MA 1024 - Calculus IV

A-Term, Fall 2021

Prof. B. S. Tilley

Department of Mathematical Sciences

Worcester Polytechnic Institute

Phone: (508) 831-6664

e-mail: tilley@wpi.edu

Tilley Home Page

Office Hours:

In Person: MR: 11:00-11:50

T: 4:00-4:50

MS Teams: W: 3:00-3:50

Course Description: This course provides an introduction to multivariable calculus. Topics covered include: vector functions, partial derivatives and gradient, multivariable optimization, double and triple integrals, polar coordinates, other coordinate systems and applications. Recommended background: MA 1023. Although the course will make use of computers, no programming experience is assumed.

Texts:

Vector Calculus, Fourth Edition, Susan Jane Colley, Pearson, ISBN-13: 978-0-321-78065-2

Infinite Powers, Steven Strogatz, Houghton Mifflin Harcourt, ISBN-13: 978-1-328-88001-7

Reference:

Multivariable and Vector Calculus, Joseph D. Fehribach, De Gruyter, ISBN-13: 978-3-11-066020-9

Lecture Schedule: Click calendar link on right.

Course Objectives

This course is both a culmination of the topics from calculus of one dimension and an introduction to topics and methods used in advanced undergraduate courses in mathematics, science, and engineering. Particular objetives of this course include:

  • Understand multivariable functions, limits, and continuity

  • Become fluent in differentials, chain rule, directional derivatives, and gradients

  • Become fluent in multivariable integrals in Cartesian, cylindrical, and spherical coordinates

  • Understand the roles of definition, theorem, and proof

  • Articulate the historical and current impact of calculus in science and society.

Course Organization

The class typically meets 5 times per week: 4 lectures on MTRF, and 1 discussion section on F. Students are responsible for all material presented in lecture and discussion. My expectations for these activities are

  • Lectures: This is the first opportunity for a student to see the material, and my expectation of students after a lecture is to have an introduction of the material, not to demonstrate mastery. The goal is to give a high-level description of the main points of the topics, and to provide some examples illustrating the topic. These lectures are recorded via Echo 360, and these videos can be accessed through the course Canvas page.

  • Discussions: Students have an opportunity to sit down and work through problems on a topic with an instructor and have their individual questions addressed. It is through the discussion that the student can get major questions asked so that after discussion, the student can continue to work through the problems to develop mastery.

  • Microsoft Teams: Course materials can be found on the Microsoft Teams team Calculus IV, as well as on the Canvas page. In the event that lectures need to be delivered remotely, they will take place through MS Teams.

Students are expected to spend an additional 8-12 hours per week studying outside of class: reading the text, organizing notes, and solving problems. In previous years, the average time, self-reported, spent outside of class on this course is 10 hours

Grade Breakdown

See the Deliverables page for more information:

  • Exams

    • Average of top 2 scores: 50%

    • Lowest score: 20%

  • Project: 10%

  • Quizzes: 10%

  • Labs: 10%

Special Arrangements

If you need course adaptations or accommodations because of a disability, or if you have medical information to share with me, please make an appointment with me as soon as possible. My office location and office hours are listed above. If you have not already done so, students with disabilities who believe that they may need accommodations in this class are encouraged to contact the Office of Accessibility Services (OAS) as soon as possible to ensure that these accommodations are implemented in a timely fashion. The OAS is in Daniels Hall, (508) 831-4908. Students who need accommodations for exams are required to make the arrangements to take these exams at the Exam Proctoring Center (EPC) on the day of the exam.

Electronics Policy

All lectures (audio and video) are captured through course capture and can be found on the course Canvas page. NO recording of audio or video by students is allowed during lecture or during discussion. Laptops, phones, and tables should be turned off during the lecture and conference sessions. If you take notes (typing/stylus only) using these devices during lecture, then you should sit somewhere in the room where your screen activity is not distracting to your neighbors.

Exam Policy

Prior to the start of each exam, you must place all of your belongings (e.g., cell phone, study materials, etc.) in your backpack and under your desk, so that no items are visible during the exam. All exams this term are closed book, closed notes, and no electronic devices are permitted. You will be required to show your WPI ID when turning in your exam to verify your identity.

Final Grades

In general, grades will follow the general distribution


A: 90-100

B: 79-89

C: 68-78

NR: < 68