Calculus and Applications
Syllabus
2013-2014
Mr. Schmid
E-mail: schmid@arrowheadschools.org
Phone: (262) 369-3611 ext 3143
Course Description
This course is intended for students who have a thorough knowledge of algebra, geometry,
trigonometry and analytic geometry. Students successfully completing Trigonometry and Precalculus
should take this course. This is designated as a college-level course in one variable calculus and will be
treated as such. We will cover all of the material needed to cover most of the AB Advanced Placement
Calculus material and will the foundation for BC Calculus and the BC Calculus Test next year.
Materials
Notebook
Loose leaf paper for problem sets.
Three Ring Binder
Pencils (Many of them)
Graphing Calculator - TI-89 or TI-nspire CAS
For the TI-89 4 Extra AAA Batteries for the Graphing Calculator (In case your batteries die)
What I Expect From You
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Be prompt to class. You should be in your seat when the bell rings.
Expect a weekly quiz, a test every 3-4 weeks, an A.P. Problem Set several times a semester.
Your assignments should be done every day and placed in your notebook. Plan on spending 3045 minutes DAILY on your assignment. Assignments will be collected on Mondays.
Honest effort at all times. If you do not understand material or are having problems make
arrangement to get extra help. I will make positive contributions in group activities and do all
that I can to work cooperatively with those around me.
Once class starts you will be focused on mathematics and the lesson at hand. It is not an hour to
catch up on homework.
In case of an absence you are responsible to get the make-up work from me.
You are in class and prepared every day. Don’t ask to be excused for giving blood, hanging
homecoming decorations, etc. Have your calculator charged and homework done.
Take care of your needs like sharpening pencils, going to the bathroom, discarding paper, etc.
before class starts. Don’t ask for locker or bathroom passes. I want 60 minutes of
uninterrupted concentration on mathematics.
Show classmates and teachers with the utmost respect. Be courteous. Everyone’s opinion
matters.
You will be asked to think and explain concepts and problems. You will be asked to explain the
“whys” instead of just giving the correct answer. Problems will be difficult and you will be ask to
persevere and work through them. This will make you uncomfortable and you will get over it.
What You Can Expect From Me
1.
2.
3.
4.
I will do all that I can to help you learn calculus. I will be available for help before school and
during free periods.
I will be prepared for class each day.
Each week you will receive a quiz, homework collected on Mondays, a test each 2-3 weeks, and
an exam each semester.
I will treat all students with respect and will do what I can to help all students feel comfortable
in my classroom.
Grading Scale
100-90%
89.99-80%
79.99-70%
69.99-60%
59.99 and below
A
B
C
D
F
18 Week Grade
45%
35%
10%
10%
Tests
Quizzes
Homework
Lab and Projects
Semester Grade
18-Week Grade
Final Exam
80%
20%
Other Policies
Dropped Quizzes –The lowest 25% of your quizzes will be dropped.
Cell Phone – Cell phones should not be seen or heard in my classroom. They will be confiscated
and given a vacation if found in the classroom when they are not suppose to be out.
KEEP THEM PUT AWAY AND USE AIRPLANE MODE!!!
Cheating/Academic Misconduct – Academic integrity is an expectation. In other words copying
or using another person’s work and claiming it as your own. This includes copying
homework and sharing answers to quizzes and tests to other students.
Tardy – BE ON TIME 1-3 offense is a warning, 4th and beyond are referrals to the office for
detention and a call home.
Mr. Schmid’s Schedule
Before
1st
2nd
3rd
4th
5th
6th
7th
8th
9th
10th
Prep
Prep
Calculus and Applications
Functions, Statistics and Trigonometry
Prep
Functions, Statistics and Trigonometry
Lunch
Functions, Statistics and Trigonometry
Prep
AP Statistics
Calculus and Applications
Most of all, I am here to help you learn. If you are having difficulties or have any issues you would like to
talk about please contact me or come to see me. I am here for you.
“This classroom welcomes all, embraces each, supports everyone and hopes that you find
yourself better for being here.”
Topics in Calculus and Applications and the AP Standards
Unit 1 Functions and Models
1.1
Function Basics
1.2
Families of Functions
1.3
Manipulating Functions
1.4
Graphing Functions and Technology
1.5
Exponential Functions
1.6
Inverse Functions and Logarithms
Chapter 2 Limits and Derivatives
2.1
The Tangent and Velocity Problems
2.2
The Limit of a Function
2.3
Calculating Limits Using Algelbra
2.4
The Precise Definition of a Limit
ε-δ definition of a limit, One-Sided Limits
2.5
Continuity
2.6
Limits at Infinity; Horizontal Asymptotes
2.7
Derivatives and Rates of Change
2.8
The Derivative as a Function
Chapter 3 Differentiation Rules
3.1
Derivatives of Polynomial and Exponential Functions
3.2
The Product and Quotient Rules
3.3
Derivatives of Trigonometric Functions
3.4
The Chain Rule
3.5
Implicit Differentiation
3.6
Derivatives of Logarithmic Functions
3.7
Rates of Change in the Natural and Social Sciences
3.8
Exponential Growth and Decay
3.9
Related Rates
3.10 Linear Approximations and Differentials
3.11 Hyperbolic Functions
Chapter 4 Applications of Differentiation
4.1
Maximum and Minimum Values
4.2
The Mean Value Theorem
4.3
How Derivatives Affect the Shape of a Graph
4.4
Intermediate Forms and L’Hospital’s Rule
4.5
Summary of Curve Sketching
4.6
Graphing with Calculus and Calculators
4.7
Optimization Problems
4.8
Newton’s Method
4.9
Antiderivatives
Chapter 5 Integrals
5.1
Areas and Distances
5.2
The Definite Integral
5.3
The Fundamental Theorem of Calculus
5.4
Indefinite Integrals and the Net Change Theorem
5.5
The Substitution Rule
Item I.1
Item I.1
Item I.3c
Item I.3c
Item I.2a
Item I.2c, 1.3a,b
Item I.2b
Item I.4a,b,c
Item I.3a,b
Item II.1, II.2
Item II.1, II.3a, II.4a, II.5f
Item II.2b, II.6a,b
Item II.6b
Item II.6a
Item II.6c
Item II.6c
Item II.5e, II.6a
Item II.2c, II.3d, II.5f
Item II.3d, II.5d
Item II.2b
Item I.4c, II.5c
Item II.3c
Item II.3b, II.4b,c, II.5a,c
Item II.5i
Item I.1
Item II.5c
Item II.4a, II.5g, III.4a, III.5a
Item III.1a, III.2
Item III.1a,b,d, III.6
Item III.1c, III.2, III.3a,b
Item III.4a, III.5a
Item III.4b
Chapter 6 Applications of Integration
6.1
Areas between Curves
6.2
Volumes
6.3
Volumes by Cylindrical Shells
6.4
Work
6.5
Average Value of a Function
Item III.2
Item III.2
Item III.2
The AP Calculus Standards and the Class
I. Functions, Graphs, and Limits
1. Analysis of graphs
2. Limits of functions (including one-sided limits)
a.
An intuitive understanding of the limiting process
b.
Calculating limits using algebra
c.
Estimating limits from graphs or tables of data
3. Asymptotic and unbounded behavior
a.
Understanding asymptotes in terms of graphical behavior
b.
Describing asymptotic behavior in terms of limits involving
infinity
c.
Comparing relative magnitudes of functions and their rates of
change (e.g., contrasting exponential growth, polynomial
growth, and logarithmic growth)
4. Continuity as a property of functions
a.
An intuitive understanding of continuity (Close values of the
domain lead to close values of the range.)
b.
Understanding continuity in terms of limits
c.
Geometric understanding of graphs of continuous functions
(intermediate value theorem and extreme value theorem)
II. Derivatives
1. Concepts of the derivative
a.
Derivative presented graphically, numerically and analytically
b.
Derivative interpreted as an instantaneous rate of change
c.
Derivative defined as the limit of the difference quotient
d.
Relationship between differentiability and continuity
2. Derivative at a point
a.
Slope of a curve at a point. Examples are emphasized,
including points at which there are vertical tangents and
points at which there are no tangents.
b.
Tangent line to a curve at a point and local linear
approximation
c.
Instantaneous rate of change as the limit of average
rate of change
d.
Approximate rate of change from graphs and tables of values
3. Derivative as a function
a.
Corresponding characteristics of graphs of f and f 
b.
Relationship between the increasing and decreasing behavior
of f and the sign of f  .
c.
The mean value theorem and its geometric consequences
d.
Equations involving derivatives. Verbal
descriptions are translated into equations involving derivatives
and vice versa.
Throughout
Section 2.1
Section 2.3
Section 2.2
Section 2.2, 2.6
Section 2.2, 2.6
Section 1.5, 1.6
Section 2.5
Section 2.5
Section 2.5, 4.1
Section 2.7, 2.8, 2.9
Section 2.7
Section 2.7, 2.8
Section 2.8
Section 2.7, 2.8
Section 2.7. 3.1
Section 2.7, 3.7
Section 2.7
Section 2.8
Sections 4.3
Section 4.2
Sections 3.7, 3.9, 9.1
4. Second derivatives
a.
Corresponding characteristics of the graphs of f , f  , and f  . Section 2.8, 4.9
b.
Relationship between the concavity of f and the sign of f  Section 4.3
c.
Points of inflection as places where concavity changes
Section 4.3
5. Application of derivatives
a.
Analysis of curves, including the notion of monotonicity
and concavity
b.
Optimization, both absolute (global) and relative (local)
extrema
c.
Modeling rates of change, including related rates problems
d.
Use of implicit differentiation to find the derivative of
an inverse function
e.
Interpretation of the derivative as a rate of change in varied
applied contexts, including velocity, speed, and acceleration
f.
Geometric interpretation of differential equations via slope
fields and the relationship between slope fields and solution
curves for differential equations
g.
Numerical solution of differential equations using Euler’s
method
h.
L ‘Hospital’s Rule, including its use in determining limits and
convergence of improper integrals and series
6. Computation of derivatives
a.
Knowledge of derivatives of basic functions including power,
exponential, logarithmic, trigonometric, and inverse
trigonometric functions
b.
Basic rules for the derivatives of sums, products, and
quotients of functions
c.
Chain rule and implicit differentiation
d.
Derivatives of parametric, polar, and vector functions
III. Integrals
1. Interpretation and properties of definite integrals
a.
Computation of Riemann sums using left, right, and midpoint
evaluation points
b.
Definite Integral as a limit of Riemann sums over equal
subdivisions
c.
Definite integral as a limit of the rate of change of a quantity
over an interval interpreted as the change of the quantity
over the interval:

d.
Section 4.3
Section 4.1, 4.3, 4.7
Section 3.9
Sections 3.5, 3.6
Sections 3.3, 4.7
Sections 4.9, 9.2
Section 9.2
Section 4.4
Sections 3.1, 3.3, 3.6
Sections 3.1, 3.2
Sections 3.4, 3.5
Sections 10.2, 10.4,
13.1, 13.2
Section 5.1, 5.2
Section 5.2
Section 5.3
b
f   x  dx  f  b   f  a 
a
Basic properties of definite integrals
(e.g., additivity and linearity)
Section 5.2
2. Applications of integrals. Appropriate integrals are used in a variety of
Sections 5.1, 5.3, 6.1,
applications to model physical, social, or economic situations. Although
6.2, 6.5, 8.1, 10.2, 10.4
only a sampling of applications can be included in any specific course,
students should be able to adapt their knowledge and techniques to solve
other similar application problems. Whatever applications are chosen, the
emphasis is on using the integral of a rate of change to give accumulated
change or using the method of setting up an approximating Riemann sum
and representing its limit as a definite integral. To provide a common
foundation, specific applications should include finding area of a region, the
volume of a solid with known cross sections, the average value of a function,
the distance traveled by a particle along a line, and the length of a curve.
3. Fundamental theorem of calculus
a.
Use of the fundamental theorem to evaluate definite integrals Section 5.3
b.
Use of the fundamental theorem to represent a particular
Section 5.3
antiderivative, and the analytical and graphical analysis of
functions so defined
4. Techniques of antidifferentation
a.
Antiderivatives following directly from derivatives of
basic functions
b.
Antiderivatives by substitution of variables (including change
of limits for definite integrals)
Section 4.9, 5.45-3
Section 5.5
5. Applications of antidifferentation
a.
Finding specific antiderivatives using initial conditions,
Sections 4.9, 5.4
including applications to motion along a line
b.
Solving separable differential equations and using them in
Sections 9.1, 9.3, 9.4
modeling (in particular, studying the equation y   ky and
exponential growth)
c.
Solving logistic differential equations and use them in modeling Sections 3.8, 9.1
6. Numerical approximations to definite integrals. Use of Riemann sums and Sections 5.2
trapezoidal sums to approximate definite integrals of functions represented
algebraically, graphically, and by tables of values.
-----------------------------------------------------------------------------------------------------------------------------------------Please Sign below confirming that you have read and agree to the conditions of the class stated above,
and cut off this portion and turn it into Mr. Schmid on the second day of class.
Parent Signature:
_________________________________________
Student Signature:
_________________________________________
Student Name (Print): _________________________________________
My goal for math class this semester is …
_____________________________________________________________________________________
_____________________________________________________________________________________
One thing I like about one of my previous math classes is..
_____________________________________________________________________________________
_____________________________________________________________________________________
-----------------------------------------------------------------------------------------------------------------------------------------Please Sign below confirming that you have read and agree to the conditions of the class stated above,
and cut off this portion and turn it into Mr. Schmid on the second day of class.
Parent Signature:
_________________________________________
Student Signature:
_________________________________________
Student Name (Print): _________________________________________
My goal for math class this semester is …
_____________________________________________________________________________________
_____________________________________________________________________________________
One thing I like about one of my previous math classes is..
_____________________________________________________________________________________
_____________________________________________________________________________________