Multivariable calculus lies in the intersection of three of the most important branches of mathematics: algebra, analysis, and geometry. It demonstrates the elegance and beauty of mathematics, as well as its sublime utility. By extending the concepts of one-variable calculus to higher dimensions, we encounter a variety of new issues and subtleties, many of which require a deep geometric understanding to resolve. Through this course you will: learn vector calculus; strengthen your geometric visualization skills; practice translating between algebraic, analytic, and geometric perspectives; and develop your technical writing skills. In addition to being a course about the power of integrating multiple mathematical perspectives, the second half of the course will be the story of a theorem - an amazing, beautiful theorem which will unify a number of course concepts. Your grade will be based on your level of achievement in each of the following student learning outcomes
- Your content knowledge
- As demonstrated on in-class exams and quizzes
- Your reasoning and visualization skills
- As demonstrated on exams and supplemental geometry problems
- Your technical writing ability
- As demonstrated on exams and and supplemental geometry problems
- Your engagement in the mathematical endeavor
- As demonstrated on WeBWork homework sets and Math Colloquium attendance
