All mathematics courses require a minimum of one year each of high school algebra and geometry. In order to accommodate diverse backgrounds and interests, several course options are open to beginning mathematics students. Courses preparatory to the calculus are offered in pairs: a recitation format and a self-paced version of the same material. The even-numbered course of each pair is self-paced. Department policy limits a student to a total of 4 credits for courses numbered 110 and below.

MATH 103/104 is the first half of MATH 105/106; MATH 107/108 is the second half. MATH 112 is designed for students of business and social sciences who require only one term of calculus. The sequence 113-114 is designed for students of the life sciences who require only one year of calculus. The sequence 115-116-215-216 is appropriate for most students who want a complete introduction to the calculus. Students planning to concentrate in mathematics should take Math 217 instead of Math 216. Math 217 is designed to provide a smoother transition to the more theoretical material in upper-division mathematics courses. Each of MATH 112, 113, 115, 185, and 195 is a first course in calculus; credit ordinarily can be received for only one course from this list. Math 109/110 is designed for students whose preparation includes all of the prerequisites for calculus but who are unable to complete one of the calculus courses successfully. Math 109/110 will be offered as a 7-week course during the second half of each term.

Admission to MATH 185 or 195 requires permission of a mathematics Honors advisor (1210 Angell Hall). Students who have performed well on the College Board Advanced Placement exam may receive credit and advanced placement in the sequence beginning with Math 115. Other students who have studied calculus in high school may take a departmental placement examination during the first week of the fall term to receive advanced placement WITHOUT CREDIT in the MATH 115 sequence. No advanced placement credit is granted to students who elect MATH 185. Students electing MATH 195 receive advanced placement credit after Math 296 is satisfactorily completed.

**112. Brief Calculus. *** Three years of high
school mathematics or Math. 105 or 106. Credit is granted for
only one course from among Math. 112, 113, 115, 185 and 195. (N.Excl). *

This is a one-term survey course that provides the basics of elementary calculus. Emphasis is placed on intuitive understanding of concepts and not on rigor. Topics include differentiation with application to curve sketching and maximum-minimum problems, antiderivatives and definite integrals. Trigonometry is not used. The text has been Hoffman, CALCULUS FOR THE SOCIAL, MANAGERIAL, AND LIFE SCIENCES, Second Edition. This course does not mesh with any of the courses in the regular mathematics sequences.

THE ELEMENTARY CALCULUS SEQUENCE CONSISTS OF FOUR COURSES OF 4 CREDITS EACH: Math . 115, 116, 215, and 216. The first three of these are calculus in content; Math. 216 is an introduction to differential equations. As an alternative fourth course, Math. 217 (Linear Algebra), will be offered as a 4 credit alternative for those students who require linear algebra, rather than differential equations, early in their programs. After completing Math. 217, students who require an introductory course in differential equations may elect 3 credit Math. 316 (Differential Equations) which is intended to cover the material of Math. 216 and Math. 404.

For students who elect Math. 216 as the fourth course of the elementary calculus sequence, Math. 417 (Matrix Algebra I) will continue to be the appropriate first course in linear algebra.

**115. Analytic Geometry and Calculus I. *** See
table. (Math. 107 may be elected concurrently.) Credit is granted
for only one course from among Math. 112, 113, 115, and 185. (N.Excl). *

Topics covered in this course include functions and graphs, derivatives; differentiation of algebraic and trigonometric functions and applications; definite and indefinite integrals and applications. Daily assignments are given. There are generally two or three one-hour examinations and a uniform midterm and final.

**116. Analytic Geometry and Calculus II. *** Math.
115. Credit is granted for only one course from among Math. 114, 116, and 186. (N.Excl). *

Transcendental functions, techniques of integration, introduction to differential equations, vectors, conic sections, infinite sequences and series. The course generally requires two one-hour examinations and a uniform midterm and final exam. Text: CALCULUS AND ANALYTIC GEOMETRY by Thomas and Finney, seventh edition.

**215. Analytic Geometry and Calculus III. *** Math.
116. (N.Excl). *

Topics covered include vector algebra and calculus, solid analytic geometry, partial differentiation, multiple integrals and applications. There are generally daily assignments and class examinations in addition to midterm and final examinations.

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

Topics covered include first order differential equations, linear differential equations with constant coefficients, vector spaces and linear transformations, differential operators, systems of linear differential equations, power series solutions, and applications. There are generally several class examinations and regular assignments.

**404. Differential Equations. *** Math. 216
or 286. (N.Excl). *

This is a second course in differential equations which reviews elementary techniques and delves into intermediate methods and equations. Emphasis varies slightly with individual instructor and student needs but usually includes power series expansions about ordinary points, perturbation series, simultaneous linear equations (solutions by matrices), numerical methods, nonlinear equations, phase-plane methods and qualitative behavior of solutions. The format is lecture/discussion, and the course is often elected by engineering students and students of the natural, physical and social sciences.

**417. Matrix Algebra I. *** Three terms of
college mathematics. No credit granted to those who have completed
513. (N.Excl). *

The course covers basic linear algebra and touches on several of its applications to many different fields. Emphasis is on introducing a diversity of applications rather than treating a few in depth. Topics emphasized include a review of matrix operations, vector spaces, Gaussian and Gauss-Jordan algorithms for linear equations, subspaces of vector spaces, linear transformations, determinants, orthogonality, characteristic polynomials, eigenvalue problems, and similarity theory. Applications include linear networks, least squares method (regression), discrete Markov processes, linear programming, and differential equations. The class is elected by a cross section of students, and usually includes some graduate students. The class format is lecture/discussion.

**450. Advanced Mathematics for Engineers I. *** Math.
216 or 286. (N.Excl). *

Topics include: vector analysis, line and surface integrals, Stokes' and Divergence Theorems, Fourier Series and Mean Square Convergence, Implicit functions, Separation of Variables for heat and wave equation.

**451. Advanced Calculus I. *** Math. 215 and one course beyond Math. 215; or Math. 285. Intended for concentrators;
other students should elect Math. 450. (N.Excl). *

Single variable calculus from a rigorous standpoint. A fundamental course for further work in mathematics. Text: ELEMENTARY ANALYSIS by Ross.

**454. Fourier Series and Applications. *** Math.
216 or 286. Students with credit for Math. 455 or 554 can elect
Math. 454 for 1 credit. (N.Excl). *

Orthogonal functions, theory of orthogonal expansions, Sturm-Liouville problems, Fourier series, applications to boundary value problems for partial differential equations, discrete Fourier transform, fast Fourier transform algorithm, applications to filtering and data smoothing, Fourier integrals, approximate computation of Fourier integrals via the FFT, band limited functions and the sampling theorem.

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.