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 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! :)
50-min Mock Exam (also available on main webpage)
Notes from overhead about mock exam, 29 November
Notes from overhead from Friday, 02 December
Problems from 2015 quizzes, to help you study for the final: link.
Hand-written solutions to the 2015 final.
(Remember the other finals have solutions on the wiki.)
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: Constant, linear, and quadratic approximations |
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 |
Topic | File | Description | |
---|---|---|---|
Limits | Limits and tangent lines | video YouTube |
Average and Instantaneous Velocity; secant and tangent line; limit notation |
One-sided limits | video YouTube |
A simple example motivating one-sided limits | |
Limits, cont'd | video YouTube |
Sometimes limits don't exist; one-sided limits; calculating limits | |
Limits at Infinity | video YouTube |
Limits at Infinity | |
Continuity | Intro to Continuity | video YouTube |
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 YouTube |
Strategies for evaluating limits; continuity; Intermediate Value Theorem | |
Extra: continuity | video YouTube |
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 YouTube |
Introduction to derivatives: interpretations, derivatives at a point, derivatives of a function |
Graphing Derivatives | video YouTube |
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 YouTube |
Find the tangent line to a curve; calculate derivatives using simple rules. | |
Differentiation | Product and Quotient Rules | video YouTube |
Derivatives of Products and Ratios |
Exponential | video YouTube |
Product rule and derivatives of exponential functions | |
Trigonometric | video YouTube |
Derivatives of trigonometric functions. | |
Chain Rule | video YouTube |
Derivatives of compound functions. | |
Review | Inverse Functions | video YouTube |
Inverse functions. |
Differentiation | Logarithms | video YouTube |
Logarithmic functions and logarithmic differentiation. |
Rates of Change | Rates of Change | video YouTube |
Rates of Change |
Exponential change | Rates of Change | video YouTube |
Exponential growth and decay, such as radioactive decay, compound interest, and population growth. Introduction to differential equations. |
Newton's Law of Cooling | video YouTube |
Exponential rates of change applied to cooling bodies. | |
Related Rates | Related Rates | video YouTube |
Calculating the rate of change in systems with lots of interconnected changing parts. |
Polynomial Approximations | First Approximations | video YouTube |
Estimating the value of a function with a constant, linear, or quadratic approximation. |
Error Bounding | video YouTube |
Give an approximation of a function, and bound the error you introduced. | |
video YouTube |
If you are given an error tolerance, which approximation should you use? | ||
Optimization | Extrema | video YouTube |
Finding maxima and minima of a function. |
Optimization | video YouTube |
||
Optimization | video YouTube |
||
MVT | Rolle's Theorem | video YouTube |
A differentiable function that takes the same value twice has a horizontal tangent line somewhere. |
Mean Value Theorem | video YouTube |
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 YouTube |
|
Curve Sketching 2 | video YouTube |
||
Symmetry | video YouTube |
Even and odd functions. | |
L'Hospital's Rule | L'Hospital's Rule | video YouTube |
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.
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.
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.