The following online courses are offered during the Fall, Spring, and Summer semesters.

### Precalculus (110.105)

This course is a pre-calculus course and provides students with the background necessary for a study of calculus. Includes a review of algebra, trigonometry, exponential and logarithmic functions, coordinates and graphs. Each of these tools is introduced in its cultural and historical context. The concept of the rate of change of a function will be introduced. This course provides a mathematically sound foundation for students who intend to study calculus.

Prerequisite: None.

Credits: 4 credits

Required Text: *College Algebra and Trigonometry,* by Dugopolski, M., 6th Ed., ISBN-13: 978-0321916525 ISBN-10: 0321916522

### Calculus I (110.108)

This is the first of a two course sequence in the differential and integral calculus of single variable functions. Topics include the basic analytic geometry of graphs of functions, and their limits, integrals and derivatives, including the Fundamental Theorem of Calculus. Also, some applications of the integral, like arc length and volumes of solids with rotational symmetry, are discussed. Applications to the physical sciences and engineering will be a focus of this course, as this sequence of courses is designed to meet the needs of students in these disciplines. 4 credits

The calculus course sequence is considered foundational to all higher-level courses in mathematics. This course satisfies the core requirement for the first of two semesters of single variable calculus for both the major and minor in mathematics.

Prerequisite: Students planning to take this course must demonstrate a proficiency in pre-calculus, either through the successful completion of a prior course in pre-calculus (such as AS.110.105 or similar) or by achieving an adequate score in the Placement Exam I offered by the Mathematics Department.

Credits: 4 credits

Required Text: *Single Variable Calculus: Early Transcendentals*, by James Stewart, 8th Ed., ISBN: 978-1-305-27033-6.

### Calculus II (110.109)

This is the second of a two course sequence in the differential and integral calculus of single variable functions. Topics include techniques of integration, applications of integrals, polar coordinates, parametric equations, Taylor’s theorem and applications, infinite sequences and series. Some applications to the physical sciences and engineering will be discussed, as this sequence of courses are designed to meet the needs of students in these disciplines. 4 credits

Prerequisite: Successful completion of AP Calculus AB, Calculus II, or equivalent.

Credits: 4 credits

Required Text: *Single Variable Calculus: Early Transcendentals*, by James Stewart, 8th Ed., ISBN: 978-1-305-27033-6.

### Calculus III (110.202)

This is a course in the differential and integral calculus of several variables. Topics include vectors in two and three dimensions, analytic geometry of three dimensions, parametric curves, partial derivatives, the gradient, optimization in several variables, multiple integration with change of variables across different coordinate systems, line integrals, surface integrals, and Green’s Theorem, Stokes’ Theorem, and Gauss’ Divergence Theorem.

Prerequisite: Successful completion of AP Calculus BC, Calculus II, or equivalent.

Credits: 4 credits

Required text:* Vector Calculus* by Marsden & Tromba, Freeman, 6th Ed., ISBN 9781429215084

### Linear Algebra (110.201)

This course is an introduction to the techniques of linear algebra in Euclidean space. Topics covered include matrices, determinants, systems of linear equations, vector spaces, linear transformations, complex numbers, and eigenvalues and eigenvectors. Diagonalization of matrices and quadratic forms, as well as applications of these topics to the biological, physical and social sciences to are also included.

Prerequisite: Successful completion of Calculus I. Recommended: Calculus II.

Credits: 4 credits

Required text: *Linear Algebra with Applications* by Bretscher, Prentice, 5th Edition, ISBN9780321796974

### Differential Equations with Applications (110.302)

This is an applied course in ordinary differential equations, which is primarily for students in the biological, physical and social sciences, and engineering. Techniques for solving ordinary differential equations are studied. Topics covered include first order differential equations, second order linear differential equations, applications to electric circuits, oscillation of solutions, power series solutions, systems of linear differential equations, autonomous systems, Laplace transforms and linear differential equations, mathematical models (e.g., in the sciences or economics).

Prerequisite: Calculus II.

Credits: 4 credits

Required text; *Elementary Diff Equations & Boundary Value Problems *by Boyce & DiPrima, Wiley, 10th edition, ISBN 9780470458310