Description of Course Goals and CurriculumProfessor Hansheng Diao really wants students to learn how to approach higher dimensional mathematics by generalizing and applying concepts in one and two dimensional calculus. This course is the advanced equivalent of MAT 201, which is a mandatory prerequisite for BSE as well as many STEM majors. It covers vector spaces, limits and differentiation of vector valued functions, Taylor’s formula, Lagrange multipliers, 2D and 3D integration, line and surface integrals, and generalization of the fundamental theorem of calculus to higher dimensions. The course starts from the basics of vector manipulation, limits, partial differentiation, and Lagrange multipliers in the first half of the semester, then moves to higher dimension integrals, line and surface integrals, and ends with Green’s Theorem, Stoke’s Theorem, and Gauss’ Theorem, which tie many of the previous concepts together. This course takes a more abstract and proof-based approach compared to MAT 201, and is recommended for prospective physics majors or those with a strong passion in applied mathematics. In addition to learning how to make computations in multivariable calculus, a student by the end of the course should be able to understand and prove how and why certain methods work. This course expects you to be knowledgeable in one and two dimensional calculus. There isn’t any particular “hidden” expectation in this course, as the professor very briefly reviews relevant 1D/2D concepts before moving onto higher dimensions, but you should brush up on calculus I and II before class begins.
Learning From Classroom InstructionProfessor Diao covers material very quickly during lecture, so it’s recommended that you read the textbook before coming to lecture. Taking good notes is essential to remembering the large amount of information being presented, but it’s more important that you are constantly listening to what the lecturer has to say. Ask questions immediately if you don’t understand something, or if you feel the lecturer is going too fast, just say so, as the professor is more than happy to help you. After lectures, you can take several steps to ensure you have a better understanding of the concepts in the future. You can read the textbook again, but this time keep in mind of what was taught in lecture; try noting discrepancies in approaches that Professor Diao took and the book takes, or note things that Professor Diao taught but the book does not. You can also go back to your notes and highlight important or difficult sections so you emphasize them during later review. If you ever miss a lecture for whatever reason, make sure you are up to date before attending the next lecture, as falling behind is extremely detrimental. You can do so by asking a fellow peer about the material covered in class, and then reading the textbook or the online lecture notes. Do keep in mind, however, that the textbook doesn’t cover everything taught in lecture, so the lecture notes will probably be more helpful. There are also optional weekly precepts. Preceptors generally review topics covered in that week, as well as key problem-solving methods.
Learning For and From AssignmentsThe problem sets in this course are designed to challenge you to think critically and apply lecture concepts to problems. Problems sets are divided into two sections: textbook problems and supplementary problems. The textbook problems focus on computational aspects of multivariable calculus and are generally easier, while the supplementary problems, made by Professor Diao, are often more abstract and proof-based, which allows the student to truly understand the how’s and why’s of methods in calculus. Never, ever save an assignment for the last second. Start early, since you will most likely have questions on these assignments, which you can ask either during office hours or during the Sunday homework sessions. Also, it’s recommended that you work in groups for the supplementary problems, as they are significantly more difficult than the textbook problems. It’s crucial that you grasp the supplementary problems completely, as they are very reflective of what the quizzes and tests will be like. As for quizzes and tests. Expect the problems that show up on exams to be somewhat like the supplementary problems in the homework. Usually the tests require you to apply familiar concepts in class to unfamiliar situations, so merely understanding the approach to a single problem in the homework is not sufficient; you want to find a way to apply that method more generally. The questions on exams are mostly never multiple choice/true or false, and if they are, they still require some mathematical explanation for your answer. For all other problems, as is the case for most math classes, show every step of your work, which can be awarded partial credit even if your answer is wrong. When using a formula for a question, explain why you are using that formula. To best study for a test, look back at the old quizzes, midterms, and finals posted on blackboard. However, remember that they may not be accurate of what the actual test is like. It’s good to note that the Professor Diao started teaching in Fall 2015, so tests from then on may be more reliable as indicators of the actual test. It’s best to start working on the past exams at least a week before the real exam, so that you have to finish and review most, if not all, of the past exams, and then ask questions you have on those to the professor or preceptor.
External ResourcesWolfram Alpha is your best friend when it comes to checking answers or making hard calculations. There are also homework help sessions available on Sunday evenings made specifically for MAT 203. There, along with the TA, you can discuss assignment problems and concepts with your peers. McGraw also has individual and study hall tutoring sessions for this course.
What Students Should Know About This Course For Purposes Of Course SelectionMost students going into STEM disciplines decide between MAT 201 and MAT 203. To reiterate, MAT 203 goes much further into proofs and theory, MAT 201 focuses on computation. MAT 203 is more challenging than 201, so if you’re taking multivariable calculus just to fulfill engineering requirements, take MAT 201. It’s okay to enroll in MAT 203 first and drop down to MAT 201 later. Certain higher level math classes accept MAT 203 but not MAT 201, such as MAT 350: Differential Manifolds. So if you’re thinking of pursuing higher level math, take this course. Expect problem sets to take about 10 hours on average. Also, Professor Diao teaches both lecture sections, so you’ll get the same experience in either one.
Advanced Vector Calculus