COURSE DESCRIPTION: Applications of calculus in mathematics, science, economics, psychology, the social sciences, involve several variables. This course extends calculus to several variables: vectors, partial derivatives, multiple integrals. There is also a unit on infinite series, sometimes with applications to differential equations. This course is the right starting point for students who have seen differentiation and integration before. Students with the equivalent of advanced placement of AB 4, BC 3 or above should enroll in Mathematics 105.
Prerequisites: Mathematics 104 or equivalent, such as satisfactory performance on an Advanced Placement Examination. No enrollment limit (expected: 45).  NOTE: We will be moving at a very fast pace. You should spend at least one if not two hours a day (every day!) on this course. I strongly encourage you to work in groups, and you should skim the reading before each class. We will not cover all the material in the book in class; you are responsible for reading the other examples at home.

GRADING / HW: Homework 15%, Midterms 40% (there will be 2 or 3), Final 45%. Exams are black tie optional. Homework is to be handed in on time, stapled and legible; there will be HW due each class. Late, messy or unstapled homework will not be graded. I encourage you to work in small groups, but everyone must submit their own homework assignment. All exams are cumulative, the lowest midterm grade will be dropped. There are also two other options, each individually worth 5%. Doing one of the options below reduces everything else to 95% of your grade, doing two reduces the above to 90%.

FLIPPED SPECIAL: One of the greatest challenges with multivariable calculus is the large amount of material and the small amount of time to combat it; in high school one meets twice more per week and for more weeks. To combat this the class will be flipped. You are expected to read the relevant sections before lecture and watch the video from the 2014 class. If you have any questions about the material / items you want to see in class, you are to enter that on the googlesheet. If you are not prepared for class you are to let me know; it is on the honor system, everyone can have three such days without penalty. Doing this will allow us to use classtime more effectively. Also, more importantly, it will help you cement a very important life skill: learning how to learn. One of the strongest items I can say in letters of recommendation is that a student can pick up material. Doing this will also give you enormous control and personalization of your education. Doing this adjusts the grading as follows: the items above now are rescaled to count for 40%, and you will receive a participation grade of 92.5 worth 60% (with the provision that you must pass the final to pass the course).

SYLLABUS GENERAL: The textbook is the seventh edition of Edwards and Penney: Calculus (Early Transcendentals). This should be the textbook used in Math 104. You may use either the 7th
edition or the 6th; unfortunately, while the content is essentially the same, the page numbering and chapter labeling differ, and you are responsible for making sure you do the right problems (I'll try and make sure the problems are the same, but it is your responsibility to make sure you do the right ones). There will also be supplemental handouts. Please read the relevant sections before class. This means you should be familiar with the definitions as well as what we are going to study; this does not mean you should be able to give the lecture. You do not need a calculator for this class, though I strongly urge you to become familiar with either Matlab or Mathematica to plot some of the multi-dimensional objects. There are many good references on the web. You can access certain books online: Calculus in Vector Spaces (Lawrence J. Corwin, Robert Henry Szczarba) and Multivariable Calculus (Lawrence J. Corwin, Robert Henry Szczarba) are somewhat theoretical expositions. Another great source is Cain and Herod's book on multivariable calculus (which you can download in its entirety for free). If you have any concerns or suggestions for the course and would prefer to communicate them anonymously, you may email me by using the account ephsmath@gmail.com  (the password is 1793williams).