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JOHN CABOT UNIVERSITY

COURSE CODE: "MA 490"
COURSE NAME: "Calculus III"
SEMESTER & YEAR: Fall 2022
SYLLABUS

INSTRUCTOR: TBA
EMAIL: [email protected]
 HOURS: TBA
TOTAL NO. OF CONTACT HOURS: 45
CREDITS: 3
PREREQUISITES: Prerequisites: MA 299 Calculus II and MA 491 Linear Algebra (both with a grade of C or above)
OFFICE HOURS:
COURSE DESCRIPTION:
This course builds on the material presented in Calculus II. It covers vector and multivariable calculus. The mathematical tools and methods introduced in the course are used extensively in the physical sciences, engineering, and economics. The main aim is to arrive at two of the most important theorems in vector calculus: Green’s Theorem and Stokes’ Theorem.
SUMMARY OF COURSE CONTENT:

Double integrals and change of variables (some revision from Calculus II, some new material). Parametric curves in 2D and 3D, vector-valued functions, tangent and normal lines to parametric curves.  Vector fields and line integrals in the plane; path independence and conservative fields; Green’s Theorem. Triple integrals. Vector fields in 3D and surface integrals; Stokes’ Theorem. Note: the pace of the course will be very fast; there is a lot of material to get through.

Many classes will be based around guided group problem-solving activities. Solving problems and being able to communicate clearly your solutions to other students and to the professor is an absolutely essential component of learning the material and passing the assessments.

In this course, the concepts count much more than computations. When doing your homework, you will are encouraged to use computation tools, except for some problems that I will ask you to solve completely manually, and where I will require that you show all the steps of your work.
LEARNING OUTCOMES:

Students will demonstrate a working knowledge of multivariable calculus topics, including knowledge of theorems with complete assumptions.

Students will demonstrate the ability to use methods of multivariable calculus and perform computations accurately and efficiently, both manually and using computational tools.

Students will demonstrate the ability to solve problems that are unlike ones they have seen before.

Students will be able to follow more complicated proofs done in class, and will be able to construct elementary proofs independently.

Students will demonstrate the ability to communicate their mathematical ideas clearly, both to me and to the other students in the class.

TEXTBOOK:
Book TitleAuthorPublisherISBN numberLibrary Call NumberCommentsFormatLocal BookstoreOnline Purchase
Calculus: Early TranscendentalsJ. StewartBrooks Cole 978-128574155     
REQUIRED RESERVED READING:
NONE

RECOMMENDED RESERVED READING:
NONE
GRADING POLICY
-ASSESSMENT METHODS:
AssignmentGuidelinesWeight
Final examThe final exam is comprehensive. You must achieve at least a 60% on the final exam in order to pass this course. 40%
CourseworkStarting from week 2, there will be a homework assignment given. Your solutions will be graded and the best 10 of your assignments will be counted towards your coursework grade. 60%

-ASSESSMENT CRITERIA:
AWork of this quality directly addresses the question or problem raised and provides a coherent argument displaying an extensive knowledge of relevant information or content. The student demonstrates complete, accurate, and critical knowledge of all the topics, and is able to solve problems autonomously.
BThis is highly competent level of performance and directly addresses the question or problem raised.There is a demonstration of some ability to critically evaluate theory and concepts and relate them to practice. The work does not suffer from any major errors or omissions and provides evidence that the student uses clear logic in their arguments.
CThis is an acceptable level of performance and provides answers that are clear but limited, reflecting the information offered in the lectures. Mathematical statements are properly written most of the time.
DThis level of performances demonstrates that the student lacks a coherent grasp of the material. Important information is omitted and irrelevant points included. Many mistakes are made in solving the problem raised. In effect, the student has barely done enough to persuade the instructor that they should not fail.
FThis work fails to show any knowledge or understanding of the task or problem. Most of the work produced is unacceptable or irrelevant.

-ATTENDANCE REQUIREMENTS:

ATTENDANCE REQUIREMENTS AND EXAMINATION POLICY

You cannot make-up a major exam (midterm or final) without the permission of the Dean’s Office. The Dean’s Office will grant such permission only when the absence was caused by a serious impediment, such as a documented illness, hospitalization or death in the immediate family (in which you must attend the funeral) or other situations of similar gravity. Absences due to other meaningful conflicts, such as job interviews, family celebrations, travel difficulties, student misunderstandings or personal convenience, will not be excused. Students who will be absent from a major exam must notify the Dean’s Office prior to that exam. Absences from class due to the observance of a religious holiday will normally be excused. Individual students who will have to miss class to observe a religious holiday should notify the instructor by the end of the Add/Drop period to make prior arrangements for making up any work that will be missed. The final exam period runs until December 16th.

DURING THE SEMESTER, MAKE-UP EXAMS WILL NOT BE GIVEN UNDER ANY CIRCUMSTANCES. If you need to miss an assessment, the weight of that assessment will be shifted to the final. If you have to miss the final, if you are in good standing with the course, you can ask for an incomplete. If you are not in good standing and miss the final, I will be unable to assign a grade for the course, other than by considering the class tests you have already completed (this means you will be assigned a D or an F as appropriate).

ACADEMIC HONESTY
As stated in the university catalog, any student who commits an act of academic dishonesty will receive a failing grade on the work in which the dishonesty occurred. In addition, acts of academic dishonesty, irrespective of the weight of the assignment, may result in the student receiving a failing grade in the course. Instances of academic dishonesty will be reported to the Dean of Academic Affairs. A student who is reported twice for academic dishonesty is subject to summary dismissal from the University. In such a case, the Academic Council will then make a recommendation to the President, who will make the final decision.
STUDENTS WITH LEARNING OR OTHER DISABILITIES
John Cabot University does not discriminate on the basis of disability or handicap. Students with approved accommodations must inform their professors at the beginning of the term. Please see the website for the complete policy.
SCHEDULE

Week 1: Double integrals and change of variable.

Weeks 2 and 3: Parametric curves in the plane, vector-valued functions and parametric curves in space. Tangent and normal lines. 

Weeks 4 to 13: Topics in Vector Calculus.

Week 14:  Time permitting, we may look also at the Divergence Theorem.