Course Syllabus
Course Description:
This course explores the basic concepts of analytic geometry, limits (including indeterminate forms), derivatives, and integrals.
The topics covered will include graphs, derivatives, and integrals of algebraic, trigonometric, exponential, logarithmic, and hyperbolic functions.
Applications will be covered, including those involving rectilinear motion, differentials, related rates, graphing, and optimization.
Office
Hours
Before school, lunch, after
school
OpenText Calculus 1: Rice University
Materials to Bring to Class:
Paper, pencil, graphing calculator—there are some graphing calculators available to be checked
out from the school (they require AAA batteries).
Proper Heading for Papers:
Name, date, assignment, period in upper RIGHT hand corner of all papers turned in. The
majority of the homework will be done on-line and there will be posted due dates with potential
penalties for late work. Majority of work will be turned in through Canvas as a pdf.
Course Syllabus:
Grading:
Grading will follow the policy adopted by Petersburg High School. As per board policy,
semester grades are calculated based on the cumulative average of the two quarters.
A = Outstanding. 4.0
A-= 3.7
B+ = 3.4
B= Above Avg 3.0
B- = 2.7
C+ = 2.4
C = Average 2.0
C- = 1.7
D+ = 1.4
D = Below Avg 1.0
D- = 0.7
F = Failing 0.0
“INC” = Incomplete
Listed below is the school adopted percentages for grades. What you see, for example, is
that for an “A” you must have 93 or above, for an A- you would need a 90 up to but not
including a 93, etc.
A 93
A- 90
B+ 87
B 83
B- 80
C+ 77
C 73
C- 70
D+ 67
D 63
D- 60
F 0
The following weights shall be used to earn a grade:
Tests/Quizzes: 75%
Homework/Assignments/Projects: 25%
Extra Credit: Assigned from time to time but not to replace missed work but to
supplement those working hard who are willing to do a bit more.
No late work without proper excuse. In a regular situation a student has 2 days to make up work
for each excused day from school. Communication is key with this.
Tests missed with no excuse cannot be made up. Other tests, not quizzes, can be retaken if the
student scores lower than 80%, AND they make corrections to their test and come in during
office hours to go over the concepts. I recommend this being done within the first few days to a
week so the material stays fresh. The score entered in the book will be the best of the two scores
on the tests, so make sure you prepare as well as possible. You will have two weeks after getting
the test back to take the re-take assessment. Quizzes may not be retaken but one quiz per unit can
be replaced with a test score if the student chooses and comes in and informs the instructor and
clearly states which one to change.
Resources/Extra Help:
I will make every effort to respond to e-mail or phone messages within one school day. I will do
my best to make students aware of my daily schedule and to provide extra assistance when
needed (see office hours above). Students and parents are encouraged to make appointments
ahead of time. There seems to be an excellent resource at http://www.khanacademy.org/ as well.
This a lecture format for a number of different topics and students can investigate the Algebra 2
or Trigonometry sections for early topics.
Behavioral Expectations:
One rule—respect your classmates and instructor. I believe students understand what proper
behavior in a classroom should be and I will require that and help them with their decisions.
Please note: Students are expected to adhere to PHS policies, as outlined in the Student
Handbook, at all times. Classroom policies may include more specific requirements, but they
cannot be relaxed beyond the minimums as set forth in the Student Handbook.
Consequences of Misbehavior:
1. Talk to student about behavior
2. Talk to parent about behavior
3. Refer student to administration (I have very rarely ever had to do this)
Please note: Any action that endangers others, seriously interferes with the learning process, or is
significantly disrespectful to staff or students may result in immediate removal from the
classroom and/or direct referral to an administrator, thus by-passing above consequences.
ACADEMIC DISHONESTY—
Cheating does not allow for any type of true analysis and is not tolerated. Cheating is defined as,
but not limited to:
1. Procuring, possessing, using, or distributing test, quizzes, answer keys, teacher manuals or
teacher textbooks and the like;
2. Any attempt to tamper with or alter a teacher's record or grades;
3. Representing the work of others as one’s own work; including materials from the Internet.
4. Making use of notes, homework assignments, information slips (“crib sheets”) except for
those notes a teacher specifically authorizes for student use during a particular test or quiz, and;
6. Plagiarism
The academic penalty for all parties involved in cheating is a zero or failing grade for any copied
or plagiarized assignment, exam, or quiz. Students will not be allowed to make-up the work.
Also, the disciplinary penalty for cheating may include an office referral for disciplinary action.
Possession and/or unauthorized distribution of materials or altering a teacher's records call for
severe disciplinary consequences. Repeat offenses could result in loss of credit for an entire
course.
Electronic Devices:
Cell phones and other electronic devices are to be turned off and out of sight during class unless
the teacher has given specific permission for their use. If an item is confiscated for violation of
class rules, it may be retrieved from the teacher on the first offense. For subsequent offenses, the
item will be turned over to your administrator for retrieval.
Please keep the information above. Return the signature form below.
I have read and understand the Academic/Discipline Plan for the class of Thompson Alg2.
Student Name: _____________________________ Period: ____________________
Student Signature: __________________________ Date: _____________________
Student Email: ____________________________
Parent Name: _____________________________
Parent Signature: __________________________ Date: _____________________
Parent Email: _____________________________
Student Learning Outcomes:
Upon successful completion of the course, students will be able to:
- compute limits of algebraic, exponential, logarithmic, and trigonometric functions.
- calculate derivatives of algebraic, exponential, logarithmic, and trigonometric functions.
- evaluate integrals of algebraic, exponential, logarithmic, and trigonometric functions.
- apply derivatives and integrals to solve physics, economic, geometric, and/or other problems.
- prove basic theorems related to limits, continuity, and differentiability.
Course Content:
- Real numbers, coordinate systems in two dimensions, lines, functions
- Introduction to limits, definition of limits, theorems on limits, one-sided limits, computation of limits using numerical, graphical, and algebraic approaches, delta-epsilon proofs; continuity and differentiability of functions, determining if a function is continuous at a real number; limits at infinity, asymptotes; introduction to derivatives and the limit definition of the derivative at a real number and as a function
- Use of differentiation theorems, derivatives of algebraic, trigonometric, inverse trigonometric, exponential, logarithmic, and hyperbolic functions, the chain rule, implicit differentiation, differentiation of inverse functions, higher order derivatives, use derivatives for applications including equation of tangent lines and related rates, and differentials
- Local and absolute extrema of functions; Rolle's theorem and the Mean Value Theorem; the first derivative test, the second derivative test, concavity; graphing functions using first and second derivatives, concavity, and asymptotes; applications of extrema including optimization, antiderivatives, indeterminate forms, and L'Hopital's rule
- Sigma notation, area, evaluating the definite integral as a limit, properties of the integral, the Fundamental Theorem of Calculus including computing integrals, and integration by substitution
-
Textbook: RICE UNIVERSITY Open Text Calculus 1
This is the first year that the course has been taught as AP and it is a requirement for all students to take the AB test in the spring.
We will cover all the topics of the from the prescribed “Topic Outline for Calculus AB,” pages 6-9, taken from the College Board’s “Calculus—Course Description—Effective Fall 2012.” Given time after the AP Test we will also cover integration by parts, shell method, and other topics students may find interesting and useful in their next math course.
Section
Topcs
Timeline
Chapter 1
Limits and Continuity
16 Days
1.1
Limits: Intuitive Approach
2
1.2
Computing Limits
2
1.3
Limits at Infinity—End Behavior
2
1.5
Continuity
3
1.6
Continuity—Trig, Exponential, Inverses
Mean Value Theorem
3
Chapter 2
The Derivative
16
2.1
Tangent Lines and Rate of Change
4
2.2
The Derivative Function
4
2.3
Introduction to Techniques of Differentiation
2
2.4
The Product and Quotient Rules
2
2.5
Derivatives of Trig Functions
2
2.6
The Chain Rule
3
Chapter 3
Topics in Differentiation
16
3.1
Implicit Differentiation
3
3.2
Derivatives of Logarithmic Functions
2
3.3
Derivatives of Exponential and Inverse Trig Functions
2
3.4
Related Rates
5
3.5
Local Linear Approximations: Differentials
2
3.6
L’Hopital’s Rule
2
Chapter 4
The Derivative in Graphing and Applications
20
4.1
Analysis of Functions I: Increase, Decrease, Concavity
2
4.2
Analysis of Functions II: Relative Extrema, Graphing Polynomials
4
4.3
Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents
2
4.4
Absolute Max and Min
2
4.5
Applied Max and Min Problems
3
4.6
Rectilinear Motion
3
4.7
Newton’s Method
2
4.8
Rolle’s Theorem: Mean Value
2
Chapter 5
Integration
26
5.1
The Area Problem
2
5.2
The Indefinite Integral
2
5.3
Integration by Substitution
3
5.4
Sigma Notation: Area as a Limit
2
5.5
The Definite Integral
1
5.6
Fundamental Theorem of Calculus
3
5.7
Rectilinear Motion and Average Value
3
5.8
Average Value of a Function and its Alpplications
2
5.9
Evaluating Definite Integrals by Substitution
3
5.10
Logarithmic and Other Functions Defined by Integrals
3
Chapter 6
Applications of the Definite Integral in Geometry
10
6.1
Area Between Two Curves
2
6.2
Volumes by Slicing: Disks and Washers
5
Average Value of a Function and Applications
1
Chapter 7
Principles of Integral Evaluation
1
7.7
Numerical Integration
1
Chapter 8
Math Modeling with Differential Equations
7
8.1
Modeling with Differential Equations
2
8.3
Slope Fields; Euler’s Method
1
8.4
First Order Differential Equations and Appications
1
AP Exam
Review
Technology: The students will be using the software program Geogebra, MacIntosh Grapher and Texas Instruments TI-84’s for graphing and analyzing functions from the very beginning of limits, through the applications, and for definite integration.
There will be portions of assessments where calculators are used and portions where they are not used. Because the TI type calculator can be used on portions of the AP exam it is important that all student become comfortable entering data gathered from simple experiments and be able to analyze or read the analysis generated. With the Geogebra software students will be able to investigate and verify principles from limits through derivatives to integrals. This technological visual piece will help students understand the concepts more deeply and help with their retention of material.
TI-84’s will be used specifically in the investigations and presentations of modules from the TI Education Website (http://education.ti.com/html/t3_free_courses/calculus84_online/). Module 16 over Related Rates and Module 19’s Applications of Integration (dealing with net area, total area, and arc length) will be assigned to small groups for an investigation into the application of calculus. These groups will collaborate and then present the work done to the rest of the class and to the instructor and two other math teachers here at the school. The students will have had practice with presenting problems orally previously as they will be required in the Chapter 3.4 material to choose, collaborate, solve, and present orally and in a short written report the solution to a challenging Related Rates problem dealing with either volume, Pythagorean Theorem, similar triangles, or areas.
As a large number of calculus students are also taking calculus, when the physics class begins their formal study of distance, velocity, and acceleration, we will collaborate with Mr. Troutman’s class using the Vernier software and lab (http://www.vernier.com/experiments/phys-am/1/motion_on_an_incline/)
Students enrolled in both calculus and physics will be required to collect, enter, and interpret the relationship between distance, velocity, and acceleration both in terms of derivatives as well as working backwards using integrals. Calculus students will be required to write a short paper on this eloquent relationship and report back to the physics class and demonstrate to the non-calculus students a summary of how the math models this relation.
The emphasis on work with functions will necessitate the students expand their knowledge and techniques with functions. This content piece will include not only the commonplace algebraic analytical function representations (as they would do in 1.2 computing limits or 2.4 using the product rule), but also work graphically (emphasized in Chapter 4 with, for example relative and global extrema), numerically (emphasized for example in limit values in Chapter 1 and rates of change in Chapter 2), and verbally (which needs to be done throughout the course as the students will be writing solutions to word problems and explaining, as with related rates, what the real world meaning of the results are).
Textbook:
Great news: your textbook for this class is online!
Calculus, Volume 1 from OpenStax, ISBN 1-947172-13-1
You have several options to obtain this book:
- View online (Links to an external site.) (Links to an external site.)
- Download a PDF (Links to an external site.) (Links to an external site.)
You can use whichever formats you want. Web view is recommended -- the responsive design works seamlessly on any device.
Important Notes:
- All first week assignments need to be completed and submitted by the due date to avoid possibly being dropped from the class.
- Any student needing accommodations should inform the instructor. Students with disabilities who may need accommodations for this class are encouraged to notify the instructor early in the quarter so that reasonable accommodations may be implemented as soon as possible.
- Academic dishonesty and plagiarism will result in a failing grade on the assignment. Using someone else's ideas or phrasing and representing those ideas or phrasing as our own, either on purpose or through carelessness, is a serious offense known as plagiarism. "Ideas or phrasing" includes written or spoken material, from whole papers and paragraphs to sentences, and, indeed, phrases but it also includes statistics, lab results, art work, etc. Please see the PHS handbook for policies regarding plagiarism, harassment, etc.
Course Summary:
| Date | Details | Due |
|---|---|---|