HARFORD COMMUNITY COLLEGE
Math 212 – Calculus with Applications
Course Information
EFFECTIVE DATE
January, 2013
DATE SUBMITTED
September 1, 2012
COURSE NUMBER
Math 212
COURSE TITLE
Calculus with Applications
PREREQUISITE(S)/CO-REQUISITES
Math 101 or Math 111 or Math 103 or Math 109 or STEM
Divisional Math Placement Exam
STEM
DIVISION
BUDGET ORG
NUMBER
1148
SUBJECT
Mathematics
INITIATOR
Dr. Supawan King
DIVISION LEADER
Deborah Wrobel
NUMBER OF CREDITS
3
TOTAL INSTRUCTIONAL HOURS
45
RECOMMENDED CLASS SIZE
25
START-UP COST
0
COURSE FEE
0
Course Description
MATH 212 - Calculus with Applications (3 credits) GM
This course is designed for students in the biological, social, and management sciences.
Differential and integral calculus with emphasis on differentiation techniques and the use of
calculus in the above fields form an important part of the course. Exponential and logarithmic
functions, partial derivatives are included. Technology will be utilized to enhance understanding
of the concepts and their applications related to their future career. This course is not open to
math, chemistry, engineering, or physics majors. Prerequisites: Math 101 or Math 111 or Math
103 or Math 109 or STEM Divisional Math Placement Exam.
Student Learning Objectives Linked to Relevant Academic Outcomes
Upon satisfactory completion of this course, the student will be able to: Upon successfully
completing the course, students will be able to
1. Demonstrate the relationship between functions and their graphs.
(Academic outcomes supported by this learning objective: Critical Thinking,
Computational Skills, Science and Technology)
2. Evaluate limits algebraically and apply to real world problems.
(Academic outcomes supported by this learning objective: Critical Thinking,
Computational Skills, Science and Technology)
3. Interpret and use derivatives to solve real world problems involving calculus.
(Academic outcomes supported by this learning objective: Communication, Critical
Thinking, Computational Skills, Science and Technology)
4. Use the definite integral to find area under curves and area between two curves.
(Academic outcomes supported by this learning objective: Critical Thinking,
Computational Skills, Science and Technology)
5. Use the basic ideas of calculus for functions of more than one variable to solve optimization
problems.
(Academic outcomes supported by this learning objective: Communication, Critical
Thinking, Computational Skills, Science and Technology)
6. Use appropriate technology to obtain the solution of mathematical problems.
(Academic outcomes supported by this learning objective: Communication, Critical
Thinking, Science and Technology)
Course Outline
I. REVIEW-THE FUNCTIONS AND THEIR GRAPHS
II. THE DERIVATIVE
A. The Slope
B. Limits and Derivatives
C. Rules for Differentiation
D. Rate of Change
III. APPLICATIONS OF THE DERIVATIVE
A. Graphs and Relation with Derivatives
B. Curve Sketching
C. Optimization Problems
IV. TECHNIQUES OF DIFFERENTIATION
A. Product Rule
B. Quotient Rule
C. Chain Rule
V. THE EXPONENTIAL AND LOGARITHM FUNCTIONS
A. Definitions and Properties of Exponential Functions
B. Definitions and Properties of Natural Logarithm
C. Derivatives of Exponential and Logarithmic Functions
VI. APPLICATIONS OF THE EXPONENTIAL AND LOGARITHMIC FUNCTIONS
A. Exponential Growth and Decay
B. Compound Interest
VII. INTEGRATION
A. Anti-differentiation
B. Area
C. Approximation by Riemann Sums
D. Applications of the Definite Integral
VIII. FUNCTIONS OF SEVERAL VARIABLES
A. Partial Derivatives
B. Maxima and Minima
C. Lagrange Multipliers
D. Least Squares
Instructional Method(s)
To achievestudent learning objectives, instruction includes: Lecture, discussion, problem
solving, computer aided instruction, group work.
Assessment Method(s)Quizzes, exams, projects, class work.
Textual Material(s)
Title:
Author or Editor:
Publisher:
Date
Calculus and its Applications (12th Edition)
Goldstein, D. Lay and D. Schneider
Prentice Hall
2009
GENERAL EDUCATION JUSTIFICATION FORM
The initiator completes this section only if requesting general education status for this
course. If a modification is for an existing general education course, the initiator must also
complete the General Education Justification form. (See the Curriculum Manual for the
guidelines and worksheet (Appendices C and D)used by the Curriculum Work Group for
evaluating general education proposals.)
1. General Education Guidelines
A. To be considered for the general education distribution, each course must emphasize
breadth rather than depth and, in most cases, be an introductory course to a discipline.
Explain in a few sentences how the proposed course meets these guidelines.
Math 212 Calculus with Applications consists of topics in differential and integral
calculus. Applications in the biological, social, and management sciences are
emphasized.
B. General Education courses shall reflect current scholarship in the discipline and provide
reference to theoretical frameworks and methods of inquiry appropriate to academic
disciplines. (Courses that are theoretical may include applications, but all applications
courses shall include theoretical components.) Explain in a few sentences how the
proposed course meets these guidelines.
The course introduces the students to concepts of differential and integral calculus with
emphasis on differentiation techniques and the use of calculus in the biological, social,
and management sciences. Technology will be utilized to enhance understanding of the
concepts and their applications related to their future career.
C. Public institutions of higher education should incorporate knowledge and skills involving
the use of quantitative data, effective writing, information retrieval, and information
literacy where possible in the General Education core. If appropriate, explain in a few
sentences how the proposed course meets these guidelines.
Students will be assigned a group project in solving the real world application. The
mathematical concepts and skills involving the use of differentiation techniques and
technology will be used to solve the problem. The use of quantitative data, effective
writing, and information literacy must be presented in the project report.
2. General Education Category
This course fits into the checked general education category:
(GB) Behavioral/Social Science
(GE) English Composition
(GH) Arts/Humanities
(GI) Interdisciplinary and Emerging Issues
(GL) Biological and Physical Laboratory Science
X (GM) Mathematics
(GS) Biological and Physical Science
3. Relation Of Course To General Education Goals
As justified by the accompanying explanation on how the course fulfills the goal and the
specific related activity, this course satisfies the following General Education goals [identify
relevant goal(s) and provide Academic Outcomes(s) and specific activity(ies)/assessments]:
General Education Category: GM
General Education Goals:
General Education Goals
1
2
4
Course Name and Number:
Math 212 Calculus with Applications
List the Student Learning Objectives that align to each General Education Goal; the Academic
Outcomes and the Specific Activity(ies) /assessments:
1. Student Learning Objective:Demonstrate the relationship between
X
X
X
functions and their graphs
Academic Outcome(s): Critical Thinking, Computational Skills,
Science and Technology
Specific activity/assessment:Quizzes, exams, class work
2. Student Learning Objective:Evaluate limits algebraically and apply to X
X
X
real world problems
Academic Outcomes:
Critical Thinking, Computational Skills,
Science and Technology
Specific activity/assessment:Quizzes, exams, class work.
3. Student Learning Objective:Interpret and use derivatives to solve real X
X
X
world problems involving calculus
Academic Outcomes:
Communication, Critical Thinking,
Computational Skills, Science and Technology
Specific activity/assessment:Quizzes, exams, projects, class work.
4. Student Learning Objective:Use the definite integral to find area
X
X
X
under curves and area between two curves
Academic Outcomes:
Critical Thinking, Computational Skills,
Science and Technology
Specific activity/assessment:Quizzes, exams, class work.
5. Student Learning Objective:Use the basic ideas of calculus for
X
X
X
functions of more than one variable to solve optimization problems
Academic Outcomes:
Communication, Critical Thinking,
Computational Skills, Science and Technology
Specific activity/assessment:Quizzes, exams, projects, class work.
6. Student Learning Objective:Use appropriate technology to obtain the
X
X
solution of mathematical problems
Academic Outcomes:
Communication, Critical Thinking, Science
and Technology
Specific activity/assessment:Quizzes, exams, projects, class work.
7. Student Learning Objective:
Academic Outcomes:
Specific activity/assessment:
8. Student Learning Objective:
Academic Outcomes:
Specific activity/assessment:
4. Transferability
Our major transfer institutions, listed below, accept this course as meeting their general
education requirement (check all that apply):
Towson:
X
Yes
No
Number of credits
granted by the
receiving institution:
Credits
3
UMCP:
X
Yes
No
Credits
3
UMBC:
X
Yes
No
Credits
3
UB:
X
Yes
No
Credits
3
Salisbury:
X
Yes
No
Credits
3
Other Institution:
Yes
No
Credits
Other Institution:
Yes
No
Credits