MA 233

Multivariable Calculus

Mark Parker

Class: MWF, 2:00 - 2:50, Simperman 114

Lab: Th, 9:30 - 10:45, Fortin 115

Recitation: T, 9:30 - 10:45, Simperman 114

Introduction

Up until now, your mathematics courses have mainly focused on functions of one variable, which has forced us to make many simplifying assumptions in our quest to model real-world phenomena. This semester, we will build upon the analytical skills you've developed in calculus of the single variable to expand beyond this limitation. In particular, we will work with multivariable and vector functions to expand our capabilities. Luckily everything you've learned in calculus up to now is important, since we will often reduce multi-dimensional problems to one-dimensional problems. But we will also go in the other direction, as we will expand the concepts of derivatives and integrals into the higher dimensions too. Because the world is multi-dimensional, this course has many real-world applications.

We will continue our threaded approach to learning mathematics by taking side tours from calculus to tie together concepts from your previous courses and demonstrate their applicability in our current setting. In our journey, we will make use of both the calculator and Mathematica. Being comfortable with both technologies will help you when trying to solve problems on your own.

My Goals for you this semester are:

1. Extend your knowledge and understanding of mathematical concepts, specifically in the study of differential and integral calculus for multivariable and vector functions.
2. Develop geometric and analytical sense of multivariable and vector calculus concepts.
3. Refine your skills in formulating and solving problems involving multivariable and vector functions, differential calculus, integral calculus, optimization, and series.
4. Mature your skills in designing mathematical models using the tools of multivariable calculus to capture the essence of real-world patterns and phenomena.
5. Classify, analyze, transform, and solve mathematical constructs involving multivariable functions.
6. Interpret mathematical models and their solutions in the context of their real-world applications.
7. Critique mathematical models to identify their strengths and weakness and modify them to make them better models.
8. Expand your knowledge and understanding of the real world through mathematical analysis.
9. Cultivate your skills to effectively use modern computing, information, and communication technologies.

Text

Multivariable Calculus, 3rd Edition

McCallum, Hughes-Hallett, Gleason, et al.

John Wiley & Sons

Grading

Your grade will translate to a letter grade as follows :

• A 90% or better
• B 80% or better
• C 70% or better
• D 60% or better
• F otherwise