See **Elementary
Courses** statement in the Spring Term.

Note: WL:3 for all courses

A * maximum total of 4 credits * may be earned in Mathematics
courses numbered 110 and below. A * maximum total of 16 credits *
may be earned for calculus courses Math 112 through Math 296, and no credit can be earned for a prerequisite to a course taken
after the course itself.

**103. Intermediate Algebra. *** Only open to
designated summer half-term Bridge students. (2). (Excl). *

This course is an in-depth review of high school algebra. It covers linear, quadratic, and polynomial functions and their graphs.

**105. Data, Functions, and Graphs. *** Students
with credit for Math. 103 can elect Math. 105 for only 2 credits.
(4). (Excl). (QR/1). *

This is a course on analyzing data by means of functions and graphs. The emphasis is on mathematical modeling of real-world
applications. The functions used are linear, quadratic, polynomial, logarithmic, exponential, and trigonometric. Algebra skills are
assessed during the term by periodic testing. Students completing
Math. 105 are fully prepared for Math. 115. Text: * Contemporary
Precalculus. * Students will need graphing calculators and should check with the Math Department office to find out what
is currently required.

**115. Calculus I. *** Four years of high school
mathematics. See Elementary Courses above. Credit
usually is granted for only one course from among Math. 112, 115, 185, and 195. (4). (N.Excl). (BS). (QR/1). *

See Mathematics 115 (Spring Term).

**116. Calculus II. *** Math. 115. Credit is
granted for only one course from among Math. 116, 186, and 196.
(4). (N.Excl). (BS). (QR/2). *

See Mathematics 116 (Spring Term).

**215. Calculus III. *** Math. 116 or 186. (4).
(Excl). (BS). (QR/1). *

See Mathematics 215 (Spring Term).

**216. Introduction to Differential Equations. *** Math.
215. (4). (Excl). (BS). *

See Mathematics 216 (Spring Term).

**417. Matrix Algebra I. *** Three courses beyond
Math. 110. No credit granted to those who have completed or are
enrolled in 217, 419, or 513. (3). (Excl). (BS). *

See Mathematics 417 (Spring Term).

**419/EECS 400/CS 400. Linear
Spaces and Matrix Theory. *** Four terms of college mathematics
beyond Math 110. No credit granted to those who have completed
or are enrolled in 217 or 513. One credit granted to those who
have completed Math. 417. (3). (Excl). (BS). *

**Background and Goals.** Math 419 covers much
of the same ground as Math 417 but presents the material in a
somewhat more abstract way in terms of vector spaces and linear
transformations instead of matrices. There is a mix of proofs, calculations, and applications with the emphasis depending somewhat
on the instructor. A previous proof-oriented course is helpful
but by no means necessary. **Content.** Basic notions
of vector spaces and linear transformations: spanning, linear
independence, bases, dimension, matrix representation of linear
transformations; determinants; eigenvalues, eigenvectors, Jordan
canonical form, inner-product spaces; unitary, self-adjoint, and orthogonal operators and matrices, applications to differential
and difference equations.

**425/Stat. 425. Introduction
to Probability. *** Math. 215. (3). (N.Excl). (BS). *

See Mathematics 425 (Spring Term).

**450. Advanced Mathematics for Engineers I. *** Math.
216, 286, or 316. (4). (Excl). (BS). *

**Background and Goals.** Although this course
is designed principally to develop mathematics for application
to problems of science and engineering, it also serves as an important
bridge for students between the calculus courses and the more
demanding advanced courses. Students are expected to learn to
read and write mathematics at a more sophisticated level and to
combine several techniques to solve problems. Some proofs are
given and students are responsible for a thorough understanding
of definitions and theorems. Students should have a good command of the material from Math 215, and 216 or 316, which is used throughout the course. A background in linear algebra, e.g., 321 Math 217, is highly desirable. **Content.** Topics include
a review of curves and surfaces in implicit, parametric, and explicit
forms; differentiability and affine approximations; implicit and inverse function theorems; chain rule for 3-space; multiple integrals;
scalar and vector fields; line and surface integrals; computations
of planetary motion, work, circulation, and flux over surfaces;
Gauss' and Stokes' Theorems, derivation of continuity and heat
equation. Some instructors include more material on higher dimensional
spaces and an introduction to Fourier series. This corresponds
to Chapters 2, 3, 5, 7, and 8 and sometimes 4 of Marsden and Tromba.

**471. Introduction to Numerical Methods. *** Math.
216, 286, or 316; and 217, 417, or 419; and a working knowledge
of one high-level computer language. (3). (Excl). (BS). *

**Background and Goals.** This is a survey of the basic numerical methods which are used to solve scientific
problems. The emphasis is evenly divided between the analysis
of the methods and their practical applications. Some convergence theorems and error bounds are proved. The course also provides
an introduction to MATLAB, an interactive program for numerical
linear algebra, as well as practice in computer programming. One
goal of the course is to show how calculus and linear algebra
are used in numerical analysis. **Content.** Topics
include computer arithmetic, Newton's method for non-linear equations, polynomial interpolation, numerical integration, systems of linear
equations, initial value problems for ordinary differential equations, quadrature, partial pivoting, spline approximations, partial differential
equations, Monte Carlo methods, 2-point boundary value problems, Dirichlet problem for the Laplace equation.

**555. Introduction to Functions of a Complex Variable
with Applications. *** Math. 450 or 451. Students with
credit for Math. 455 or 554 can elect Math. 555 for one hour credit.
(3). (Excl). (BS). *

See Mathematics 555 (Spring Term).

University of Michigan | College of LS&A | Student Academic Affairs | LS&A Bulletin Index

This page maintained by LS&A Academic Information and Publications, 1228 Angell Hall

The Regents
of the University of Michigan,

Ann Arbor, MI 48109 USA +1 734 764-1817

Trademarks of the University of Michigan may not be electronically or otherwise altered or separated from this document or used for any non-University purpose.