Calculus

Description:
Calculus will study functions and their limits, derivatives, and integrals. Students will also discover how these main concepts are used and applied in other areas of study such as physics, biology, business, and architecture. This class will help students to further develop and refine their problem-solving skills as they work through the challenges calculus problems provide. Finally, students will use technology such as graphing calculators to assist in the understanding of the ideas presented.

Textbook:
Finney, R. L., et al. (1999). Calculus: Graphical, numerical, algebraic. Menlo Park, CA: Scott Foresman, Addison Wesley.

Course Pre-requisites:
Algebra I, Geometry, Algebra II/Trigonometry, and Pre-Calculus

Overall Course Objectives:
Upon successful completion of this class, the students will be able to:
1. Employ problem-solving techniques to solve calculus problems.
2. Analyze functions and graphs to see what relationships exist.
3. Demonstrate knowledge of limits and continuity.
4. Use knowledge of limits to determine derivatives.
5. Determine a definite integral.
6. Apply derivative and integral knowledge to real world examples.
7. Discover multiple ways to perform integration.
8. Determine vectors and use them effectively.

Classroom Policy:
The atmosphere of the classroom is based on the acronym GROW.
1. GOD should be number one in everyone’s life in the classroom. This means that all people in the classroom are expected to treat one another with Christian love and respect. Also, we are all sinful creatures; therefore as God forgave each person we should forgive one another when we make mistakes.
2. Everyone in the class needs to be READY. This means that students should come to class prepared to learn – have all supplies, and an open mind to learning.
3. OTHER people are important and their ideas and feelings are valuable. This means that when someone else is speaking, the rest of the class is listening. Also, building on what others have said is welcome. Whatever is said should be done so in an uplifting and constructive manner in order to encourage one another.
4. Everyone in the classroom should be WILLING. This means that their minds are open to new thoughts and ideas and they are willing to serve their Lord and Savior.

General Classroom Expectations:
Students are expected to come prepared for class (book, notebook, writing implements, TI-83+ calculator, and open mind for learning). As a part of a days activity students may be asked to demonstrate that they are completely prepared for class and receive a small amount of credit for it. They are also expected to be active and positive participants in class each day. Finally, they are expected to follow directions as given in class.

Attendance:
Students are expected to be in class on time everyday. A student will be considered tardy if he or she is not in the room when the bell rings or has not talked with me first.

Class Evaluation:
The grades for each quarter will be based upon the following items: homework, notebook, projects, activities, and tests.

Homework (in class) 5 points each
Homework (collected) varying
Notebooks 15 points
Activities/Projects 10-50 points each
Quizzes 10-40 points each
Tests 50-100 points each
Quarter Exam/Project 100 points

The number of points for each quarter will depend on how quickly the class moves along. If a student is actively participating in class on a regular basis and showing effort it will be positively reflected in the grade at the end of the quarter.

Homework will be checked for completeness in class and then gone over or collected at other times. Projects and activities will be assigned at varying times throughout the year to enrich students’ learning. Quizzes may be given sporadically during a unit, especially if it is particularly long or challenging. This will serve as another form of assessing how the class is doing. They may be oral or written, and will usually be announced. Tests will be given at the end of the unit as a final assessment. All tests will contain some elements from previous units to make sure that knowledge is being retained. Finally, at the end of each quarter an exam or culminating activity will be given.

Late Work:
Late work and missing work is expected to be turned in. Anything that has not been turned in at the end of the unit it was a part of will receive a 0. When a student is absent, he or she has the number of days he or she was absent plus one to turn in the work after returning to school before the assignments are considered late. If a quiz or test is missed arrangements are made, usually during study hall, to have it made up. Any assignments that are not completed on the due date may be turned in for partial credit (3 out of 5 points if checked in class, 3 points off if collected assignment).

Topics of Instruction and Methods:
The following is a list of possible topics for the year. All of these may not be covered given time constraints.

Success in Math Skills
Limits and Continuity
Derivatives
Applications of Derivatives
The Definite Integral
Applications of Definite Integrals
Differential Equations, Mathematical Modeling
L’Hôpital’s Rule, Improper Integrals, Partial Fractions
Infinite Series
Parametric, Vector, and Polar Functions
Multivariable Functions, Multiple Integrals

The methods used to cover these topics include lecture, hands-on activities, and the use of manipulatives when possible.