MA 233

Multivariable Calculus and Linear Algebra

Mark Parker

MWF, 2:00 - 2:50, Simperman 123

T, 9:30 - 10:45, Simperman 123

Th, 9:30 - 10:45, Simperman 146

Introduction

Up until now, your mathematics courses have mainly focused on functions of one variable, and this has meant essentially working in the xy-plane. Since the real world is three-dimensional, we need to consider functions of more than a single variable! 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 focus on the role of linear algebra, especially linear transformations, in modeling. 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 multivariable and vector functions, differential and integral calculus for multivariable and vector functions, and linear algebra.
2. Refine your skills in formulating and solving problems involving multivariable and vector functions, differential calculus, integral calculus, optimization, series, and linear algebra.
3. Mature your skills in designing mathematical models using the tools of multivariable calculus to capture the essence of real-world patterns and phenomena.
4. Classify, analyze, transform, and solve mathematical constructs involving multivariable functions.
5. Interpret mathematical models and their solutions in the context of their real-world applications.
6. Critique mathematical models to identify their strengths and weakness and modify them to make them better models.
7. Expand your knowledge and understanding of the real world through mathematical analysis.
8. Cultivate your skills to effectively use modern computing, information, and communication technologies.

Text

Thomas' Calculus 10th Edition

Finney, Weir, and Giordano

Addison Wesley Longman

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