â€‹Introduction: The information
presented here is intended to describe the course goals for current and
prospective students as well as others who are interested in our courses. It is
not intended to replace the instructional policies and course materials
presented in class.
The following information applies to the Newark
campus.
Every
effort is made to update this information on a routine basis. However, if you have questions about
enrollment, purchasing materials, and prerequisite skills, please check with
your advisor or instructor.
The most updated Course Description can be found at the UD Course Description Search. Information on the sections currently offered can be found at the UD Course Search. Additional information about Math 115 offered in the
recent semesters can be found in the Math 231 and Math
232â€‹ departmental syllabi.â€‹
Additional Course Description: Math 231/232 Integrated Calculus IA and IB is a twosemester course sequence that develops the core topics of Calculus I, with relevant and critical Precalculus topics woven in and developed alongside the calculus topics. Thus, this course sequence provides an alternative to the traditional Precalculus to Calculus (MATH 117 / MATH 241) pathway. Instead of first completing a full semester of Precalculus, Math 231 students begin to study Calculus topics immediately, and learn the necessary Precalculus topics along the way.
Course Content: All MATH 241 topics are developed by the end of the twosemester course sequence, along with the necessary Precalculus topics from MATH 117.
Math 231: Integrated Calculus IA (first semester) â€“ Topics
 Functions and key characteristics of functions
 The limit of a function
 Finding limits graphically and numerically
 Linear and piecewisedefined functions, and the absolute value function
 Composition of functions, transformations of functions, and inverse functions
 Polynomial functions
 Rational functions
 Calculating limits using limit laws
 Limits at infinity and horizontal asymptotes
 Continuity
 The tangent line problem
 Derivatives and rates of change
 Derivatives of polynomial and rational functions
 The Product and Quotient Rules
 The Chain Rule
 Implicit differentiation
 Related rates
 Linear approximations
 Maximum and minimum values
 The Mean Value Theorem
 Exponential functions
 Logarithmic functions
 Derivatives of exponential and logarithmic functions
 Exponential growth and decay
 How derivatives affect the shape of a graph
 Optimization problems
Math 232: Integrated Calculus IB (second semester) â€“ Topics
 Antiderivatives
 Areas and Distances
 The Definite Integral
 The Fundamental Theorem of Calculus
 Indefinite Integrals and the Net Change Theorem
 The Substitution Rule
 Introduction to trigonometric functions
 Right triangle trigonometry
 Trigonometric functions of any angle
 Graphs of trigonometric functions
 Inverse trigonometric functions and their graphs
 Trigonometric applications and models
 Trigonometric identities
 Solving trigonometric equations
 Sum, Difference, and DoubleAngle Formulas
 Limits of trigonometric functions
 Derivatives of Trigonometric and Inverse Trigonometric Functions
 Integration of Trigonometric and Inverse Trigonometric Functions
 Hyperbolic functions and their derivatives
 Models for population growth
 PredatorPrey systems (optional)
Required Math Placement Test Level: 65 or above, or a grade of C or better in Math 010. For more information regarding math placement please see the Math Placement Exam webpage.
Additional Prerequisite Information: A strong algebra background is critical for success in this course. This includes the ability to perform operations with rational expressions and numerical fractions (without the use of a calculator), working with radicals and rational exponents, factoring polynomials, and solving equations. A minimum of two years of high school algebra is required. Precalculus or Algebra II in the senior year is preferred.
Course Materials: The following course materials are usually required in this course:
 Online math program for homework, access to the textbooks, and testing
 Course pack that includes class activities
Students should always check with their instructor before purchasing any course materials.
Course Format: On the Newark campus during the regular semesters, Math 231 and Math 232 is taught in the Mathematical Sciences Learning Lab (MSLL). During much of the class, students work in small groups on activities that focus on concepts and connections between ideas. Students practice outside of class using an online homework system.
Math 231 meets four times a week, on a MTWF or MWRF schedule. Math 232 meets three times a week, on a MWF schedule. Typically, there are two outofclass midterm exams and a cumulative final exam taken during Final Exam week.
This course is not offered during the short sessions (winter and summer).
Tutorial Resources: There are several campus resources that provide additional assistance.
 Mathematical Sciences Learning Laboratory (MSLL) Open Lab: MSLL Open Lab provides free tutorial support for this course. The lab is staffed by qualified undergraduate students. This is a dropin site â€“ no appointment is needed. Students can work on their math homework, study for a math quiz or exam, and receive free tutorial assistance. More information can be found at the web page: MSLL Open Lab.
 Office of Academic Enrichment: Located at 148150 South College Avenue, this site provides a number of different course resources for students. Please visit their websiteâ€‹ for more information.â€‹â€‹â€‹â€‹
Satellite Campus Information: This course is not available at the satellite campuses.
Guidelines about this Course from the Department of Mathematical Sciences
The Department of Mathematical Sciences provides the following guidelines to other departments when addressing further questions about this course sequence. Students must check with the department of their major and with their advisor before making enrollment decisions, as departments may have different requirements.
Program requirement/ Situation  Department of Mathematical Sciences Recommendation â€“ See your advisor or department of your major to verify. 
Requires MATH 117, D or better  Math 232, D or better 
Requires MATH 117, C or better  Math 232, C or better 
Requires MATH 117 as a corequisite  Math 231 as a corequisite, or Math 232 as a corequisite, depending on student major's department requirements. 
Requires MATH 221 as a corequisite  Math 231 as a corequisite 
Requires MATH 241, D or better  Math 231 and Math 232, D or better in both courses 
Requires MATH 241, C or better  Math 231 and Math 232, C or better in both courses 
Requires MATH 241 as a corequisite  Math 231 as a corequisite, or Math 232 as a corequisite, depending on student major's department requirements. 
Requires both MATH 117 and MATH 241 (C or better in both courses)  Math 231 and Math 232, C or better in both courses 
Requires both MATH 117 and MATH 241 (D or better in both courses)  Math 231 and Math 232, D or better in both courses 
Students who need to complete MATH 242 in the shortest amount of time  Take Math 231 in the Fall, Math 232 in the Spring, and MATH 242 in subsequent summer session. 
Premed (or other programs) may require two semesters of calculus. Will Math 231/Math 232 count as one semester or two semesters of calculus?  Math 231 and Math 232 count as one semester of calculus. 
A student does not take consecutive semesters of this sequence.  Not recommended, but possible. Students may find it difficult to take subsequent course as skills are not current. 
A student only takes Math 231. Does Math 231 fulfill a requirement for at least one threecredit math course?  Yes. 
Are there any restrictions (other than math placement score) to enrolling in Math 231?  Anyone can enroll, as long as they have completed MATH 010 with a C or better, or their math placement score is 65 or aboveâ€‹. 
Can a student receive credit for both Math 231 and MATH 117, MATH 115, MATH 114, MATH 113, MATH 221, and/or MATH 241?  Restrictions apply. See the UD policy on Courses of Similar Content for more detail. Also, MATH 231 has significant content overlap with MATH 117, 221 and 241. 
Can a student receive credit for both Math 232 and MATH 117, MATH 115, MATH 114, MATH 113, MATH 221, and/or MATH 241?  Restrictions apply. See the UD policy on Courses of Similar Content for more detail. Also, MATH 232 has significant content overlap with MATH 117, 221 and 241. 
Can students take Math 231 and/or Math 232 as pass/fail?  Students should follow the guidelines of their major department regarding MATH 241 and the pass/fail grading option.â€‹ 
