Calculus at UAF

The UAF Calculus sequence of MATH 251, 252, 253 primarily serves engineering, natural science and mathematics majors. Our curriculum follows national norms for student training, and reflects discussions with UAF faculty in these fields. These courses give students a solid basis for more advanced studies in their chosen major.

In addition to science and engineering majors, we welcome all students who are simply interested in obtaining a thorough understanding of one of the key intellectual developments that underlies the modern technological world. However, we also offer MATH 230: Essential Calculus with Applications, a one-semester course which focuses on the most important topics for students of business, economics and the life sciences.

Courses in the Calculus sequence build strongly on their predecessors, and must be taken in order. We recommend continuing the sequence in consecutive semesters, since breaks between courses can create an extra burden in getting back up to speed on earlier material.

Entry into MATH 251 is by placement exam or successful completion of either MATH 156 or MATH 151 and 152. Students with AP or CLEP credit for predecessor courses may begin in MATH 252 or 253.

For questions, please contact the Department of Mathematics and Statistics, email:, phone: 907-474-7332.

Course materials:

Syllabi, exams, and exam solutions from recent offerings are openly available at links below. We encourage current students to use these as study materials.


In Fall 2021, we begin transitioning to a new textbook series from OpenStax, chosen in part to reduce student costs. Books are available as free pdfs, or can be ordered in print, through the links:

Calculus I, starting Fall 2021

Calculus II, starting Spring 2022

Calculus III, starting Fall 2022

These open resource books are being adopted by a growing number of universities around the country. Use of an on-line homework system will involve a student charge, but will be considerably more affordable than those of mainstream commercial textbook publishers. As the new texts roll into use, the information on topic coverage below will be updated, but content change will be minimal.

MATH F251X: Calculus I

This course introduces the fundamental mathematical concepts used to describe change, as well as their basic applications. The derivative can be described physically as a rate of change, or geometrically as a slope on a curve. The integral physically represents total accumulated change, or geometrically the area under a curve. Applications include the relationships between position, velocity, and acceleration; optimization; and approximation.

Sections of Math 251 are typically taught by several different instructors, but are tightly coordinated with a common syllabus, schedule, and examinations. For the current semester, these materials and many other resources (homework assignments, quizzes and exams for past years, etc.) can be found at:

MATH F252X: Calculus II

Building on its predecessor, this course has three distinct parts: 1) further methods for computing integrals, 2) more in-depth applications of integration in the sciences and engineering; and 3) a new topic, infinite series, in which functions are represented by sums with infinitely many terms.

Course Overview & Guidelines   pdf   tex
Typical daily schedule   pdf   tex

Sample course materials: Syllabus, Exam 1, Exam 1-solutions, Exam 2, Exam 2-solutions, Exam 3, Exam 3-solutions, Final exam

Materials from previous semesters (.zip files): Spring 2021, Fall 2020, Spring 2020a, Spring 2020b, Fall 2019, Spring 2019, Fall 2018, Spring 2018, Fall 2017

MATH F253X: Calculus III

This course takes the basic concepts of calculus from its predecessors and moves them into the 3-dimensional world. It provides the framework for analyzing motions of objects through space, changes in quantities (such as temperature) that vary throughout space, and velocity and force fields (such as a gravitational field) that not only vary through space but act on objects in specific directions. The mathematical concept of a vector plays a key role throughout.

Course Overview & Guidelines   pdf   tex
Typical daily schedule   pdf   tex

Sample course materials: Syllabus , Exam 1, Exam 1-solutions, Exam 2, Exam 2-solutions, Final exam

Materials from previous semesters (.zip files): Spring 2021, Fall 2020a, Fall 2020b, Spring 2020, Fall 2019, Fall 2018a, Fall 2018b, Spring 2018a, Spring 2018b