Open Course Site Multivariable Calculus

The Open Course Site Initiative

This site is part of the Open Course Project (OCP), which aims to support student success in undergraduate mathematics courses. Through support from the Center for Promoting Inclusion and Equity in the Sciences, this project involves the development of open curriculum through public websites that Georgia Tech students can use as a refresher or as a supplement to their learning.

The OCP aims to benefit several student groups who need a refresher and/or additional practice, including undergraduate students enrolled in these courses, students in upper-level courses that use our courses as pre-requisites, and transfer students and other students who are re-entering college for an undergraduate or graduate program after an extended time away from college.

The OCP is developing Canvas sites for College Algebra, Precalculus, Multivariable Calculus and Introductory Statistical Methods. This particular site focuses on multivariable calculus.

Multivariable Calculus

Multivariable Calculus is a required course for students in a wide range of undergraduate degree programs. It is also an important topic for many research projects across campus. The curriculum in this site is meant to help students involved in these projects and programs that require an understanding of the calculus of functions of several variables.

Multivariable calculus extends concepts introduced in differential and integral calculus to functions of more than one variable. Applications to mathematical modeling and practical problems, such as constrained optimization problems and least-squares are introduced as a means to help students prepare for the eventual application of calculus to their particular areas of study.

Required Materials

Students should not need a calculator to complete the activities on this site. Having an up to date web browser and a high speed internet connection should be sufficient.

Recommended Prerequisites

Before starting this course it is recommended that students have completed:

a differential calculus course, such as MATH 1551, and
an integral calculus course, such as MATH 1552.

Recommended Textbooks

There are many free, open textbooks that can be found online that are meant to introduce students to multivariable calculus.

This site will follow the Calculus Volume 3 Textbook on OpenStax. This textbook is designed for a typical college level multivariable calculus course, as it guides students through core concepts of calculus and helps them to understand how those they can be applied to their lives and the world around them. It covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and more.

Coruse Objectives

Students using the materials in this site will be able to do the following.

Analyze and construct examples of three-dimensional vectors, surfaces and multivariable functions using both algebraic and geometric relationships.
Analyze vector-valued functions using calculus to characterize motion and paths in two and three dimensions.
Calculate and interpret derivatives of multivariable functions to describe how such functions change.
Analyze and solve multivariable optimization problems.
Construct and evaluate integrals of multivariable functions using Cartesian and other coordinate systems.
Construct and evaluate integrals of scalar and vector functions over curves and surfaces using the theorems of Green, Gauss, and Stokes, and apply these theorems to model physical quantities such as flux and circulation.
Contextualize mathematical quantities involving multivariable functions to interpret their meaning within problems that arise in everyday life.