# V63.0123-1 Calculus III : Multivariable calculus

#### Instructor: Alex Barnett email: `barnett at cims.nyu.edu` tel: 212-998-3296, rm 1122 Warren Weaver Hall (WWH) Office hours (note change): 5-6pm Mondays and 11am-noon Tuesdays.

 Find the volume of cool and unusual geometric shapes. Electric fields are vector fields. Charges are responsible for divergence (sources of the field). Fluid flow velocity is also a vector field. Vortices are localized regions of high curl.

In this course we generalize ideas of differential and integral calculus to two and three dimensions. As well as giving us tools to model the real, three-dimensional world through physics, chemistry, engineering, etc (as in the pictures above), this is also essential to understanding functions of many variables in more abstract situations, such as arise in computer science, economics, and statistics and probability. The emphasis will be on intuition, visualization, and problem-solving, rather than theorem-lemma-proof. I am a physicist by training and I am sure this will show.

#### Exams:

• Midterm1, in class W Feb 19, 9am-10am. No calculators or cheat sheets. You will be given the harder-to-remember formulae. Please practise with the Sample Midterm1, eventually checking against answers (corrected).
• Midterm1 solutions: I made a mistake in 3. Method A. You should replace it with d = |r_o|sin theta = |r_o cross v| divided by |v|. Best is to get notes from lecture 10 (W Feb 26).
• Midterm2, in class M Apr 7, 9am-10am. Calculators allowed. You may bring a single-page formula sheet of your own (few standard formulae will be provided). Practise with Sample Midterm2 (including lists of Stewart practise problems), with answers. This sample exam may be a little longer than the real one.
• Final, in usual classroom, Wed May 7, 10am-11:50. Calculators and double-sided formula sheet allowed. Answers (not full solutions) are here. Practise with Sample Final (including lists of Stewart practise problems), with answers.

#### Homeworks:

PS You will be pleased to know my research in physics and medical imaging relies heavily on partial derivatives (in the form of partial differential equations) and almost every other aspect of this course. I am not special - almost any practicing scientist would say the same. So... keep studying - it's useful!