HERE ARE A FEW MORE PRACTICE PROBLEMS!
The final exam (which will take place on April 19th, from 9am -- 12pm, in AA112) will cover all the material discussed in lecture, including:
Click here for some practice problems on u-substitution (for more examples, look at your lecture notes).
Here is a bonus problem. It is due by 2pm on April 19th. If you solve it perfectly and completely, your lowest quiz score will be replaced by a perfect mark.
Instructor: Leo Goldmakher
Email: leo.goldmakher at utoronto dot ca
Office hours: Tuesday and Thursday 3:10--4:00 pm, Tuesday 11:10--12:00, and by appointment.
(due 1 week from date posted)
|QUIZ||QUIZ SOLUTIONS||DOCUMENTS|| || || || || || ||Jan. 5||
motivating integration (average speed example);
intuition for derivative (zoom in!);
Andy likes my shirt.
| || || ||Course syllabus||Jan. 7||
Sets (e.g. natural numbers, integers, rationals, reals,
undergraduates at UTSc, etc.)
The square root of 2 is not rational.
Functions -- definition, examples, non-examples.
|Assignment 1|| || || ||Jan. 12||Functions: domain, range, examples|| || || || ||Jan. 14||Inverse functions, exponential functions||Assignment 2||Quiz 1||Solution 1|| ||Jan. 19||Logarithmic functions; compounded interest|| || || || ||Jan. 21||
General formula for compounded interest;
Menagerie of functions and order of growth;
The number e and the natural logarithm;
Frequently compounded interest and e;
Exponential decay and half-life.
|Assignment 3||Quiz 2||Solution 2|| ||Jan. 26||
Set the midterm date for March 4th (in class);
Practiced manipulating exponentials and logs;
Discussed APR, nominal rates, effective rates,
future value, and present value;
Started a problem on carbon dating and half-life.
| || || || ||Jan. 28||
Redid half-life example (carbon dating);
Example of future value: borrowing from parents;
Continuously compounded interest;
Equations of Value: two arguments, same conclusion;
|Assignment 4||Quiz 3||Solution 3||Puzzler||Feb. 2||
More on equations of value;
Sequences vs series; geometric series;
| || || || ||Feb. 4||
More on series, sigma notation, geometric series (Zeno's paradox);
RRSP and annuities: amount (future value) and present value.
|Assignment 5||Quiz 4||Solution 4|| ||Feb. 9||
Reviewed how to calculate PV and FV of an annuity;
| || || || ||Feb. 11||
Continuity (on an interval, at a point);
Types of discontinuities:
Examples of determining limits pictorially and algebraically.
|Assignment 6||Quiz 5||Solution 5||Midterm Practice Problems||Feb. 23||
Overview of finding limits;
Problem on making a piecewise function continuous.
| || || || ||Feb. 25||
Making a piecewise function continuous;
Geometric definition of derivative;
Limit definition of derivative;
Examples of exactly evaluating a derivative;
Examples of approximating a derivative.
Read sections 11.1 and 11.2
through page 492, and
study for midterm!
|Quiz 6||Solution 6|| ||Mar. 2||
The derivative function;
Sketch f '(x) given the graph of f(x);
Basic properties of derivatives.
| || || || ||Mar. 4||Midterm exam||Assignment 7|| ||Midterm Solutions|| ||Mar. 9||Derivative of x^n, ln(x), e^x; product rule.|| || || || ||Mar. 11||More differentiation, including chain rule, quotient rule, a^x, x^x, etc.||Assignment 8|| || || ||Mar. 16||GUEST LECTURE: 11.3|| || || || ||Mar. 18||GUEST LECTURE: 11.4--11.5||Assignment 9||Quiz 7||Solution 7|| ||Mar. 23||
Differentiating logarithms to any base;
| || || || ||Mar. 25||
Implicit differentiation problem (find equation of tangent line!);
The second derivative and acceleration;
Optimization: finding absolute / relative maxima and minima;
Applications of optimization to economics, and gardening.
|Assignment 10||Quiz 8||Solution 8|| ||Mar. 30||
The second derivative test;
Distance traveled is area under the speed function.
| || || || ||Apr. 1||
The definition of the integral (area, but possibly negative);
Finding the average of a continuous function (e.g. weather, speed);
Integration using geometry;
The fundamental theorem of calculus;
| ||Quiz 9||Solution 9|| |