Syllabus

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

-Albert Einstein

Calculus AB Syllabus

Teacher: Mr. Fawcett

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

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

AB 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.

AB 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

Review for AP Calculus Exam (minimum 3 wks)

Instructional Methods:

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

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 make up 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 35-55 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.

Grading Scale:

Regina AP classes will be graded using the following scale. The rationale for this is that AP classes require more work than a regular class. The following grade scale will be used in all Regina AP classes:

There are no A+ grades in AP courses.

A 95-100 4.50

A- 90-94.9 4.17

B+ 87-89.9 3.58

B 83-86.9 3.25

B- 80-82.9 2.92

C+ 77-79.9 2.43

C 73-76.9 2.10

C- 70-72.9 1.77

All students completing AP classes are required to take the AP exam in the Spring. Students not taking the AP Test will not receive grade weighting for the year nor an AP designation for their course on their official transcript.

All AP students will be evaluated quarterly. Students receiving grades below 70% at the quarter will need to meet with the teacher of the AP course to determine a plan of action. Students receiving below a C- at the semester in an AP class will be required to drop that specific AP course.