Heartland Community College
Master Course Syllabus
Division: Math, Science
Days and Time the course meets: MTRF 12:00 – 12:50 p.m.
Instructor Information:
Instructor’s Name:
Phone Numbers:
E-mail Address:
Office:
Office Hours:
Cynthia Pulley
268-8665 (office)
cindy.pulley@heartland.edu
ICB 2421
MTRF 9:30 – 10:00 a.m.; W 1 – 2 p.m.; TR 2 – 3 p.m.
Or by appointment
CATALOG DESCRIPTION (Include specific prerequisites):
Prerequisite: MATH 162 with a grade C or higher, or equivalent. The third semester of the
Calculus sequence, focusing on multivariable functions. Topics include differentiation and
integration of functions with multiple variables, partial derivatives, the differential,
directional derivatives, gradients, two- and three-dimensional motion, vector fields, and line
integrals. Concepts are examined in three representations: numerically, graphically, and
symbolically. Note, a graphing calculator is required for this course (instruction will be
based on a TI 89).
TEXTBOOKS:
Larson R., Hostetler R. & Edwards B. (2002) Calculus with Analytic Geometry, 7th ed.
Houghton Mifflin Co.
RELATIONSHIP TO ACADEMIC DEVELOPMENT PROGRAMS AND
TRANSFERABILITY:
MATH 163 fulfills 4 of the 3(AA), 6(AS), or 12(AAT) semester hours of credit in
Mathematics. MATH 163 should transfer as part of the General education core curriculum
described in the Illinois Articulation Initiative to other Illinois colleges and universities
participating in the IAI. However, students should consult an academic advisor for transfer
information regarding particular institutions. Refer to the IAI web page for information as
well as www.itransfer.org.
COURSE OBJECTIVES (Learning Outcomes)
Learning Outcomes
Understand functions of many variables from graphical,
symbolic, and numerical perspectives.
Represent multiple quantities with vectors.
GE
code
C3
CO2
Understand vector-valued functions.
Apply differentiation techniques to functions with multiple
variables.
Optimize functions of several variables, with and without PS4
constraints.
Apply integration techniques to multivariable functions.
Determine mass, moments, and motion of particles in 2space and 3-space.
CT3
Understand the properties and theorems (e.g., Stoke’s,
Greene’s, etc.) essential for vector analysis.
Assessment
Exam, assignment,
or project
Exam, assignment,
or project
Exam, assignment,
or project
Exam, assignment,
or project
Exam, assignment,
or project
Exam, assignment,
or project
Exam, assignment,
or project
Exam, assignment,
or project
COURSE OUTLINE:
1.
2.
3.
4.
5.
Vectors in the Plane and in Space
Vector-Valued Functions
Differentiation of Multivariable Functions
Integration of Multivariable Functions
Analysis of Vector Fields
Method of Evaluation (Tests/Exams, Grading System):
Student grades are based on successful completion of homework, quizzes, tests and
other assignments as the instructor feels are necessary. Your grade is based upon
cumulative total points. There is no weighting of grades for quizzes or exams, but
these will be worth more points than your assignments. Exams may include
comprehensive material and you will have a comprehensive final. Typically, you
will have 4 – 6 exams throughout the semester and quizzes on a weekly basis. Your
final exam will be worth approximately 20% of your final grade in this course.
Grade Scale:
100 - 90%
89 - 80
79 - 70
69 - 60
59 -0
A
B
C
D
F
Missing an exam and assignments policy: There are NO make-ups for exams or
assignments except for excused absences from prior notification of the absence.
Participation (or Attendance)
Regular attendance is not only expected, but a must in order to be successful in this
class. If a student is absent, it is his/her responsibility to obtain class notes and
assignments from someone in the class.
Incompletes
An incomplete grade may be given to a student who, by the withdrawal date, can
reasonably by expected to pass the course. Incompletes may be granted only when
justified by extreme circumstances (e.g., serious illness, accident, death or serious
illness in the immediate family). Incomplete grades are not given for such reasons as
unjustified failure to appear for the final examination. A written agreement, outline
the requirements to be met, must be signed by the instructor and the student. The
agreed upon requirements must be completed no later than the end of the following
semester. By the agreed upon date, the instructor will assign a grade or the
incomplete will be changed to an F if the requirements are not completed.
Required Writing and Reading:
Required writing will be part of most assignments and tests. Students will be
expected
to explain how they found the solution, describe the solution graphically, and interpret the
answer in the context of the problem. Students are expected to read the material in the
textbook for each section studied.
Student Responsibilities
Before coming to class:
 Read assigned sections of the text.
 Attempt some of the assigned homework problems for the new section.
During class:
 Ask questions regarding problems that gave you difficulty in solving.
 Actively listen and participate in class discussions and presentations of
solutions.
 Take notes, not just what is written on the board, but any verbal explanations
or clarifications given by the instructor or other students.
After class:
 Reread notes and highlight what does not make sense or what you still do not
understand so that you can ask clarifying questions during office hours or at
the beginning of the next class.
 Do all of the assigned homework problems for the section discussed in class.
 Seek tutoring or instructor help when needed.
 Redo any missed problems on the homework, quizzes or tests.
Student Conduct, Academic Integrity, Plagiarism
Please refer to the Student Conduct Policy in the Heartland Community College
CATALOG for specific policies concerning discipline, academic integrity and
plagiarism.
Heartland Library Information http://www.heartland.edu/library
The Library, located in the Students Commons Buildings at the Raab Road campus, provides
Heartland students with a full range of resources including books, online journal databases,
videos, newspapers, periodicals, reserves, and interlibrary loan. Librarians are available to
assist in locating information.
Tutoring Center:
http://www.heartland.edu/asc/tutor.html
(309) 268-8231
Testing Center:
http://www.heartland.edu/asc/testing.html
(309) 268-8231
Academic Disabilities
If you have a documented disability and wish to discuss academic accommodations, please
contact Anita Moore at 268-8249 or anita.moore@heartland.edu.
Syllabus Disclaimer: This syllabus is subject to change. Any changes will be announced in
class.
Important Dates
Classes Begins
Drop course with refund
Labor Day (college closed)
Mid-Term Break (college closed)
Last day to withdraw and receive a “W”
Thanksgiving Break (college closed)
Class ends:
Final Exam:
I AM HERE TO HELP. I WILL DO MY BEST TO ANSWER QUESTIONS, PROVIDE
ASSISTANCE WHEN REQUESTED AND SPEND EXTRA TIME WITH YOU AS
NEEDED. YOUR SUCCESS IS IN YOUR HANDS. STUDY CONSISTENTLY AND
DILIGENTLY, AND SEEK THE HELP YOU NEED.
Appendix for AAT students
Course Objectives/Standards for AAT students:
based on the Illinois Mathematics Standards (IMS) for Teachers
Upon completion of this course a student should be able to:
Knowledge Objectives
 Graph, differentiate and integrate parametric curves. (IMS 2A, 3A, 4B, 5A)
 Graph, differentiate and integrate curves given in polar coordinates, including conic
sections. (IMS 2A, 3A, 5A)
 Write equations of lines and planes in space, including equations of tangent planes
and equations of normal lines. (IMS 2A, 3A)
 Differentiate and integrate vector functions in two & three dimensions. (IMS 3A, 4B)
 Apply calculus, using vectors, to study motion in space and in other situations. (IMS
2A, 3A, 4B)
 Explain the concept of limits & continuity in functions of several variables. (IMS 3A)
 Find differentials, directional derivatives and gradients of functions of several
variables. (3A, 5A)
 Find extrema of functions in two variables, including using Lagrange Multipliers.
(IMS 3A, 4B, 5A)
 Simplify indefinite and evaluate definite double integrals. (IMS 3A)
 Use double integrals in applications. (IMS 2A, 3A, 4B, 5A)
 Simplify indefinite and evaluate definite triple integrals, including triple integrals
using cylindrical and spherical coordinates. (IMS 3A)
 Use triple integrals in applications. (IMS 2A, 3A, 4B, 5A)
Performance Objectives
 Graph, differentiate and integrate parametric curves. (IMS 2C, 3B, 6C1, 7C8, 8C1,
8C4, 8C5, 8C6)
 Graph, differentiate and integrate curves given in polar coordinates, including conic
sections. (IMS 2C, 3B, 6C1, 6D1, 7C8, 8C1, 8C2, 8C5, 8C6)
 Use cylindrical & spherical coordinates to write equations of three dimensional
figures. (IMS 2C, 6C2, 6D1, 7C8, 8C6)
 Write equations of lines and planes in space, including equations of tangent planes
and equations of normal lines. (IMS 2C, 7C8, 8C5, 8C6)
 Differentiate and integrate vector functions in two & three dimensions. (IMS 2C,
6C1, 7C8, 8C1, 8C5, 8C6)
 Apply calculus, using vectors, to study motion in space and in other situations. (IMS
2C, 6C2, 7C8, 8C1, 8C2, 8C5, 8C6)
 Explain the concept of limits & continuity in functions of several variables. (IMS 2C,
3B, 7C8, 8C4, 8C5, 8C6)
 Find partial derivatives of functions of several variables. (IMS 2C, 3B, 6D1, 7C8,
8C1, 8C4, 8C6)
 Find differentials, directional derivatives and gradients of functions of several
variables. (6D1, 7C8, 8C1, 8C5)





Find extrema of functions in two variables, including using Lagrange Multipliers.
(IMS 2C, 6C1, 6D1, 7C8, 8C1, 8C4, 8C5, 8C6)
Simplify indefinite and evaluate definite double integrals. (IMS 2C, 3B, 6C1, 6D1,
7C8, 8C5, 8C6)
Use double integrals in applications. (IMS 2C, 3B, 6C1, 6D1, 6D3, 7C8, 8C5, 8C6)
Simplify indefinite and evaluate definite triple integrals, including triple integrals
using cylindrical and spherical coordinates. (IMS 2C, 3B, 6C1, 6D1, 7C8, 8C5, 8C6)
Use triple integrals in applications. (IMS 2C, 3B, 6C1, 6D1, 6D3, 7C8, 8C5, 8C6)
The following competencies/objectives are strongly recommended for inclusion in
Calculus III. However, they are not part of the IAI description for Calculus III.
Knowledge Objectives
• Understand vector fields. (IMS 2A, 3A, 4B)
• Find/evaluate line integrals. (IMS 2A, 3A, 4B)
Performance Objectives
• Understand vector fields. (IMS 2C, 3C, 6D1, 7C8, 8C5, 8C6)
• Find/evaluate line integrals. (IMS 2C, 3B, 6C1, 7C8, 8C5, 8C6)
• Use Green’s Theorem. (IMS 8C5, 8C6)
AAT students should be collecting assignments, assessments and artifacts that show
competence in the following standards. Some suggestions for what to collect are as follows:
Sample of Acceptable Course Assignments/Assessments/Artifacts
(by Standard and Indicator)
2A Knowledge Indicator The competent teacher of mathematics understands the many
strategies for problem solving.
 Evaluations of homework problems or class discussions or problem/project
presentations or quizzes/exams;
 Reflective writing on problem solving;
 Writing/analyzing multiple solution strategy problem solving;
 Peer tutoring on problem solving strategies
2C Performance Indicator The competent teacher of mathematics generalizes results of
problems and extends them to other problem situations.
 Evaluations of homework problems or class discussions or problem/project
presentations or quizzes/exams that demonstrate the ability to generalize
mathematical properties from specific cases/problems and formulate theorems or
discover more general situations where such properties apply.
3A Knowledge Indicator The competent teacher of mathematics understands various ways
of reasoning with respect to concepts procedures and conjectures.
 Evaluations of homework problems or class discussions or problem/project
presentations or quizzes/exams;
 Reflective writing on reasoning;
 Completion of proofs;
 Peer tutoring on reasoning.
3B Performance Indicator The competent teacher of mathematics applies mathematical
reasoning and appropriate technologies in the development of concepts, procedures and
conjectures.
 Evaluations of homework problems or class discussions or problem/project
presentations or quizzes/exams;
 Reflective writing on reasoning with technology;
 Completion of proofs;
 Peer tutoring on reasoning with technology.
3C Performance Indicator The competent teacher of mathematics generalizes reasoning
skills within the study of mathematics and applies or extends them to other contexts.
 Evaluations of homework problems or class discussions or problem/project
presentations or quizzes/exams;
 Reflective writing on reasoning;
 Completion of proofs;
 Peer tutoring on reasoning.
4B Knowledge Indicator The competent teacher of mathematics understands mathematical
connections to other disciplines.
 Evaluations of homework problems or class discussions or problem/project
presentations or quizzes/exams;
 Reflective writing on mathematics and how it relates to other disciplines.
4E Performance Indicator The competent teacher of mathematics connects mathematics to
other disciplines.

Evaluation or class discussions of problem/project presentations

Reflective writing on mathematics and how it relates to other disciplines
5A Knowledge Indicator The competent teacher of mathematics becomes familiar with the
capabilities and benefits of current and emerging technologies.
 Evaluations of appropriate use of technology on homework problems or class
discussions or problem/project presentations or quizzes/exams requiring the use of
technology: programming language or graphing calculator or mathematics software
or internet resources or power point.
6A5 Knowledge Indicator The competent teacher of mathematics knows and understands
polar and vector representations of complex numbers.
 Evaluations of homework problems, class discussions, problems/project
presentations, quizzes/exams
6C1 and 6C2 Performance Indicator The competent teacher of mathematics uses number
sense to judge the reasonableness of results and applies proportional reasoning to solve
problems.
 Use number sense and proportional reasoning in the solving of calculus problems
(finding extrema, points of inflections, asymptotes, max/min problems, related rates,
Newton’s Method) as evaluated by homework problems or class discussions or
problem/project presentations or quizzes/exams;
 Reflective writing;
 Peer tutoring on number sense and proportional reasoning.
6D1 and 6D2 Performance Indicator The competent teacher of mathematics chooses
appropriately from mental math, paper and pencil, manipulative, and technology to perform
calculations and models, develops and applies algorithms with technology.
 Evaluations of appropriate use of algorithms with or without technology to solve
problems as evidenced by homework problems or class discussions or
problem/project presentations or quizzes/exams.
 Reflective writing;
 Peer tutoring on use of algorithms with or without technology to solve problems.
6D3 Performance Indicator The competent teacher of mathematics demonstrates the uses
of numerical approximations as a basis for numerical integration and numerical-based
proofs.
 Evaluations of ability to apply and use numerical integration to approximate results
and solve problems as evidenced by homework problems or class discussions or
problem/project presentations or quizzes/exams;
 Reflective writing.
7C8 Performance Indicator The competent teacher of mathematics uses modeling and
visualization to hypothesize about and predict measurements.
 Evaluations of homework problems or class discussions or problem/project
presentations or quizzes/exams on modeling areas under curve as summation of
rectangles and use of slices and shells to visualize volume.
8C1, 8C2, and 8C4 Performance Indicator The competent teacher of mathematics
understands concepts of rates of change, patterns leading to limits, distance, area, volume,
shapes that lead to limits, and concepts of limits.
 Evaluations of homework problems or class discussions or problem/project
presentations or quizzes/exams;
 Reflective writing;
 Completion of proofs involving limits and how they relate to rates of change,
distance, area, and volume.
8C5 and 8C6 Performance Indicator The competent teacher of mathematics understands
the basic concepts of calculus, analytic geometry and their applications.
 Evaluations of homework problems or class discussions or problem/project
presentations or quizzes/exams;
 Reflective writing;
 Completion of proofs on ALL aspects of calculus: derivatives, integrals, continuity,
limits, applications.
8G3 Performance Indicator The competent teacher of mathematics uses differentiation,
integration, and other concepts of calculus to solve problems and interpret results.
 Evaluations of homework problems or class discussions or problem/project
presentations or quizzes/exams