Calculus
590 Assignments: Fall –Spring 2008-2009
Why would I post the midterm exam study
guide in August? Simply because as you progress through these next two academic
quarters, you will want to use this guide to organize your
studying.
(not all-inclusive)
A major fact: You will know all of these topics by January but only if YOU take personal responsibility
for your learning. Organize yourself and develop strong, steady study habits.
MIDTERM AND TEST TOPICS
Know what a derivative of a function means geometrically, analytically, verbally, graphically
Know the Product Rule, Chain Rule, Quotient rule, Power Rule for ALL functions including exponential and logarithmic functions and double angle trig functions.
Know how to find the equation of the tangent line to curves that are expressed as a quotient at a certain point.
Know the geometrical significance of a difference quotient of a function.
Given a particle moving along the x-axis at any time t, know how to find the acceleration of a particle at a particular time. Know that acceleration is the second derivative of the velocity function whaich is the first derivative of the position function. If you are not starting out with a position function, the velocity and acceleration functions are not known unless you employ integration(spring20090
Know how to find finite and infinite limits using rules regarding the numerator and denominator of rational functions.
Know L’Hopitals Rule
Know how to connect the graph of a function f with characteristics of the graph of the derivative of f.
Know how to find the second derivative of ln functions and use the Chain Rule and be sure you know the difference between the log derivative and the ln derivative.
Know how to implicitly differentiate
Know what characteristics of a graph of a function guarantee differentiability and continuity.
Know how to answer continuity and differentiable questions regarding piecewise functions.
Know how to take the derivative of the natural exponential function(y=e to the x power) along with the product rule applied to the product of an exponential and a ln or log function
Know the shortcut definition (theorem) of what makes a function continuous using a limit as x approaches a particular number.
Know how to use the quotient rule and how to find the derivatives of trig and inverse trig functions
Know how to find the 50th derivative of a function
Know what a horizontal asymptote means graphically and algebraically.
Given a derivative graph, be sure you can assume what the original graph looks like
Write the equation for normal lines.
Know that if you need the slope of a tangent line to a curve you need the derivative of the function at that point to find that.
Know that a derivative is a limit of the difference quotient.
Know that a difference quotient is the slope of a secant line.
What is the difference between the slope of a secant line and the slope of a tangent line?
Know what the slope of a secant line means analytically and graphically as well as conceptually and compare and contrast that knowledge with a derivative.
Know exactly what continuity of functions means
Find all critical numbers, extreme values, and increasing and decreasing functions. Be sure you know how to use derivatives to show that a fnc is increasing or decreasing.
Know how to apply calculus to quadratic functions particularly motion problems like arrows shot through the air and maximum heights.
TIP: GO THROUGH EACH TOPIC AND MATCH IT
WITH THE INFO IN YOUR BOOK AS WELL AS ALL YOUR CLASS NOTES AND ODD PROBLEMS IN
THE BACK OF EACH SECTION: PRACTICE PRACTICE PRACTICE AND USE YOUR ANSWER KEYS TO CHECK YOUR WORK.
Homework
assignments beginning First class in August,2008:
Note well:
These assignments are the BARE BONES of the course.
The letters RO means “Read and outline”. Outlining must be done thoughtfully and carefully otherwise you are wasting precious time.
The letters DP means, “Do
problems”. If for any reason class is cancelled,
(snow, ice, other issues) you must stay on schedule
and complete the homework for the assigned class day. Be sure your work is properly labeled for
full credit.
You are responsible for
organizing them according to class date and topic order.
The letters CN means “Class Notes”. You
are responsible for all class notes whether you are in class or you miss class
due to illness.
Criteria
for Class Notes: CN
You must learn how to take college class notes
as soon as possible. Everything discussed in class and everything written in
the blackboard must be documented under CN for the class. Every CN , DP and RO must be dated and documented with the topics
covered.
It is your responsibility to follow the class
lectures for
your CN grade and parallel them to the
Topic DP assignments below in a timely fashion. Most of your RO will be done
before class.
********** Throughout the
year and possibly daily, there will be additions
to these assignments either given in class or
posted on the web.
Check this
site daily.Also check your email. Usually when I
update I send an email to
everyone!!!
Be sure to label each assignment topic and date in the top right hand
corner of all three of your components(RO-CN-DP) and
the actual assignment written below.
Criteria
for reading and outlining assignments :_(RO)
__________
Only record facts and information
that you think are important. DO NOT
COPY THE BOOK WORD FOR
WORD.
Throughout the next two terms, expect to spend 1-2 hours PER class hour each
week. So on a three class week, 4.5 class hours will yield a 4.5-9 hour study
week!!
Criteria for
doing problems: (DP)______________________________
As soon as a topic is covered in class that parallels the section that correlates to the problems assigned in bare bones, you are responsible for doing those problems THAT NIGHT. The next class you will be accountable (either quizzed or homework collection or oral examination) for the work and the DP component will be graded.
Take advantage of your video skillbuilder CD which came with your book. Use it to test your understanding of what is being covered in class
*****As soon as a section is covered in class you are responsible
for completing the corresponding numbered assignment as DP and the
corresponding RO must be done also if not assigned prior to the class
presentation.
NEW RULE: I CAN NOT ACCEPT
ASSIGNMENTS PAST THEIR DUE DATE
Note well: If an assignment is classified as a Hand-in, it is due on my desk the next class for a HW or Quiz grade. I will underline those particular assignments which will be additional grading entities to the three grading components of RO-CN-DP. List date the topic was introduced in class to the left of each section
Bare Bones
Date Class Topic Assignment (RO-DP)
1.1 Functions and Models: Chapter I: RO p.10-20 ONLY write down the
Important definitions. Read and assimilate the rest.
1.1 Functions and Models: DP: On p.20, DP #1,2,5,7,19,23,27,33,34,37,40.
Style
Points count: Hand-In: p.23 #21,22,27,28,29
1.2 Functions and Models: RO p.24-34
1.2
Functions and Models: Pass in HW: Style Points count:DP p.34-36 #2,8,10 11,15
1.3 New Functions from Old Functions:RO p.38-42 study carefully. What does “compressing
horizontally” mean?
1.3 New Functions from Old
Functions: RO p.42
-45. Style Points Count: Hand In:DP p.46 #3,4 6
1.3
New Functions from Old Functions: Hand-In:DP 46-48
#35,47,50,53-56 all
Test #1 date:____________________________
Test Review
Problems: slope intercept form for lines, piecewise functions, domain and range of functions,finding the slope using two points, use linear regression steps to find equations from tabular data, test for even or odd functions,know how to compute the composition of two functions,all transformations,and composition of functions. Know how to graph any of the functions that are referred to as parent functions. Find the equation for a line given two points and graph.
2.1 Limits and derivatives Chapter 2. RO p.61-64
2.1 Limits and
derivatives Hand in:
DP p.65 1,3,5
2.2 Limits and
derivatives RO p.66-74
2.2 One –sided limits chapter 2.2 p.74 #1,4,6,7
2.2 Limit of a
function: DP p.106
#3,5,23 Hand In : p.106 #7
2.3: Limit Laws RO p.77-84
2.3: Limits: p.84-85 1-10 evens and #34 PASS IN Style Points Count. In your NB do p.85 11-30 odds for practice. Check your answers.
2.4: Precise definition of a Limit RO p.87-94. Pass in: p.95 #8,#11,#15-18 odds
2.5 Continuity
RO p.97-105 Quiz next class on RO so read carefully.
2.5 Continuity Hand In: SPC: p.105 #1, 3,4,10,13,21,27,49,61
ADD IN FOR ECE 4.4:
Limits at infinity p.230-240. In class quiz on RO so read carefully.
4.4 limits at
Infinity p.240 Hand in SPC: #1, #3. Practice:
p.241 #9-29 odds
3.1: Derivatives RO p.112-119 Quiz on RO so
read carefully.
3.1: Derivatives p.119 DP #1,#3,#5,#11,16,17,47,49
3.2: The Derivative as
a Function RO
p.123-131 In class quiz on RO next class
3.2: p.131 Hand In: p.131#1-9 odds and #12 and #13,#32.
Use analysis then verbally express your conclusions for #12-13,and #32
3.3 Differentiation Formulas RO p.135-144. Quiz in class
on RO so read carefully.
3.3 p.144-145 #1-20 evens
3.4: Derivatives of
Trig Functions RO p.148-154.In class quiz:
make sure you know the table on p.152 and how to compute higher derivatives.
3.5: The Chain Rule RO p.155-161.Quiz on RO. Read carefully
3.5: The Chain Rule DP 161-164 #1-28 odds,#47-50 all
3.6: Implicit Differentiation RO p.164-168. Quiz on RO.Make special note of class notes on the trick of knowing
how and when to implicitly differentiate.
3.6: Implicit
Differentiation RO
p.169#5-20 odds, #25-26
7.6Derivative of inverse trig fncs derived with Implicit Differentiation RO p.455-460.You
must know by heart the derivative of inverse sin and inverse tan.Do problem on p.461 #22-25
3.6: Implicit Differentiation:DP p.238 3-12 odds
3.7: Derivatives Of Log RO p.240-245. Be sure to
separate your notes into derivatives of log functions, log. Differentiation,
and the number e.
3.7: Derivatives Of Log DP p.245 2-8 odds
Rates of change in Natural
and Social Sciences
Exponential Growth and Decay
Related
Rates
Linear
Approximations and Differentials
Maximum
and Minimum Values
Mean
Value Theorem
How
derivatives affect the shape of a graph
L’Hopitals Rule
Summary of
curve sketching
Graphing
with Calculus and Calculators
Optimization Problems
Antiderivatives
4.1:Applications of
Differentiation RO
p.263-266.PASS IN QUIZ GRADE:DP p.266-267 #1,3,9 ,12 For #9 follow the
hints above the problem PASS IN AS QUIZ GRADE DUE_____________ Note well: the
distance from the base of the streetlight to the tip of the shadow is the
length used in the calculations to find
the rate at which the tip of the
shadow is moving.
4.2: Max and Min values and Critical
numbers RO p.269-
274. This is the
basis for optimization
problems.
4.2: Max and Min values DP p.274-275 # 1-15 first odds. Hand In: p.274 #24,26,32
4.3: Derivatives and Shapes of Curves RO p.278-286 . Take very careful notes.
4.3: Derivatives and Shapes of Curves DP p.286-287 #3,4,5,6,7,19,29 Hand In: p.287 #8,#30
4.6: Optimization Problems: RO p.306-311. Be sure you
understand what the first derivative says. Hand In
p.311 #5,#6
4.6: Optimization Problems DP p.311 3,9
STUDY FOR TEST Date______________________________
4.9: Anti-derivatives RO p.327-332.
4.9: Anti-derivatives p.332-333 # 1-10 odds .Hand –in:
p.332 1-10 evens
START SEMESTER TWO SPRING 2008______________________________
Course outline for Math 113Q:
Chapters 4-7 including the following topics for the final exam in May:
Optimization
Anti-derivatives
Sums and Sigma Notation
Area
The Definite Integral
Fundamental Theorem of Calculus
Integration by substitution
Numerical Integration
Area between
curves
Volume
Natural Logarithm
Inverse
functions
Exponential Functions
Growth and decay
Inverse
Trig Functions
Calculus of Inverse trig functions
Formula and
techniques
Integration by Parts
Trig techniques of Integration
Integration
of Rational Functions Using Partial Fractions
New rules starting January,2008
1) You are responsible for all class notes that are supplementary to what we are doing in class.(This material will not be in your book) Future tests and quizzes will include supplementary material so you are responsible for retrieving it from a classmate if you are absent from class due to trips or illness.
2) There will be more quizzes on your bare bones assignments and more collection of the DP so be prepared.
3) Be sure to have your calculator with you for every class.
4.1:Applications of
Differentiation RO
p.263-266.PASS IN QUIZ GRADE:DP p.266-267 #1,3,9 ,12 For #9 follow the
hints above the problem PASS IN AS QUIZ GRADE DUE_____________ Note well: the
distance from the base of the streetlight to the tip of the shadow is the
length used in the calculations to find
the rate at which the tip of the
shadow is moving.
4.2: Max and Min values and Critical
numbers RO p.269-
274. This is the
basis for optimization
problems.
4.2: Max and Min values DP p.274-275 # 1-15 first odds. Hand In: p.274 #24,26,32
4.3: Derivatives and Shapes of Curves RO p.278-286 . Take very careful notes.
4.3: Derivatives and Shapes of Curves DP p.286-287 #3,4,5,6,7,19,29 Hand In: p.287 #8,#30
4.6: Optimization Problems: RO p.306-311. Be sure you
understand what the first derivative says. Hand In
p.311 #5,#6
4.6: Optimization Problems DP p.311 3,9
STUDY FOR TEST
Date______________________________
4.9: Anti-derivatives RO p.327-332.
4.9: Anti-derivatives p.332-333 # 1-10 odds .Hand –in:
p.332 1-10 evens
5.1 Integrals
RO p. 343-350
For PASS-IN Quiz grade DUE
___________________In Chapter 5.1: DP p.352-353 #1 and #2 BECAUSE one problem is an increasing function
another is a decreasing function.
5.2: Integrals RO p.354-360.
5.2: Integrals RO p.360-364
Due :____________
Pass-in HW CHAPTER 5.2: DP p. 364-365 #3,5,9,17,31
5.3: Evaluating
Definite Integrals RO
p.366-373
Hand In Hw ASSIGNMENT
DUE__________ 5.4: DP p.374
3,6,11,19,23,25,27,29
5.4: Fundamental
Theorem of Calculus
DP p375 47-54 all
5.4: Fundamental
Theorem of Calculus
RO p.377-383. Know everything about the Fundamental Theorem of Calc : Call the theorem NOT part one Part two but rather Accumulation
Theorem of FTC and Evaluation Theorem of FTC.
5.4: Fundamental
Theorem of Calculus Pass
in HW due___________ DP p.383 # 5,6,7,9
5.5: Substitution Rule RO p.386-392
5.5.Pass In Quiz GradeDue____________ DP p.392 #2,4,6,7,9,17,22,25
5.6: Integration by
Parts RO p.393-397
up to ex 6.
5.6: Integration by
Parts DP p.398 #1,2,8,9,18
In class Chapter 5 review for Test Date_____________
6.1:Area between Curves RO p.441-445.DP p.446 #1-7 odds Hand In : p.446 #2,#4
6.4: Average Value for a Function.RO p. 467-469. DP p.469 1-12 odds Hand In p.469 #6
7:3 Differential Equations RO p.513-516 DP
p.519 1-6 odds Hand In p.519,#14
Test for
Quarter 4 Date:_______________________________________
Selected Topics: Slope Fields and Models of Exponential growth--------------------
Seniors: God bless you !
Juniors: You are still with me till June!!!!