) LimitsAndVelocity.pdf
Chapter 2 2.1-2.3 Introduction to the Derivative Sept 19 - 26 (MWF), Sept 20 - 22 (TR) Deriv_Conceptual.pdf
2.4-2.9 Differentiation Rules: Sum, Power, Product, Quotient;
Derivatives of exponential functions and trig functions
Sept 28 - Oct 3 (MWF), Sept 27 - Oct 4 (TR) DiffRules.pdf
2.10-2.12
0.6, A.13
More Differentiation: Chain Rule, logarithmic differentiation,
implicit differentiation, derivatives of inverse trigonometric functions.
Oct 5 - 14 ? (MWF), Oct 4 - 13 (TR) MoreDifferentiation.pdf
Chapter 3 3.1 Rates of Change Oct 17 (MWF), Oct 18 (TR) RatesofChange.pdf
3.3 Exponential Growth and Decay Oct 19 - 21 (MWF), Oct 18 - 20 (TR) ExponentialGD.pdf
3.2 Related Rates Oct 24 (MWF), Oct 25 (TR) RelatedRates.pdf
3.4.1-3.4.3 Approximating functions with polynomials:
Oct 26-28 (MWF), Oct 25 (TR) Approximations.pdf
Kumar's slides
3.4.4, 3.4.5, 3.4.8 Taylor polynomials and their error Oct 28-Nov 2 (MWF), Oct 25-Nov 1 (TR) Taylor.pdf
3.5.1, 3.5.2 Finding global and local extrema Nov 2-7 (MWF), Nov 1-3 (TR) MaxMin.pdf
Chapter 2 2.13 Rolle's Theorem and Mean Value Theorem Nov 7-9 (MWF), Nov 3-8 (TR) MeanValue.pdf
Chapter 3 3.6 Sketching Curves Nov 9 - 16 (MWF), Nov 8 -11 (TR) Sketch.pdf
3.5.3 Word problems with optimisation Nov 18-21 (MWF), Nov 15 (TR) Optimization.pdf
3.7 L'Hôpital's Rule Nov 23-25 (MWF), Nov 17-22 (TR) Lhospital.pdf
Chapter 4 4.1 Antiderivatives Nov 28 (MWF), Nov 24 (TR) Antiderivatives.pdf

## VideosUpdate: a lot of these weren't working on your computers, so I've tried putting them on YouTube. If any of these links don't work, please email me! elyse@math.ubc.ca

Topic File Description
Limits Limits and tangent lines video
Average and Instantaneous Velocity; secant and tangent line; limit notation
One-sided limits video
A simple example motivating one-sided limits
Limits, cont'd video
Sometimes limits don't exist; one-sided limits; calculating limits
Limits at Infinity video
Limits at Infinity
Continuity Intro to Continuity video
Before we learn the formal definition of a continuous function, dwell a little on what it means for a function's limit to differ from its value at a point. Being used to this behaviour will help you build intuition about continuity.
Limits, Continuity, IVT video
Strategies for evaluating limits; continuity; Intermediate Value Theorem
Extra: continuity video
Think you understand continuity? Test yourself with a graph that has no limit... anywhere. (This video goes beyond the course material. Think of it as recreational.)
Derivatives Intro to Derivatives video
Introduction to derivatives: interpretations, derivatives at a point, derivatives of a function
Graphing Derivatives video
Use the graph of a function to create the graph of its derivative. Review the interpretation of positive and negative derivatives, and get used to looking at a line and intuiting its slope.
Tangent Lines video
Find the tangent line to a curve; calculate derivatives using simple rules.
Differentiation Product and Quotient Rules video
Derivatives of Products and Ratios
Exponential video
Product rule and derivatives of exponential functions
Trigonometric video
Derivatives of trigonometric functions.
Chain Rule video
Derivatives of compound functions.
Review Inverse Functions video
Inverse functions.
Differentiation Logarithms video
Logarithmic functions and logarithmic differentiation.
Rates of Change Rates of Change video
Rates of Change
Exponential change Rates of Change video
Exponential growth and decay, such as radioactive decay, compound interest, and population growth. Introduction to differential equations.
Newton's Law of Cooling video
Exponential rates of change applied to cooling bodies.
Related Rates Related Rates video
Calculating the rate of change in systems with lots of interconnected changing parts.
Polynomial Approximations First Approximations video
Estimating the value of a function with a constant, linear, or quadratic approximation.
Error Bounding video
Give an approximation of a function, and bound the error you introduced.
video
If you are given an error tolerance, which approximation should you use?
Optimization Extrema video
Finding maxima and minima of a function.
Optimization video
Optimization video
MVT Rolle's Theorem video
A differentiable function that takes the same value twice has a horizontal tangent line somewhere.
Mean Value Theorem video
A differentiable function has a point where its instantaneous rate of change is equal to is average rate of change over an interval.
Curve Sketching Curve Sketching 1 video
Curve Sketching 2 video
Symmetry video
Even and odd functions.
L'Hospital's Rule L'Hospital's Rule video

## Resources

Lots of people find their first calculus class challenging, and lots of people find their first few years in university challenging. If you find yourself struggling, I hope you'll take advantage of some of the resources available to you on campus.

### Help with Registration

If you have problems registering in a math course, please find the appropriate math advisor.

If you have questions related to your major, like which flavour of calculus you should be taking, OR if you have a major life event that might prevent you from completing the semester, you should talk to your faculty advisor.

### Help with Course Content

It's good for your brain to work hard! But if you find yourself feeling overwhelmed, please do take advantage of some of these marvellous resources available to you.
• The Math Learning Center is staffed with tutors, and you can go there to meet other students. More information here: Math Learning Center.
• Other students in the course are an important resource. Ask the person sitting next to you if they want to work on homework together, or meet at a coffee shop to study for the next exam. Talking to strangers is hard, but having a community is helpful and important. If someone asks for help, keep in mind that teaching someone is a fantastic learning opportunity. Being able to do a problem on the homework is great, but often we learn even more when we're put in the position of explaining it to someone else.
• Free tutoring: AMS. For independent, paid tutors, check bulletin boards around the math building.
• The internet has pretty much everything. There's our class discussion board, where you can pose a question to the class. Apart from the CLP notes and problem book, there's lots of free online textbooks and notes you can search for. (I recommend MOOCulus and APEX Calculus in particular, but find a textbook that clicks for you.) There's also tutoring videos, like Khan Academy. If you look hard enough, the UBC pages have old exams.
• Talk to your teacher! Office hours are time I set aside to meet with students. You can grab me after class or email me at elyse@math.ubc.ca to ask a short question, or schedule an in-person meeting if office hours don't work for you.

### Help with Other Issues

Student Services at UBC has a variety of programs to help you stay happy and healthy. A good place to start is here: LiveWell

UBC provides services to address, among other things: illness and injury, mental health and wellbeing, sexual assault (for people of all genders), other violence, discrimination and harrassment, diversity, disability, and ongoing medical considerations. If you have legal issues, you might be able to get help from the Law Students' Legal Advice Program. The Office of Equity and Inclusion is a good place to go if you want more information about maintaining an environment that is respectful, especially with regards to interculturality, LGBT*QIA status, race, students who are parents, etc. The Office of Access and Diversity provides disability support.

If something comes up during the semester that interferes with your academic progress (such as an illness, or caring for a loved one) contact your faculty advising office as soon as possible. You can find them here.

The province has an excellent website with information on mental health, including an online screening tool and resources: Here To Help. The Vancouver Access & Assessment Centre (AAC) is a point of entry for concerns about mental health and substance abuse, and they also have a call line if you just want to talk to someone. Education is a tool for a better life, from increased earning potential to a heightened appreciation for the beauty and complexity in the world. Your real life extends far beyond the boundaries of this campus. It's important that you don't let your education interfere with your physical or emotional health.

### Addressing Issues with the Course

Full disclosure: I'm not a perfect instructor. If there's something about this course that bothers you, I'd like the chance to address it. You can contact me in person after class or during office hours, or write me an email. If you are uncomfortable discussing it with me, you can talk to the Instructor in Charge, Professor Andrew Rechnitzer: andrewr@math.ubc.ca.

If it isn't feasible to change the thing that's bothering you, we still might be able to come up with strategies for addressing it. At the very least, you can get an explanation of why things are the way they are.