This course provides an introduction to functions of multiple variables with a focus on functions of two- and three-variables.\u00a0 In the course we extend the definition of the derivative to a multi-dimensional context, find local approximations of functions, identify maxima and minima of a function of multiple variables subject to constraints on the independent variables, and learn to integrate functions of several variables.\u00a0 We also touch on analytic geometry in order to define and explore graphs, surfaces, curves, and solids in 3-space.<\/p>\n
In most areas of inquiry where functions arise, they are functions of multiple variables, so this extension of calculus is important to understanding problems in statistics, economics, biology, engineering, and physics.<\/p>\n
The course also includes an introduction to vectors, vector operations, and vector notation.\u00a0 We use vectors to describe points in two- or three-space, and use vector valued functions to generate mappings from a line to a curve and from a plane to a surface, as well as to describe vector fields.\u00a0 Vector fields arise in the context of motion of water and of air, as well as in many more abstract contexts.\u00a0 After defining flux of a vector field through a surface and circulation around a curve, we will study the vector calculus analogs of the Fundamental Theorem of Calculus.\u00a0 Our course will conclude with a brief introduction to complex numbers.<\/p>\n
<\/p>\n
Course materials\u00a0 |\u00a0 Discussion board\u00a0 | \u00a0 Check Yourself Qs \u00a0 |\u00a0\u00a0Assignments<\/a>\u00a0 |\u00a0 WeBWorK<\/a>\u00a0 |\u00a0 Quiz Info\u00a0 |\u00a0 Exams\u00a0 |\u00a0 Calendar\u00a0 (calendar will be updated as needed)<\/p>\n","protected":false},"excerpt":{"rendered":" This course provides an introduction to functions of multiple variables with a focus on functions of two- and three-variables.\u00a0 In the course we extend the definition of the derivative to a multi-dimensional context, find local approximations of functions, identify maxima and minima of a function of multiple variables subject to constraints on the independent variables, […]<\/p>\n","protected":false},"author":8032,"featured_media":0,"parent":5,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-50","page","type-page","status-publish","hentry"],"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/P7E5LF-O","jetpack-related-posts":[{"id":11,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/teaching\/f16-multivariable-calculus\/","url_meta":{"origin":50,"position":0},"title":"F16 Multivariable Calculus","author":"siams","date":"16 June 2016","format":false,"excerpt":"This course provides an introduction to functions of multiple variables with a focus on functions of two- and three-variables.\u00a0 In the course we extend the definition of the derivative to a multi-dimensional context, find local approximations of functions, identify maxima and minima of a function of multiple variables subject to\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":40,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/teaching\/f17-multivariable-calculus\/am21a-assignment-information\/","url_meta":{"origin":50,"position":1},"title":"Assignment Information","author":"siams","date":"21 August 2016","format":false,"excerpt":"Assignment information: A pdf with the assignments for the course to-date will be available at this location.\u00a0 Assignments information is also available on Canvas. Assignment formatting: Assignments for this course are to be submitted on Canvas.\u00a0 Since assignments are being submitted online, but this is a mathematics course, many students\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":5,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/teaching\/","url_meta":{"origin":50,"position":2},"title":"Teaching","author":"siams","date":"16 June 2016","format":false,"excerpt":"I currently teach and advise in the undergraduate Applied Mathematics program at Harvard University. Previous courses taught include multivariable calculus, differential equations, linear algebra, and nonlinear dynamical systems.\u00a0 I have taught or worked on courses at Cornell University, Bowdoin College, Northwestern University and Harvard. See the sidebar at https:\/\/scholar.harvard.edu\/siams for\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/pages\/50","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/users\/8032"}],"replies":[{"embeddable":true,"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/comments?post=50"}],"version-history":[{"count":2,"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/pages\/50\/revisions"}],"predecessor-version":[{"id":55,"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/pages\/50\/revisions\/55"}],"up":[{"embeddable":true,"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/pages\/5"}],"wp:attachment":[{"href":"https:\/\/archive.blogs.harvard.edu\/siams\/wp-json\/wp\/v2\/media?parent=50"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}