Math 423/673, Spring 2008

Differential Geometry

John Zweck

Course Materials

Why Take Differential Geometry?

Schedule and Homework (Updated Daily)

Syllabus [pdf]
Diagnostic Quiz [pdf]

Solutions to Diagnostic Quiz [pdf]

Background from multivariable calculus and linear algebra

Ideally, you should be very comfortable with the following topics. However, we will spend time in class (rapidly) reviewing some of these topics.

(1) The following sections and topics from "Calculus" by James Stewart:

(13.5) Equations of lines and planes
(13.6) Quadric surfaces
(13.7) Cylindrical and spherical coordinates
(14.1-3) Vector functions and space curves; Derivatives and integrals of vector functions; Arc length and curvature
(15.1-6) Functions of several variables; Limits and continuity; Partial derivatives; Tangent planes and linear approximations; Chain rule; Directional derivatives, gradient
(16.1-3) Double integrals over rectangles and general regions
(17.1-7) Vector fields; Line integrals and Fundamental Theorem; Green's Theorem; Parametric surfaces and their areas; Surface integrals; Divergence and curl

(2) Concepts from linear algebra:

Linear independence; basis; solution of 2x2 matrix system Ax=b; eigenvalues and eigenvectors of 2x2 matrices.

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]

Exam One

Exam One will cover 1.2, 1.3, 1.4, 1.7, 2.2, 2.3, 4.1, 4.2, 4.3, and Stewart Chapter 17.

Exam Two

Exam Two will cover 1.5, 1.6, 4.4, 4.6, and other material from class on differential forms and Fundamental Theorem of Calculus, and 5.1-5.4

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