Math 423/673, Spring 2012

Differential Geometry

John Zweck

Course Materials

Syllabus [pdf]
Diagnostic Quiz [pdf]
Study Skills Compulsary Homework [html]

Information on Written Report for Math 673 Project [html]

Lecture Notes (Updated Regularly)
Schedule (Updated Weekly)


Exam I will be held Tuesday March 6th in class. It will cover Sections 1.1, 1.2, 1.3, 1.4, 1.7, 2.2, and 2.3.

Exam I Solutions [pdf]


Exam II will cover O'Neill 1.5, 4.1, 4.2, 4.3 and Stewart 16.2-16.9.

Exam II [pdf]

Exam II Solutions [pdf]

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 (Early Transcendentals) 6E" 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:12.5, SM:10.5) Equations of lines and planes (by Jan 31)
(S:12.6, SM:10.6) Quadric surfaces (by Feb 16)
(S:12.7, SM:13.6,13.7) Cylindrical and spherical coordinates (by Feb 16)
(S:13.1-3, SM:11.1,2,4) Vector functions and space curves; Derivatives and integrals of vector functions; (both by Feb 2) Arc length and curvature (by Feb 9)
(S:14.1-6, SM:12.1-6) Functions of several variables; Limits and continuity; Partial derivatives; Tangent planes and linear approximations; Chain rule; (all by Feb 16) Directional derivatives, gradient (by Feb 2)
(S:15.1-3, SM:13.1-3) Double integrals over rectangles and general regions (by Feb 28)
(S:16.1-7, 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 Feb 28)
(S:16.8-9, SM:14.7-8) Stokes' Theorem and Divergence Theorem (by Feb 28)

(2) Concepts from Linear Algebra:

Linear independence; basis; (by Feb 14) solution of 2x2 matrix system Ax=b; eigenvalues and eigenvectors of 2x2 matrices; matrix of linear transformation; similarity. (all by April 5)

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]

Exams From Spring 2010

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