# Advanced Multivariable Calculus

### MATH222

Partial differentiation, multiple integrals, and topics in differential and integral vector calculus, including Green's theorem, Stokes's theorem, and Gauss's theorem for students with a background in linear algebra. Not open to students who have taken Mathematics 202 or 212. Prerequisite: Mathematics 221. One course.

##### Additional Notes

##### Information for Math Majors and Potential Math Majors

Math 222 is offered in Spring semesters. One of Math 212 or Math 222 is a prerequisite for the mathematics major.

Prospective math majors who enter with advanced placement credit for Math 21 and Math 22 are encouraged to take Math 221 Linear Algebra and Applications in their first semester followed by Math 222 Advanced Multivariable Calculus in their second semester.

This sequence is also suggested for students who are curious about the math major, or who are interested in getting a more solid mathematical foundation.

We recommend this sequence because vector calculus naturally depends on concepts and techniques of linear algebra. As a result, a vector calculus class which assumes linear algebra as a prerequisite can offer a more sophisticated treatment of the material.

##### Information for Engineering Majors, and Engineering/Math Double Majors

Engineering students should make sure their engineering major approves swapping the typical math sequence for engineers--Math 212, 216, 353--with Math 221, 222, and 356. Consult with your Director of Undergraduate Studies.

**Question: **As an engineering major, does getting a double major with math mean that in effect Math 216 Linear Algebra and Differential Equations is being replaced by two courses, Math 221 Linear Algebra and Applications and Math 356 Elementary Differential Equations?**Answer: **Math 221 and Math 356 together cover everything in Math 216, and quite a bit more; but neither one alone covers everything in Math 216. This is because Math 216 covers some of both linear algebra and differential equations. In addition to completing the material of Math 216, Math 356 also covers most of Math 353. Math majors should have the depth and thoroughness contained in Math 221, and Math 356. Math 453 then covers most of the remainder of Math 353, and goes into more depth on partial differential equations; it might not be required by Pratt in this alternative sequence, but it would be a great choice as part of your math major electives as it would cover materials very relevant to engineering. Math 551 is also a great choice.

**Question: **What if I take Math 221 Linear Algebra and Applications and then decide I do not want to take Math 222 Advanced Multivariable Calculus? May I still take Math 212 Multivariable Calculus?**Answer:** This is at the discretion of your Pratt dean; however, you cannot take Math 216 after getting credit for Math 221.

**Question:** What if I'm an engineering student, and after completing Math 216 Linear Algebra and Differential Equations, I decide I want to be a math major?**Answer:** You'll need to meet with the Director of Undergraduate Studies in Mathematics concerning the missed material in linear algebra.

**Question:** As an engineering student who is considering majoring in math, suppose I take Math 221 and then decide that I do not want to get a double major with math. Am I locked into taking Math 356 Elementary Differential Equations?**Answer:** Probably yes, but you should consult with your major advisor or the Director of Undergraduate Studies in your engineering department about your plans.