# Calculus I (full year)

**COURSE SYLLABUS FOR CALCULUS I **

CVCC Course Number - MATH 263 - 4 credit hours

**INSTRUCTOR:** Mrs. Shifflett **ROOM:** 112

**COURSE DESCRIPTION:** A college level study of differential calculus, this course includes the study of limits, continuity, derivatives (concept and definition), derivatives of parametric equations and polar curves, differentiation techniques (including inverse trigonometric functions), curve sketching, optimization applications and an introduction to antiderivatives and definite integrals with applications. Upon completion of the course the students earn 4 semester hours from the Central Virginia Community College.

**COURSE MATERIALS:** The text for this course is “Calculus Early Transcendental Functions by Larson, Hostetler and Edwards, 4^{th} edition. It is essential that you have a graphing calculator you are comfortable using.

**COURSE CONTENT:** At the end of the semester, the student will be able to:

- explain the concept of and evaluate limits
- find intervals of continuity for a function
- ‘construct’ the definition of the derivative
- explain how the secant and tangent line relate to the derivative, average and instantaneous rates of change, velocity and acceleration
- find approximations for the derivatives at a point
- use local linearity to estimate functional values
- apply appropriate techniques of differentiation (product, quotient, chain, exponential, logarithmic)
- use the definition of the derivative to derive selected derivative formulas
- differentiate trigonometric functions
- perform implicit differentiation
- find the tangent to parametric curves
- derive derivative formulas and take derivatives of inverse trigonometric functions
- use differentials to find relative and percentage error
- solve related rates applications
- determine increasing and decreasing intervals of a function
- determine concavity of a function and points of inflection
- sketch curves using appropriate techniques
- solve optimization problems
- apply Newton's method when finding roots
- setup and evaluate Riemann Sums
- interpret the definite integral
- find antiderivatives of power, polynomial, exponential, logarithmic and trigonometric functions
- perform integration using u-substitution
- approximate the definite integral using Riemann Sums
- evaluate definite integrals using the Fundamental Theorem of Calculus
- apply the indefinite integral to position-velocity-acceleration problems

**COURSE OBJECTIVES:** At the end of the semester, students will have an understanding of the concepts and techniques listed above. This understanding will be enhanced, when appropriate, through directed group and individual computer exercises and group and individual projects.

**HONOR CODE:** Students are required to pledge all work that they turn in for a grade. Refer to CVGS Student Handbook for complete requirements.

**CLASS METHODOLOGY:** A typical class will consist of lecture, but student involvement is highly encouraged. Homework due dates are listed on the calendar, but may change at my discretion. Homework will be turned in at the beginning of class. Select problems will be graded. Tests will typically be at the end of a chapter. Throughout the semester there may also be projects or extra assignments given. I have an open door policy for extra help, please seek me out early! Small questions can be covered before or after class. Large issues can be tackled on Fridays or Saturdays. I will also have days built into the calendar specifically for questions during class. Be prepared on these day. No questions means we move on!

All notes and supporting documents will be available online for student viewing. I will post the notes-outline prior to class and then post the notes that were taken during class. I strongly advise you to print out any notes that you have missed (or copy them from a classmate). Use these notes and the book to help prepare for assignments and tests. If you are having trouble, use the extra problems in the book as extra practice!

**GRADING:** The semester grade will be determined as follows:

Tests: 40%

Homework: 5%

Projects: 15%

Quizzes: 20%

Exam: 25%

**ABSENCES/TARDINESS:** If a student is absent (excused) for only one class meeting, then upon return, he/she is expected to have completed the work which was due on the day of absence. If a test was missed, then the student is expected to take the test on the day of return. If a student misses two or more consecutive class meetings, then he/she should talk to the instructor to devise a game plan to catch up. Absences __for any other reason__ need to be discussed with the instructor in advance. Failure to do so will result in an unexcused absence. Work missed because of an unexcused absence cannot be made up. If a test is missed because of an unexcused absence, then that test grade will be lowered by 10 points for each day late. You are expected to be in class ** on time**. You will be allowed

**tardy "on the house" each 9-weeks. After that you will pay 1/2 a point off your semester grade for any additional tardies!**

__one and only one__