MATA32: Calculus for Management I (Winter '10)

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.

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

Office:

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
Sophia Peng

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

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