Multivariable Calculus
Multivariable Calculus steps into the Calculus of 3D, studying how the Calculus of single variable translates and generalizes into the Calculus of many variables - or multivariable Calculus.Multivariable Calculus is a course known by many different names at various Colleges/Universities, including:
- Calculus III
The third semester of a 4-credit hour Calculus sequence, as it is in our Distance Calculus program. - Calculus IV
Usually the fourth quarter of a 3-credit hour Calculus sequence. - Vector Calculus
An appropriate title in that we study vector fields and the generalization of the derivative; most textbooks for this course entitled this way, too. - Multivariable Calculus
The most descriptive moniker, encompassing all aspects of Calculus of more than 1 variable.
For the student, Multivariable Calculus is where you usually learn - really learn - the topics from Calculus I and II - not because Multivariable Calculus is harder, but just that you revisit the topics from Calculus I and II, but now looking for how these concepts will generalize from a single variable to multiple variables. It is through this generalization process that many students have the "ah-ha!" moment with the original topics from single variable calculus.
Now The Computer Graphics Get Fun!
While graphing in 2D is very powerful and illustrative for exploring the topics of Calculus I and II, it is the 3D graphics that solidify Multivariable Calculus as being the course that demands the usage of a computer algebra and graphing system.We utilize the LiveMath™ software, where its power and ease to investigate 3D graphs shines: you may pick up a 3D graph, and spin it around, and even "throw" it to set it in motion.
LiveMath's ability to investigate the 3D objects from all viewpoints easily - just by dragging on the graph window - gives us the right tool we need to explore this 3D world from the top, the bottom, the right, the left, the front, the back - all just by dragging the mouse.
Curriculum: Calculus&LiveMath™
The curriculum for Multivariable Calculus is the e-textbook Vector Calculus&LiveMath™, which is converted from the original Vector Calculus&Mathematica™ courseware series by Davis/Porta/Uhl (published by MathEverywhere, Inc.To accompany these LiveMath™ notebooks from this e-text, we also present Video Commentary Lectures on the Basics and Tutorials notebooks in the Vector Calculus&LiveMath™ e-text. These videos demonstrate how to use LiveMath™ as well as discuss the Calculus topics, as if reading and exploring along with the professor (which is exactly what you are doing!).
The Vector Calculus&LiveMath™ e-text is a very challenging curriculum - more difficult that your average multivariable calculus textbook. While this may seem a bit daunting at first, it is actually quite rewarding as you work your way through the course, and discover that the topics are rich and captivating, and really not all that difficult when presented with the expertise of Davis/Porta/Uhl supported by the power of the LiveMath™ computer algebra and graphing software.
Examples of the Curriculum
Below are some PDF "print outs" of a few of the LiveMath™ notebooks from Vector Calculus&LiveMath™ by Davis/Porta/Uhl. Included as well is an example homework notebook completed by a student in the course, demonstrating how the homework notebooks become the "common blackboards" that the students and instructor both write on in their "conversation" about the notebook.- Basics Notebook Example: VC.02.B3 - Normal Vectors for Curved Surfaces in 3D
- Basics Notebook Commentary Movie: iTunes or VLC
- Homework Notebook Example: VC.02.G1 - Plane Fundamentals
Course Catalog Listing
Course Description: Applications of differential and integral calculus to vector-valued functions, partial derivative, multiple integrals, vector field analysis, line and surface integrals, Jacobian transformations, Green, Stokes, and Gauss Theorems.
Prerequisite: Calculus II
Detailed Course Syllabus in PDF