All courses are taught from June 11 to August 3, 2018.

Add/Drop dates follow Summer Programs deadlines.

**Calculus I (110.108) **Syllabus

This is a two course sequence in the differential and integral calculus of functions of one independent variable. 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

This course is part of a two course sequence and precedes AS.110.109 Calculus II (Physical Sciences and Engineering). 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 by achieving an adequate score in the Placement Exam I offered by the Mathematics Department. This sequence of courses is considered foundational to all higher-level courses in mathematics. This sequence satisfies a core requirement of two semesters of single variable calculus for both the major and minor in mathematics.

Single Variable Calculus: Early Transcendentals, *8 ^{th} Edition*, James Stewart, Brooks-Cole, February 2015, ISBN-10: 1305270339, ISBN-13: 978-1305270336.

**Calculus II (110.109) **Syllabus

Differential and integral calculus. Includes analytic geometry, functions, limits, integrals and derivatives, polar coordinates, parametric equations, Taylor’s theorem and applications, infinite sequences and series. Some applications to the physical sciences and engineering will be discussed, and the courses are designed to meet the needs of students in these disciplines.* *4 credits

Single Variable Calculus: Early Transcendentals, *8 ^{th} Edition*, James Stewart, Brooks-Cole, February 2015, ISBN-10: 1305270339, ISBN-13: 978-1305270336.

**Calculus III (110.202)** Syllabus

Calculus of functions of more than one variable: partial derivatives, and applications; multiple integrals, line and surface integrals; Green’s Theorem, Stokes’ Theorem, and Gauss’ Divergence Theorem. Prerequisite: 110.107, 110.109, or 110.113. 4 credits

*Vector Calculus* by Marsden & Tromba, Freeman, 6th Edition, ISBN 9781429215084

**Linear Algebra (110.201)** Syllabus

Vector spaces, matrices, and linear transformations. Solutions of systems of linear equations. Eigenvalues, eigenvectors, and diagonalization of matrices. Applications to differential equations. Prerequisite: Calculus I. Recommended: Calculus II. 4 credits

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

**Differential Equations with Applications (110.302) **Syllabus** **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. 4 credits

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