JEFFERSON COLLEGE
COURSE SYLLABUS
MTH180
ANALYTIC GEOMETRY AND CALCULUS I
5 Credit Hours
Prepared by:
Karen Knight
Revised Date: January 29, 2007
by
Linda Hoppe
Arts & Science Edcuation
Dr. Mindy Selsor, Dean
MTH180 ANALYTIC GEOMETRY AND CALCULUS I
I.
CATALOGUE DESCRIPTION
Prerequisite: ACT score of 24 or higher plus high school trigonometry, MTH141, or
MTH133 and MTH134 with a grade of “C” or better. 5 semester hours credit
Calculus I covers limits, continuity, differentiation, and integration. This course meets the
mathematics requirement for the Associate of Arts degree. (F,S,Su)
II.
GENERAL COURSE OBJECTIVES
Upon completion of this course the student will be able to:
III.
IV.
A.
Demonstrate understanding of vocabulary and concepts from precalculus courses.
B.
Understand the theory related to limits of functions and use it on specific
applications.
C.
Understand the theory related to derivatives of functions and use it on specific
applications.
D.
Understand the theory related to antiderivatives of functions and use it on specific
applications.
E.
Understand the theory related to definite integrals of functions and use it on specific
applications.
COURSE OUTLINE
A.
Limits and Rates of Change
B.
Derivatives
C.
The Mean Value Theorem and Curve Sketching
D.
Integrals
E.
Applications of Integration
UNIT OBJECTIVES
A.
Limits and Rates of Change
1.
The Tangent and Velocity Problems
2.
3.
4.
5.
6.
The Limit of a Function
Calculating Limits using the Limit Laws
The Precise Definition of a Limit
Continuity
Tangents, Velocities, and other Rates of Change
B.
Derivatives
1.
Derivatives
2.
Differentiation Formulas
3.
Rates of Change in the Natural and Social Sciences
4.
Derivatives of Trigonometric functions
5.
The Chain Rule
6.
Implicit Differentiation
7.
Higher Derivatives
8.
Related Rates
9.
Differentials; Linear and Quadratic Approximations
10.
Newton’s Method
C.
The Mean Value Theorem and Curve Sketching
1.
Maximum and Minimum Values
2.
The Mean Value Theorem
3.
Monotonic Functions and the First Derivative Test
4.
Concavity and Points of Inflection
5.
Limits at Infinity; Horizontal Asymptotes
6.
Curve Sketching
7.
Graphing with Calculus and Calculators
8.
Applied Maximum and Minimum Problems
9.
Antiderivatives
D.
Integrals
1.
Sigma Notation
2.
Area
3.
The Definite Integral
4.
The Fundamental Theorem of Calculus
5.
The Substitution Rule
E.
Applications of Integration
1.
Area between Curves
2.
Volume
3.
Volume by Cylindrical Shells
V.
VI.
METHOD OF INSTRUCTION
A.
Class Discussion of Homework
B.
Lecture
REQUIRED TEXTBOOK (WITH PUBLICATION INFORMATION)
Stewart, Calculus, 4th ed., Brooks/Cole Publishing Company, 1999
VII.
REQUIRED MATERIALS (STUDENT)
Graphics Calculator
VIII.
METHOD OF EVALUATION (STUDENT)
A.
Unit Examinations
B.
Comprehensive Final Exam