Foundations of Multivariable Calculus – MATH 530

Course Description

For information regarding prerequisites for this course, please refer to the Academic Course Catalog.

Rationale

This course is an introduction to real multivariate calculus at the graduate level. After successful completion of this course the student should be able to calculate and explain all the major theorems and results of standard multivariable calculus. Topics covered include the analysis of limits, continuity, differentiation, integration and power series for functions in one or more variables are developed. In addition, applications to optimization in several variables are discussed. The analytic geometry of curves and surfaces are analyzed with calculus. Integration of vector fields along curves and surfaces is developed and the major theorems of vector calculus are detailed and applied. This course of study should prepare both teachers and students for further study or instruction of multivariable calculus.

Course Assignment

Textbook readings and lecture presentations/notes

Course Requirements Checklist

After reading the Course Syllabus and Student Expectations, the student will complete the related checklist found in the Course Overview.

Video Discussion: Student Introduction

The purpose of this video is to introduce the student and prepare the student for future video presentations.

Video Demonstration Assignments (4)

The student will create 4 video demonstrations based on the provided prompts. Videos must be precise, well-practiced, and a maximum of 8 minutes.

Homework Assignments (6)

Homework problems are essential to this course and students will be assigned homework problems to complete throughout the course. One homework problem out of the assigned problems will be submitted for grading in its assigned Module: Week.

Quiz: Homework Portfolios (2)

Homework will be assigned weekly. Homework assignments in the first half of the course will be scanned into a single document and submitted to Quiz: Homework Portfolio Midterm before the Midterm Exam. Homework assignments in the second half of the course will be scanned into a single document and submitted as Quiz: Homework Portfolio Final before the Final Exam. Many exam problems will come from the assigned homework.

Quizzes (8)

Each quiz will be timed, handwritten, and open-book/open-notes/open-video and will cover material from the videos in the assigned modules. The time limit for each quiz is 30 minutes. The quizzes are some combination of T/F, multiple choice and/or fill in the blank questions.

Quiz: Exams (2)

Each exam will be timed, handwritten, and open-book/open-notes/open-video and will cover the course material for the assigned modules. The time limit for the Midterm Exam is 90 minutes (1 hour, 30 minutes) while the time limit for the Final Exam is 180 minutes (3 hours). On all written work, the student is expected to write correct mathematics to avoid point deductions.