Math 423/673, Spring 2010

Differential Geometry

John Zweck

Course Materials

Why Take Differential Geometry?

Syllabus [pdf]

Diagnostic Quiz [pdf]

Solutions to Quiz [pdf] (Solutions to 10, 11 will be handed out in class.)

Schedule (Updated Weekly)

Background from Multivariable Calculus and Linear Algebra

I strongly recommend you review the following material before class begins and/or in the first two weeks of class. However, we will spend time in class (rapidly) reviewing some of these topics.

You should aim to both do problems and understand the theory.

The diagnostic quiz (see above) represents the bare minimum knowledge you should aim to review. Do it when you are ready, but please hand in to me no later than the second day of class.

I encourage you to use the resources I have available on my web site:

Math 251 Exams (some with solutions)
Math 251 Homework from Stewart (do the odd numbered problems!)
Math 251 Homework from Smith and Minton (do the odd numbered problems!)
Math 221 Exams
Math 221 Homework

(1) Topics from Multivariable Calculus. My preferred textbook is "Calculus" by James Stewart. (Sections from Stewart are labeled S:XY.Z) However many of you may have "Calculus" by Smith and Minton (Sections from Smith and Minton are labeled SM:XY.Z). The date by which you should have reveiwed this material is also indicated.

(S:13.5, SM:10.5) Equations of lines and planes (by Feb 2)
(S:13.6, SM:10.6) Quadric surfaces (by Feb 18)
(S:13.7, SM:13.6,13.7) Cylindrical and spherical coordinates (by Feb 18)
(S:14.1-3, SM:11.1,2,4) Vector functions and space curves; Derivatives and integrals of vector functions; (both by Feb 4) Arc length and curvature (by Feb 11)
(S:15.1-6, SM:12.1-6) Functions of several variables; Limits and continuity; Partial derivatives; Tangent planes and linear approximations; Chain rule; (all by Feb 18) Directional derivatives, gradient (by Feb 4)
(S:16.1-3, SM:13.1-3) Double integrals over rectangles and general regions (by Mar 2)
(S:17.1-7, SM:14.1-7) Vector fields; Line integrals and Fundamental Theorem; Green's Theorem; Parametric surfaces and their areas; Surface integrals; Divergence and curl (all by Mar 2)
(S:17.8-9, SM:14.7-8) Stokes' Theorem and Divergence Theorem (by Mar 2)

(2) Concepts from Linear Algebra:

Linear independence; basis; (by Feb 16) solution of 2x2 matrix system Ax=b; eigenvalues and eigenvectors of 2x2 matrices; matrix of linear transformation; similarity. (all by April 1)

Math 423 Past Exams

Exams From Spring 2004

Exam 1 [pdf]
Exam 2 [pdf]
Final [pdf]
Solutions to Exam 1 [pdf]
Solutions to Exam 2 [pdf]

Exams From Spring 2006

Exam 1 [pdf]
Exam 2 [pdf]
Final Exam [pdf]
Solutions to Exam 1 [pdf]
Solutions to Exam 2 [pdf]

Exams From Spring 2008

Exam 1 [pdf]
Exam 2 [pdf]
Final Exam [pdf]
Solutions to Exam 1 [pdf]
Solutions to Exam 2 [pdf]

Math 423/673 Information Regarding Exams

Exam I will be held in-class on Tuesday March 9th. It will cover Sections 1.1, 1.2, 1.3, 1.4, 1.7, 2.2, 2.3, 4.1, and 4.2.

Solutions to Exam I

EXAM II will be a take home exam. You will receive a pdf file with the exam by email late Friday Apr 30th. It will be due by 12 noon Monday May 3rd at Math Office. The exam will be open book, open notes, but you are not allowed to talk or communicate in any way with anyone else (except me) about any aspect of the exam until after 12 noon Monday May 3rd.

The exam will cover
O'Neill: 1.5, 1.6, 4.1, 4.2, 4.3, 4.4, 4.6, 5.1, 5.2, 5.3, 5.4
Stewart: 17.2, 17.5-17.9

Note that I will be testing the material on forms the way I discussed it in class rather than the way it is dealt with by O'Neill. (Of course there is some overlap.)

Exam 2 [pdf]
Exam 2 Solutions [pdf]

Information on Written Report for Math 673 Project [html]

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