Download MATH 110 PRECALCULUS SYLLABUS Fall

MATH 110
Text:
Author:
PRECALCULUS SYLLABUS
Fall 2010
Precalculus: A Prelude to Calculus
Sheldon Axler
INSTRUCTOR:
OFFICE HOURS:
EMAIL:
Dr. Yun Yoo
Mondays between 4 pm and 6 pm at Korman 247
[email protected] (The best way to contact me)
Attendance: Attendance will be taken. The third absence will influence your grade in a negative way. Missing 9 or more classes
will result in a failing grade.
HELP: In addition to your instructor, help is available at the Mathematics Resource Center in Korman 247. The Center is open from
10:00am to 7:00pm Mondays through Thursdays and 10:00am to 4:00pm on Fridays. There is always someone there that can answer
your questions
TECHNOLOGY: A calculator will not be allowed during the exams. Cell phones must be turned off and put away during exams and
during class. Anyone using a cell phone or other electronic device during an exam will receive a grade of 0.
GRADING: There will be weekly homework, two one hour mid-terms, and a two hour final. The midterms and final are common
exams held outside of class time.
Online homeworks
20%
mid-terms each count 25%
50%
final
30%
Academic Honesty: The Academic Honesty policy of Drexel University is in effect for this course. A copy of this policy is available
on http://www.drexel.edu/studentlife/judicial/honesty.html
Responsibilities and Strategies: You are expected to read and understand assigned sections of the text, attend class regularly, and
participate in class discussions and worksheets. A good way to keep up is to read ahead as directed in the syllabus, read again after a
new topic is introduced, and work on practice problems as assigned. Working in teams of two or three outside of class is an excellent
way to reinforce the concepts. Plan on spending at least one to two hours outside of class for each hour of scheduled class time.
Schedule, Objectives and Homework Assignments
Week Section Objectives
1
2.1
Linear Functions and Lines
- Understand the concept of the slope of a line;
- Be able to find the equation of a line given various
information
- Understand why parallel lines have the same slope.
Quadratic Functions and Parabolas
- Be able to use the completing-the-square
2.2
technique with quadratic expressions;
- Be able to find the vertex of a parabola;
- Understand how the quadratic formula was
discovered;
- Be able to solve quadratic equations.
- Be able to graph parabolas
2
2.4
2.5
3
2.3
3.1
Polynomials
- Understand the connection between factorization
and the zeros of polynomial;
- Be able to do algebraic manipulations with
polynomials;
Rational Functions
- Be able to do algebraic manipulations with rational
functions;
- Be able to divide polynomials
Integer Exponents
- Understand why x0 is defined to equal 1 (for x ≠ 0);
- Understand why x-1 is defined as 1/xm (for m a
positive integer and x ≠ 0);
- Be able to manipulate and simplify expressions
involving integer exponents.
Rational and Real Exponents
Homework
Page 127
3, 5, 7, 9, 13, 15, 19, 21, 25, 27, 29, 31, 35, 37, 41,
Page 141
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 27, 29, 31, 33, 35,
37, 51
Page 170
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 32,
34, 38, 39
Page 184
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31,
33, 35, 37, 39, 41, 46
Page 153
1, 2, 3, 4, 5, 7, 9, 15, 17, 19, 21, 23, 25, 27, 29, 33,
35, 37, 41, 43, 49, 64, 65
Page232
Understand why x1/m is defined to equal the number
1, 3, 5, 7, 9, 11, 13, 17, 21, 23, 29, 35, 37, 39, 41, 45,
whose mth power equals x;
47, 49, 59, 67, 77
n/m
1/m n
- Understand why x is defined to equal (x ) ;
- Be able to manipulate and simplify expressions
involving exponents.
Logarithms and Inverses of Exponentiation
Page 243
- Understand the definition of the logarithm with an
All odd from 1 to 29, all odd from 37 to 61, 77
arbitrary base;
- Understand the consequences of thinking of
logarithms as inverse functions;
- Be able to evaluate logarithms in simple cases.
Algebraic Properties of Logarithms
Page 2521, 3, 17, 18, all odd from 19 to 37, 57
- Be able to use the formula for the logarithm of a
product and quotient;
Be able to use the formula for the logarithm of a
power.
e and the Natural Logarithm
- Page 329
- Understand how to use the rectangles to
All odd from 1 to 21, 25, 27, 35, 37
approximate the area under a curve;
- Understand the definition of e;
- Understand the definition of the natural logarithm
and its connection with area;
- Be able to work comfortably with the exponential
and natural logarithm functions
-
4
3.2
3.3
5
4.3
6
5.1
Unit Circle
- Understand the angle corresponding to a radius of
the unit circle;
- Understand negative angles;
- Understand angles greater than 360º;
- Be able to compute the length of a circular arc;
- Be able to find the coordinates of the endpoint of
Page 365
All odd problems from 1 to 41.
the radius of the unit circle corresponding to any
multiple of 30º or 45º.
7
5.2
8
5.3
5.4
Radians
Page 378
- Understand radians as a unit of measurement for
1, 3, 5, 7, 9, 11, 13, 15, 17, 23, 25, 29, 31, 33, 45
angles;
- Be able to convert from radians to degrees;
- Be able to convert from degrees to radians;
- Be able to compute the length of a circular arc that
is described by radians.
Cosine and Sine
Page 391
- Understand the definitions of cosine and sine;
All odd from 1 to 23, 31, 37
- Be able to compute the cosine and sine of any
multiple of 30º or 45º (π/6 or π/4);
- Be able to determine whether the cosine (or sine)
of an angle is positive or negative from the location
of the corresponding radius;
- Understand why cos2ө + sin2ө = 1.
More Trigonometric Functions
- Understand the definition of the tangent of an
angle;
- Be able to compute the tangent of any multiple of
30º or 45º (π/6 or π/4);
- Be able to determine whether the tangent of an
angle is positive of negative from the location of
the corresponding radius;
- Be able to compute cos ө, sin ө, tan ө if given just
one of these quantities and the location of the
corresponding radius.
Trigonometry in Right Triangles
- Understand the right triangle characterization of
Page 402
All odd from 1 to 31, 37
Page 412
All odd from 1 to 27, all odd from 49 to 75
5.5
9
5.7
6.3
10
6.6
cosine, sine and tangent;
Be able to compute the cosine, sine and tangent of
any angle of a right triangle if given the lengths of
two sides or the triangle;
Be able to compute the lengths of all three sides of
a right triangle if given any angle in addition to the
right angle and the length of any side.
Inverse Trigonometric Functions
Page 439
- Understand the definition of cos-1 ө, sin-1 ө, and
1, 3, 5, 7, 9, 25
-1
tan ө;
- Understand the domain and range of cos-1 ө, sin-1 ө,
and tan-1 ө;
- Be able to use the inverse trigonometric functions
to find angles in a right triangle, given the lengths
of two sides.
Double-Angle and Half –Angle Formulas
Page 489
- Be able to use double-angle formulas for cosine,
All odd from 11 to 57
sine and tangent;
- Be able to use half-angle formulas for cosine, sine
and tangent.
Addition and Subtraction Formulas
Page 501
- Be able to use the addition and subtraction
All odd from 5 to 31, 37, 40
formulas for cosine, sine and tangent.
Polar Coordinates
- Understand polar coordinates
- Be able to convert from polar to rectangular
coordinates;
- Be able to convert from rectangular to polar
coordinates;
- Understand graphs in polar coordinates
Page 530
All odd from 1 to 19, 29, 30, 35
11
Review
Review
and
Final
Exam