Manchester Community College
Course Content Outline
Department: Math & Science
Date: September 2006
Program: All
Prepared by: Janice G. Kaliski & Danielle
Tarnow
Course Number: MATH 204
Course Title: Calculus I
Theory Hours: 4
Credits: 4
Lab Hours: 0
Prerequisites: Satisfactory placement test scores as defined by the mathematics faculty or
MATH171 with C or better or permission from the instructor.
Catalog Description:
A first calculus course that is designed to explore functions, limits, continuity, derivatives; rules for
differentiating algebraic, trigonometric, exponential and logarithmic functions; chain rule; implicit
differentiation; related rate problems; max-min problems; curve sketching; integrals, areas and volumes.
Prerequisite: MATH171.
Desired Student Competencies:
The student will:
1. Review graphing and functions (P.1-P.5)
2. Understand limits and continuity (1.1-1.6)
3. Demonstrate knowledge of basic derivative rules (2.1-2.6,6.1-6.4)
4. Complete related rates problems (2.7)
5. Compute relative and absolute extrema and sketch curves (3.1, 3.3-3.5)
6. Solve optimization problems (3.6)
7. Complete basic integrals and understand the fundamental theorem of calculus (4.1, 4.5-4.7)
8. Find areas and volumes using calculus (5.1-5.4)
9. Understand the uses of exponential and logarithmic functions (6.5)
10. Use L’Hospital’s rule properly (6.6)
11. Understand relative rates of growth (6.7)
Required Text(s):
Title: Single Variable Calculus
Author: James Stewart
ISBN #: 0-534-39366-7
Publisher: Thomson Learning Brooks/Cole
Other Related Issues:
5.
6.
Lectures
Classroom and homework Problem Solving
7.
8.
Exams
Projects, Group Work, Presentations, Class Participation and Other Types of
Assignments (as decided by the instructor)
Course Number: MATH204
Course Title: Calculus I
Outline of Topics to be Covered
P.1
P.2
P.3
P.4
P.5
1.1
1.2
1.3
1.4
1.5
1.6
2.1
2.2
2.3
2.4
2.5
2.6
2.7
3.1
3.3
3.4
3.5
3.6
4.1
4.5
4.6
4.7
5.1
5.2
5.3
5.4
6.1
6.2
Real Numbers and the Real Line
Coordinates, Lines and Increments
Functions
Shifting Graphs
Trigonometric Functions
Rates of Change and Limits
Rules for Finding Limits
Target Values and Formal Definitions of Limits
Extensions of the Limit Concept
Continuity
Tangent Lines
The Derivative of a Function
Differentiation Rules
Rates of Change
Derivatives of Trigonometric Functions
The Chain Rule
Implicit Differentiation and Rational Exponents
Relative Rate of Change
Extreme Values of Functions
The First Derivative Test for Local Extreme Values
Graphing with y’ and y”
Limits as x approaches +/- infinity, Asymptotes and Dominant Terms
Optimization
Indefinite Integrals
Riemann Sums and Definite Integrals (Complete Only Integrals that do NOT
Require Substitution)
Properties, Aresa and the Mean Value Theorem (Complete Only Integrals that
do NOT Require Substitution)
The Fundamental Theorem (Complete Only Integrals that do NOT Require
Substitution)
Area Between Curves (Complete Only Integrals that do NOT Require
Substitution)
Finding Volumes by Slicing (Complete Only Integrals that do NOT Require
Substitution)
Volume of Solids of Revolution (Complete Only Integrals that do NOT Require
Substitution)
Cylindrical Shells (Complete Only Integrals that do NOT Require Substitution)
Inverse Functions and their Derivatives (No integration, derivatives only)
Natural Logarithms (No integration, derivatives only)
6.3
The Exponential Function (No integration, derivatives only)
6.4
a× and loga x (No integration, derivatives only)
6.5
Growth and Decay (No integration, derivatives only
Course Number: MATH204
Course Title: Calculus I
6.6
6.7
L’Hospital’s Rule (No integration, derivatives only)
Relative Rates of Growth (No integration, derivatives only)
Note: Chapter 6 material may be covered before Chapter 4 material.
Assessment Addendum
5. Lectures
a. The teacher will review graphing and functions, and introduce limits,
continuity and derivatives; related rates; relative and absolute extrema and
curve sketching techniques; optimization; integration and the fundamental
theorem of calculus; areas and volumes exponential and logarithmic
functions; L’Hospital’s rule and relative rates of growth.
b. The teacher should be aware of student’s involvement and understanding
6. Classwork and Homework
a. The teacher should create classwork and homework assignments that
give students practice in the graphing of functions; evaluating limits; checking
for continuity; understanding derivatives and the basic derivative rules;
computing related rates problems; computing relative and absolute extrema
and sketching curves; solving optimization problems; completing basic
integrals and gaining understanding of the fundamental theorem of calculus;
finding areas and volumes; understanding and using exponential and
logarithmic functions; calculating limits using L’Hospital’s rule and
understanding relative rates of growth.
b. In order to measure the success of classwork and homework, the teacher
should grade the assignments, according not only to the correctness of
their answers, but also according to the overall process used to solve the
problems.
7. Exams
a. Exams should be given that test student knowledge of graphing and
functions; limits and continuity; the basic derivative rules; related rates;
relative and absolute extrema and curve sketching; optimization; integration;
areas and volumes; exponential and logarithmic functions; L’Hospital’s rule
and relative rates of growth.
b. The exams should also be evaluated not only for correct answers, but
also for correct solution techniques. Standardized department exams are
appropriate if more than one instructor at a time is teaching the course.
8. Projects, Group Work, Presentations, Class Participation and other types of
assignments (as decided by the instructor).
a. These types of assignments may be used by the instructor to bolster
learning in the areas mentioned above.
Course Number: MATH204
Course Title: Calculus I
b. These assignments should be assessed according to criteria laid down
instructor for a particular assignment.