CALCULUS IN THREE DIMENSIONS (21-259) SPRING 2015 Instructor: Dr. Dana Mihai, 8128 Wean Hall [email protected] Lecture: Lecture 1: MWF, DH A302, 12:30-1:20 pm Lecture 2: MWF, BH A51, 9:30-10:20 am Course website: Office hours: Posted on Blackboard *LEARNING OBJECTIVES These objectives should help you understand the level of preparation you should achieve in this class (a list of learning goals will be provided for each section covered). After completing this course, you should be able to: -Solve mathematical models, given as such or obtained from real life problems, by using calculus concepts and techniques (e.g., vector operations, level sets, continuity and differentiability, integration in various coordinate systems, optimization methods, Gauss-Green Theorems) -Interpret and analyze the results in the context of the problem (for example, what is the significance of the value of the Lagrange multiplier in an optimization problem, does a negative value make sense for an area) -Formulate real life problems (word problems) into mathematical language, and solve them by using calculus concepts and techniques -Recognize situations in which calculus in 3d concepts can be applied to physics, engineering, economics (or other fields), and identify which concepts and techniques are necessary to solve a specific problem You will be expected to understand how various formulas and results are obtained. *COURSE DESCRIPTION Calculus in Three Dimensions is a course which will expand all concepts discussed in Calculus of Functions of one variable to functions of two variables: domain, graph, limits and continuity, derivatives, chain rule, optimization, integrals in various coordinate systems. Some topics that are specific to calculus in three dimensions will also be introduced: parametric surfaces and curves, line integrals, surface integrals, Green-Gauss theorems. Students will be expected to have a solid understanding of these concepts and be able to apply them to solve various problems. We will discuss how most of the formulas are obtained and also the interpretation of the various quantities involved. The present course has a pyramid-like structure, it builds on concepts covered from the beginning of the semester. Due to this structure, the Vector Calculus chapter (the last chapter covered in the course) uses all the previous chapters. If you study well throughout the semester, this should not be a challenge.

*PREREQUISITES: 21-122: Integration and Approximation. In addition, you are expected to be thoroughly familiar with all concepts and formulas from Calculus of Functions of one variable (which is a prerequisite for 21-122). Calculus in three dimensions builds onto the prerequisites: if it has been a while since you’ve studied Calculus of functions of one variable or if you don’t master the material even if you took it recently, I strongly suggest you review the material before the beginning of the course. In addition, you are expected to be familiar with vectors and vector operations in two dimensions.