01:640:151 - Calculus I for the Mathematical and Physical Sciences



Math 151–152 is the introductory year course in the calculus sequence in New Brunswick for majors in the mathematical sciences, the physical sciences, and engineering.

  • The first semester, Math 151 or 153, presents the differential calculus of the elementary functions of a single real variable: the rational, trigonometric and exponential functions and their inverses; various applications via the Mean Value Theorem; and an introduction to the integral calculus.
  • The second semester, Math 152, continues the study of the integral calculus, with applications, and covers the theory of infinite series and power series, touching on differential equations and a few other topics as well.


Transitioning from Math 135 to Math 152:

Students who intend to go directly from Math 135 to Math 152 will need to fill in some gaps through self-study. Details are in the document: "Transferring From 135 to 152".


Textbook:  For current textbook please refer to our Master Textbook List page

Course Materials

Math 153

Math 153 is an intensive form of Math 151 with an extra meeting time, covering the same syllabus. Most of the information given here for Math 151 applies to Math 153 as well.

Math 135

The calculus sequence for most business, economics, and life science majors is 135 followed by 136 or 138. Any students planning to continue the study of mathematics beyond two semesters will need the sequence beginning with 151 and 152.

Math 151-152 in Summer Session

Math 151 and Math 152 have the same content and essentially the same format during summer session as during the fall or spring semesters. Workshops are part of these courses at any time of year, though during the summer there is no TA or peer mentor.

The summer versions of Math 151 and Math 152 do not have a common final exam, and instead each section has a final written by its own instructor. The links below to materials from previous semesters may be helpful in preparing for these exams.

SAS Core Curriculum Learning Goals

QQ: Formulate, evaluate and communicate conclusions and inferences from quantitative information.

QR: Apply effective and efficient mathematical or other formal processes to reason and to solve problems.

Learning Goals

Course Learning Goals for Math 151:

To acquire the ability to compute limits, derivatives and integrals of certain algebraic, trigonometric, exponential and logarithmic functions. To achieve understanding of the notions of continuity and differentiabitily. To develop the ability to use first and second derivatives to determine the shape of the graph of a function. To acquire practice solving optimization problems using calculus.

Course Learning Goals for Math 152:

To acquire practice using the method of disks, washers and cylindrical shells to compute volumes of solids of revolution. To develop the ability to use integration by parts, trigonometric substitution, partial fractions and other techniques to evaluate many indefinite integrals. To acquire practice using the integral test, comparison tests, the Leibniz test and the ratio test to determine convergence or divergence of a series. To acquire practice solving problems involving parametric equations and polar coordinates.

Schedule of Sections:

Disclaimer: Posted for informational purposes only

This material is posted by the faculty of the Mathematics Department at Rutgers New Brunswick for informational purposes. While we try to maintain it, information may not be current or may not apply to individual sections. The authority for content, textbook, syllabus, and grading policy lies with the current instructor.

Information posted prior to the beginning of the semester is frequently tentative, or based on previous semesters. Textbooks should not be purchased until confirmed with the instructor. For generally reliable textbook information—with the exception of sections with an alphabetic code like H1 or T1, and topics courses (197,395,495)—see the textbook list.