MTH 125 COURSE
OUTLINE
Fall 2007
INSTRUCTOR: K.W.NICHOLSON email: nnicholson@cacc.cc.al.us
OFFICE HOURS: POSTED ON DOOR OF RM 224 Ph
256-215-4336 or 4343
(and
Physics Lab)BS 214 webpage
located at: http://caccphysics.cacc.cc.al.us
TEXT: Larson, Hostetler & Edwards's "Essential
Calculus"
TOPICS COVERED:
Functions, derivatives, curve sketching, max & min word problems,
integration of polynomial, trig
and exponential
functions. (Essentially, Chapters
1 through 5)
PURPOSE OF THIS COURSE:
Til
now most of your math has dealt with static situations and functions. Calculus introduces the math of dynamic
situations. This course will develop the symbols and language of math that will
enable you to solve some really interesting problems. Your objective should be to become familiar
enough with differentiation and integration that it becomes part of your
vocabulary and your thinking.
EVALUATION:
|
Item |
Date |
Discussion |
|
4-100 point tests |
Sept. 6, Oct 4, Oct. 25, Nov. 29 |
No make up tests will be given. A missed test will be replaced by 1/2
of your final exam score. |
|
1-200 point Final Exam |
Dec 11, 10:30 - 12:30 |
Final will be comprehensive. |
|
Online Quizzes |
Weekly |
Can replace up to two test scores |
|
DDFD's -100 pts total |
daily |
These will be straight forward drill on
diff & integ formulas |
The above total, excluding bonus points,
is 700, (plus a few points, depending on miscellaneous assignments), and your
accumulative total will be divided by that amount to calculate your final
average.
90 - 100 = A, 80 - 89 = B, 70 - 79 = C, 60 - 69 = D, 0 - 59 = F
NOTES:
l.
Final percentage will be rounded UP, i.e., a final percent of
79.00000001 will be rounded up to 80.
2.
You should keep all returned papers. You should also keep track of the ratio (your accumulative
total)/(The accumulative total possible to date) as the quarter
progresses. If this average
is not above 70 by midterm, you should consider dropping the course to avoid a
bad grade.
3.
If you stop attending this class without obtaining a drop slip from
student services the registrar will give you a grade of F in this course.
4.
Words of wisdom regarding Math homework.
I hear........ and I forget,
I see..........and I remember,
I
do...........and I understand.
1. Review some basic essentials
in Algebra.
(a + b)n is never equal to an + bn
for any n, so (a + b)2 = a2
+ 2ab + b2, not a2 + b2.
And since n_a = (a)1/n,
= (a + b)1/n, so
= (a + b)1/2 is never a1/2 + b1/2 .
Never cancel the same thing from top and bottom of a
fraction. Instead you divide numerator and denominator by the same factor, thereby reducing that factor to 1 on
both top and bottom.
|
Rules for exponents. anam = am+n,
so 3234 = 36, not 96. (ab)n = anbn
so (x3y4)2 = x6y8, but
what is (x3 + y4)2 ?
1 a-n = an |
Special products x2 - y2 =
(x-y)(x+y) x3 + y3 = (x+y)(x2-xy+y2) x3 - y3 = (x-y)(x2+xy+y2) x2 + 2ax + a2 =
(x+a)2 |
Analytical geometry
Points in the xy plane, distance and
midpoint formulas.
A line and its essential components.
Slopes of parallel and perpendicular
lines.
A circle and its essential components.
Course Overview.
1.
Discuss the definition of functions and limits.
2.
Discuss the true meaning of a derivative, to get an idea of its
usefulness, and learn the differentiation formulas that make differentiation a
powerful, easy to use tool that permeates all of science, and increasingly,
business as well.
3. Practice using derivatives to graph
functions, and solve applied problems.
4.
Learn what an integral is, what it means, and what exactly was "the
discovery of the Calculus", that made Newton and Leibniz so famous.
Notation & Vocabulary by section
1.2 Functions & Polynomials
Function notation
Domain & Range
vertical line test
increasing & decreasing fcts.
degree of polynomials
quadratic functions
transformations Pg 17
composition of functions
RBD
or "No. 1 Pet Peeve"
A trig function without an argument has no meaning!
1.3 Inverses of Functions
Descrete Sets of Points
Graphically
Algebraically
1-1 functions (means no x2 in
the expression)
Notation f-1(x) RBD -Know what it is NOT!
Notation sin-1 x = ?
Know what it is NOT!
1.4 Log & Exponential Functions
Graph y = ax and give domain
& range
e = ?
Graph y = loga x and give
domain & range
Evaluate log expressions
Know loga au = u
Expand & contract expressions using
laws of logs
RBD eln x = x
ln ex = x
ln e = 1
ln 1 = 0
1.5 Limits concept
Definition: 
if and only if left and right limits = L
1.6 Limit Laws
Plus the one I couldnŐt find in the
book. 
functions
Direct Substitution Property (also
couldnŐt find) Says all
polynomials, rational functions, & trig functions have limits everywhere
they exist.
RBD -It is ok to "alter" the
expression using algebra in order to try to find a limit.
Also note worthy - Squeeze thm.
1.7 Define Continuity
1.8 Infinite Limits
Infinite Limits - VA's
3.5 Limits at infinity - HA's
2.1 Derivatives defined
pt - slope form of linear equation
Define- tangent line
Define - slope of a
curve at a point
Definition of a derivative
Conceptually
Graphically
Algebraically
2.2 Differentiable Functions
Know where functions NOT differentiable Pg
89
2.3 - 2.6 Differentiation Formulas
Implicit Differentiation
f"(x) & f"'(x)
f(4)(x)
2.7 Steps to solve Related Rates Problems Pg 129
3.1 Max & Min problems
3.2 MVT & RolleŐs Thm (Skip)
3.3 Increasing & Decreasing
functions
3.4 Concavity problems
3.6 Optimization Problems
Steps to solving Optimization
Problems (Applied Max & Min
Problems)
3.7 Differentials
4.1 Define Antiderivatives
4.2 skip
4.3 Definition of definite integrals
4.4 FTC
MVT for Integration 
4.5 Integration by substitution (or
change of variable)
4.7 Integration of du/u
4.8 Integration involving inverse trig
functions
THE BIG PICTURE
Class time: Tuesday & Thursday 10:50 - 12:35
Assignment Notation:
B - Means 5 pt Bonus problems due at
beginning of next class period.
DAILY SCHEDULE
|
Date |
Topic |
Stewart Homework assignment |
|
Th 8-16 |
Sections 1.2 Background info |
1-16, 33-47, make up piecewise probs |
|
T 8-21 |
1.3 Inverses of functions descrete, graphical, algebraically |
9-15, 21-31,83-90, 105-110, 117-123 |
|
Th 8 -23 |
1.4 Exponential & logarithmic
functions |
1-9, 43-67 |
|
T 8-28 |
1.5 Limit Concepts |
1.5 1-18, 21,23 |
|
Th 8 - 30 |
1.6 Laws of Limits 1.8 Infinite Limits - Vertical Asymptotes |
1.6 3-35 1.8 3-20, 25-29 |
|
T 9-4 |
3.5 Limits at Infinity - Horizontal
Asymptotes 2.1 Drill on equations of lines |
3.5 11-35, 57-69 -- |
|
Th 9-6 |
Test 1 Derivatives, definitions of derivatives |
Sect. 2.1 1,5,7,9,19-23, 59-61,71 |
|
T 9-11 |
2.2 Differentiable Functions & Not Differentiable |
Sect. 2.2 1-54, 79,81,85,87,89,91B93B |
|
Th 9-13 |
2.3 Differentiation Formulas I Product Rule & Quotient Rule |
Sect. 2.3 1-33,49,51,52,57B, 69-78,89B, 95, 97 |
|
T 9-18 |
2.4 Chain Rule: |
Sect. 2.4 1-24,33-98 |
|
Th 9-20 |
2.5 Implicit Differentiation |
Sect. 2.5 1-20,25-45,51-55,63-75 |
|
T 9-25 |
2.6 Inverse Trig Functions |
Sect. 2.6 11-31,39B |
|
Th 9-27 |
|
|
|
T 10-2 |
2.7 Related Rates |
Sect. 2.7: 1-8,13,15,16,19,23 |
|
Th 10-4 |
Test 2 2.7 Continued |
|
|
T 10-9 |
3.1 Max & Min, (extrema) |
1-29 |
|
Th 10-11 |
3.3 Increasing & Decreasing
functions |
1-16, 63, 65,67,69 |
|
T 10-16 |
3.4 Concavity |
1,3,5,9,11,13,19,31,35 |
|
Th 10-18 |
3.6 Optimazation Problems |
3-11, 19,21,24B,39,44 |
|
T 10-23 |
3.7 Differentials |
Sect. 3.7 5-13 |
|
Th 10-25 |
Test 3 4.1 Antiderivatives defined |
4.1 3-27, 41,43,45,47 |
|
T 10-30 |
4.3 Definition of definite integrals |
3-7,15-19,21-25,31,33,37 |
|
Th 11-1 |
4.4 FTC |
5-13, 19-25,31-35,43,45,73,75,81B |
|
T 11-6 |
4.5 Integration by Substitution |
7-21,33-58, 69-75, 89-91 |
|
Th 11-8 |
4.7 Integration of du/u |
1-25 |
|
T 11-13 |
|
|
|
Th 11-15 |
4.8 Integration involving inverse trig
functions |
4.8 1-33 |
|
11-19 to 11-23 |
No Class Happy Thanksgiving |
|
|
T 11-27 |
|
|
|
Th 11-29 |
Test 4 |
|
|
T 12-4 |
|
|
|
Th 12-6 |
Last Day of Class Review for Final |
|
|
T 12-11 |
Final Exam 10:30-12:30 |
|