Syllabus for MAT-332



Calculus IV is an intensive, higher-level course in mathematics that builds on Calculus II and III. The course aims at serving the needs of a wide student audience, including students in engineering, mathematics, the physical and life sciences, and economics. It is constructed around multiple focal points with the intention of helping students become creative and efficient problem solvers.

This course focuses on the calculus of real- and vector-valued functions of one and several variables. Topics covered include infinite sequences and series, convergence tests, power series, Taylor series, and polynomials and their numerical approximations. Applications of multiple integrals and integral transformations in two and three dimensions are also covered.  It also discusses topics of vector integral calculus such as line and surface integrals, theorems of Green, Gauss and Strokes, and  their applications to the physical sciences. This course also provides an introduction to first-order and second-order differential equations.



After completing this course, you should be able to:

  1. Solve first-order ordinary differential equations using separation of variables and Euler’s method.
  2. Solve a system of first-order differential equations.
  3. Test the convergence of infinite series using different methods.
  4. Construct and use Taylor series to approximate functions and integrals.
  5. Find the Fourier series expansion for different functions.
  6. Evaluate double integrations over a general area in rectangular and polar coordinates.
  7. Evaluate triple integrals in rectangular, cylindrical and spherical coordinates.
  8. Find the gradient field associated with a given scalar function.
  9. Determine if a given vector field is conservative using line integrals.
  10. Use Green’s theorem and Stokes’ theorem to evaluate integrals.
  11. Solve second-order differential equations.
  12. Use second-order differential equations to model physical problems.


You will need the following materials to do the work of the course. The required textbook is available from the College's textbook supplier, MBS Direct.

Required Textbook

ISBN-13: 978-0-07-353232-5

ISBN-13: 978-0-07-723590-1


Calculus IV is a three-credit online course, consisting of six (6) modules. Modules include topics, learning objectives, study materials, and activities. Module titles are listed below.


For your formal work in the course, you are required to participate in online study group activities, complete written assignments, and take two proctored examinations—a midterm and a final. See below for more details.

Consult the course Calendar for assignment due dates.

Online Participation/Study Group Activities

This course requires you to participate in six (6) graded study group activities using group discussion forums. There is also an ungraded but required Introductions Forum in module 1.

The Study Group activities in this course provide an opportunity for you to practice and apply analytical and computational skills within an interactive group setting. In so doing, you can benefit from the help of your classmates and share your understanding of chapter concepts. These activities take place in two phases: group problem solving (or group work) and posting worked-out solutions.

Phase 1: Group Work

Phase 1 (Group Work) involves group problem solving and discussion and counts 60 percent toward your activity grade. Participation in group work entails posting draft solutions to textbook exercises and discussing them with other group members in the module’s Group Work Forum.

Phase 2: Posting Solutions

Phase 2 (Posting Your Solutions) involves posting worked-out solutions to the study group exercises and counts 40 percent toward your activity grade. Participation in phase 2 entails posting your worked-out solutions to the exercises selected in phase 1 and discussing them in the module’s Solutions Forum.

Written Assignments

You are required to complete six (6) written assignments. The written assignments draw on even-numbered exercises from the textbook. For each assignment, answer all assigned exercises, and show all work.

Assignments must be prepared electronically with a word processor, preferably using whatever equation editor comes with your word processing software. However, if your word processor is not compatible with your mentor's word processor, you will need to save your document as a rich-text file (.rtf) before submitting it. Check with your mentor first to determine file compatibility. (Important: Use the equation editor to insert equations into your word-processed document, not to create the document itself.)

When preparing your answers, please identify each exercise clearly by textbook section and exercise number. Be sure to include your name at the top of the paper, as well as the course name and code and the

semester and year in which you are enrolled. To receive full credit for your answers, you must show all work and include complete solutions.


You are required to take two (2) proctored online examinations: a midterm exam and a final exam. Both exams require that you use the College's Online Proctor Service (OPS). Please refer to the "Examinations and Proctors" section of the Online Student Handbook (see General Information area of the course Web site) for further information about scheduling and taking online exams and for all exam policies and procedures. You are strongly advised to schedule your exam within the first week of the semester.


Online exams are administered through the course Web site. Consult the course Calendar for the official dates of exam weeks.

Midterm Examination

The midterm exam is two and half hours long and covers modules 1 to 3 of the course (textbook chapters 7, 8, and 13). It consists of thirty multiple-choice questions.

The exam is open book, but not open notes. In this regard you are permitted to use only a scientific (nongraphing) calculator and the authorized textbook. But you are not allowed to consult a solutions manual, notes of any kind (including graded or ungraded activities), or any other reference sources or sources of information. The use of blank scratch paper for doing math calculations is permitted during online test administrations.

Final Examination

The final exam is two and half hours long and covers modules 4 to 5 of the course (textbook chapters 14 and 15). It consists of twenty-seven multiple-choice questions.

The exam is open book, but not open notes. In this regard you are permitted to use only a scientific (nongraphing) calculator and the authorized textbook. But you are not allowed to consult a solutions manual, notes of any kind (including graded or ungraded activities), or any other reference sources or sources of information. The use of blank scratch paper for doing math calculations is permitted during online test administrations.

Statement about Cheating

You are on your honor not to cheat during an exam. Cheating means:

If there is evidence that you have cheated or plagiarized in an exam, the exam will be declared invalid, and you will fail the course.


Your grade in the course will be determined as follows:

All activities will receive a numerical grade of 0–100. You will receive a score of 0 for any work not submitted. Your final grade in the course will be a letter grade. Letter grade equivalents for numerical grades are as follows:






























Below 60

To receive credit for the course, you must earn a letter grade of C or better (for an area of study course) or D or better (for a nonarea of study course), based on the weighted average of all assigned course work (e.g., exams, assignments, discussion postings, etc.).


First Steps to Success

To succeed in this course, take the following first steps:

Study Tips

Consider the following study tips for success:


Students at Thomas Edison State College are expected to exhibit the highest level of academic citizenship. In particular, students are expected to read and follow all policies, procedures, and program information guidelines contained in publications; pursue their learning goals with honesty and integrity; demonstrate that they are progressing satisfactorily and in a timely fashion by meeting course deadlines and following outlined procedures; observe a code of mutual respect in dealing with mentors, staff, and other students; behave in a manner consistent with the standards and codes of the profession in which they are practicing; keep official records updated regarding changes in name, address, telephone number, or e-mail address; and meet financial obligations in a timely manner. Students not practicing good academic citizenship may be subject to disciplinary action including suspension, dismissal, or financial holds on records.


Academic Dishonesty

Thomas Edison State College expects all of its students to approach their education with academic integrity—the pursuit of scholarly activity free from fraud and deception. All mentors and administrative staff members at the College insist on strict standards of academic honesty in all courses. Academic dishonesty undermines this objective. Academic dishonesty can take the following forms:

Please refer to the Academic Code of Conduct Policy in the College Catalog and online at




Using someone else’s work as your own is plagiarism. Thomas Edison State College takes a strong stance against plagiarism, and students found to be plagiarizing will be severely penalized. If you copy phrases, sentences, paragraphs, or whole documents word-for-word—or if you paraphrase by changing a word here and there—without identifying the author, or without identifying it as a direct quote, then you are plagiarizing. Please keep in mind that this type of identification applies to Internet sources as well as to print-based sources. Copying and pasting from the Internet, without using quotation marks and without acknowledging sources, constitutes plagiarism. (For information about how to cite Internet sources, see Online Student Handbook > Academic Standards > “Citing Sources.”)

Accidentally copying the words and ideas of another writer does not excuse the charge of plagiarism. It is easy to jot down notes and ideas from many sources and then write your own paper without knowing which words are your own and which are someone else’s. It is more difficult to keep track of each and every source. However, the conscientious writer who wishes to avoid plagiarizing never fails to keep careful track of sources.

Always be aware that if you write without acknowledging the sources of your ideas, you run the risk of being charged with plagiarism.

Clearly, plagiarism, no matter the degree of intent to deceive, defeats the purpose of education. If you plagiarize deliberately, you are not educating yourself, and you are wasting your time on courses meant to improve your skills. If you plagiarize through carelessness, you are deceiving yourself.

For examples of unintentional plagiarism, advice on when to quote and when to paraphrase, and information about writing assistance and originality report checking, click the links provided below.

Examples of Unintentional Plagiarism 

When to Quote and When to Paraphrase

Writing Assistance at Smarthinking

Originality Report Checking at Turnitin


Disciplinary Process

First-time incidents of academic dishonesty concerning plagiarism may reflect ignorance of appropriate citation requirements. Mentors will make a good faith effort to address all first-time offenses that occur in courses. In these cases, the mentor may impose sanctions that serve as a learning exercise for the offender. These may include the completion of tutorials, assignment rewrites, or any other reasonable learning tool including a lower grade when appropriate. The mentor will notify the student by e-mail. Decisions about the sanctions applied for subsequent plagiarism offenses or other violations will be made by the appropriate dean’s office, with the advice of the mentor or staff person who reported the violation. The student will be notified via certified mail of the decision. Options for sanctions include:

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