Syllabus

“Pure mathematics is, in its way, the poetry of logical ideas.”

-Albert Einstein

General Calculus Syllabus

Teacher: Mr. Fawcett

Website: http://sites.google.com/site/fawcettsmathclass/

Book used for class: Calculus – Graphical, Numerical, Algebraic (Third Edition)

Calculus Course Description

The following is an outline of the topics we cover and a typical sequence in which those topics are covered. The time spent is only an estimate of the average number of days allotted to the topic because the actual time varies from year to year depending upon the students' abilities and interest, and also upon the richness of the class discussion that is generated. Also, with the wealth of interesting problems that are being supplied by those committed to reform calculus, and with the always changing capabilities of technology, it is difficult to anticipate extra days a class might spend in exploration or discovery. Each student must have a graphing calculator of his/her own, and is expected to have it in class each day. The calculator of choice for our mathematics department is the TI-83Plus, however some students own and use the TI-89. In my class, we use graphing calculators daily to explore, discover, and reinforce the concepts of calculus. Students may use the graphing calculators on some, but not all, assessments.

Calculus Course Outline

Prerequisites for Calculus

1.1 Lines

1.2 Functions and Graphs

1.3 Exponential Functions

1.4 Parametric Equations

1.5 Functions and Logarithms

1.6 Trigonometric Functions

Review Exercises/Test

Limits and Continuity

2.1 Rates of Change and Limits

2.2 Limits Involving Infinity

2.3 Continuity

2.4 Rates of Change and Tangent Lines

Review Exercises/Test

Derivatives

3.1 Derivative of a Function

3.2 Differentiability

3.3 Rules for Differentiation

3.4 Velocity and Other Rates of Change

3.5 Derivatives of Trigonometric Functions

3.6 Chain Rule

3.7 Implicit Differentiation

3.8 Derivatives of Inverse Trigonometric Functions

3.9 Derivatives of Exponential and Logarithmic Functions

Review Exercises/Test

Applications of Derivatives

4.1 Extreme Values Functions

4.2 Mean Value Theorem

4.3 Connecting f’ and f” with the Graph of f

4.4 Modeling and Optimization

4.5 Linearization (not Newton’s Method)

4.6 Related Rates

Review Exercises/Test

The Definite Integral

5.1 Estimating with Finite Sums

5.2 Definite Integrals

5.3 Definite Integrals and Antiderivatives

5.4 Fundamental Theorem of Calculus

5.5 Trapezoidal Rule

Review Exercises/Test

Differential Equations and Mathematical Modeling

6.1 Slope Fields and Euler’s Method

6.2 Antidifferentiation by Substitution

6.4 Exponential Growth and Decay

6.5 Logistic Growth

Review Exercises/Test

Applications of Definite Integrals

7.1 Integral as Net Change

7.2 Areas in the Plane

7.3 Volumes

7.4 Lengths of Curves

7.5 Applications for Science and Statistics

Review Exercises/Test

Instructional Methods:

Cooperative Learning, Board Work (board points), Lecture, Class Discussions, Individual Work, Writing, Application of Content to Real-Life, etc.

Bellwork:

There will be some kind of bellwork that will be assigned at the start of EVERY class. This usually short assignment (5-min) can be taken as a grade or will be used to review topics previously learned. Sometimes the bellwork could be as simple as checking answers and/or asking questions with fellow classmates. There will then be a time to review the bellwork and to go over the previous assignment afterwards. THIS WOULD BE THE TIME TO ASK ANY QUESTIONS!!!

Required Materials:

The following materials will be REQUIRED for every student when he/she enters the classroom:

- required book, calculator, loose-leaf paper, pencil, & Brain.

*The teacher is not responsible for any materials needed for this class. This responsibility falls upon you, the student!!

Classroom Procedures/Policies:

1. You are expected to do all homework assigned. You will have until the Chapter Exam to turn in any missing work.

2. You are expected to come to class prepared; i.e.: books, notebooks, calculator, and pencils are to be brought every day (unless told otherwise).

3. You are to follow and uphold the criteria established in the student-parent handbook.

4. You are to respect the property and rights of all individuals in the class; no disruptive or hurtful behavior.

Homework:

Students can expect about 10-35 minutes of homework almost every night, depending on the days events, tests, etc. It is the responsibility of the student to make up homework within one day of his/her absence. The student can ask either the teacher or a fellow classmate for the assignment missed. Homework will be collected and/or reviewed on a regular basis.

A list of the weekly assignments can be found on the blackboard in the back of the room. Also, if the student is missing any worksheets and/or tests/quizzes, then he/she can find them in the designated folders located in the back corner of the room.

Homework Quizzes:

Students can expect at any given time a Homework Quiz. Instead of collecting that days assignment, the teacher will give a quiz reflecting problems/questions similar to that particular assignment. In most cases, homework quizzes are worth as much as the assignment would have been if turned in. These are graded as a class and each solution is discussed/explained thoroughly.

If a student is absent on this day, then all he she must do is turn in that assignment when he/she comes back to school to get the credit for that Homework Quiz.

Note-taking:

It is strongly suggested that each student take notes from each learned section. The student will benefit from doing so since he/she will be allowed to then utilize these notes during any Quiz on that section. The student may NOT, however, use these notes on the chapter tests! Note cards will be permitted on each chapter test as long as it is made by the student and is turned in along with the test.

Attendance:

Students must be present to pass. No student will leave the classroom once the bell has rang indicating the start of the class period. No student shall enter after the bell has rang without a signed excuse from the designated staff member/parent.