# HELP!

## Announcements:

Here are solutions to some problems from the 2007 and 2008 exams which I think might be most useful.

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:

Chapters 1--5, 10 (except 10.4), 11, and sections 12.1, 12.2, 12.4, 12.7, 13.1, 13.2, 13.4, 13.6, 14.7, 15.4.

Here is the 2007 final exam; here is the 2008 final exam. You should check out these notes before working on these two finals.

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

Office: PO103, Room 118 (PO103 is one of the portables just outside the Science Wing)

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.

Teaching Assistants:
• Lisa Passalacqua
email: lisa.passalacqua at gmail dot com
Office hour: Thursday, 5:00--6:00 pm in S506F (Math Aid Room)
• Sophia Peng
email: sophia_peng_xp at yahoo dot ca
Office hours: Thursday, 12:00--1:00 and 3:00--4:00 in AC312

 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. 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. 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. Feb. 11 Continuity (on an interval, at a point); Types of discontinuities: end of domain, bulletholes, jump discontinuities, vertical asymptotes; Horizontal asymptotes and limits; 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; Implicit differentiation. 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; u-substitution. Quiz 9 Solution 9