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:
Here is the 2007 final exam; here is the 2008 final exam. You should check out these notes before working on these two finals.
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
Telephone: 416-208-2784
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.
DATE | LECTURE SUMMARY |
ASSIGNMENT (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. |
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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; Geometric series. |
Assignment 4 | Quiz 3 | Solution 3 | Puzzler |
Feb. 2 |
More on equations of value; Sequences vs series; geometric series; Sigma notation. |
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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; Loan amortization. |
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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. |
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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. |
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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; Implicit differentiation. |
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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. |
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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; u-substitution. |
Quiz 9 | Solution 9 |