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
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.
Note: MATH 267A (Integrated Calculus IA) and MATH 267B (Integrated Calculus IB) are temporary course numbers. New permanent numbers for these courses will be announced in Spring 2019. Students who are enrolling in this course should carefully note the course title so they enroll in the appropriate course.
MATH 267A: Integrated Calculus IA. (4 cr.)
Calculus topics of limits, continuity, derivatives, and applications of derivatives are developed in the context of polynomial, rational, exponential, and logarithmic function classes, along with relevant Pre-calculus topics. First semester of a two-semester course, partial coverage of MATH 241 topics.
a C- or better in MATH 010 or students much achieve an acceptable score on the
Math Placement Exam in accordance with current standards determined by the
Department of Mathematical Sciences. See the math placement website for more information.
Only four credits from
any combination of MATH 113, MATH 115, MATH 117, MATH 127, or MATH 267A can
count toward graduation.
MATH 267B: Integrated Calculus IB. (3 cr.)
Calculus topics of integration in the context of polynomial, rational, exponential, and logarithmic function classes. Trigonometric functions introduced and followed with limits, derivatives, integrals, and applications in the context of trigonometric functions. Differential equations modeling exponential growth and decay. Second semester of a two-semester course, partial coverage of MATH 241 topics.
Pre-requisite: MATH 267A
- Integrated Calculus IA
Only one course from
MATH 221, MATH 241, or MATH 267B may count toward graduation.
Additional Course Description: Integrated Calculus IA and IB is a two-semester course sequence that develops the core topics of Calculus I, with relevant and critical Pre-calculus topics woven in and developed alongside the calculus topics. Thus, this course sequence provides an alternative to the traditional Pre-calculus to Calculus (MATH 117 / MATH 241) pathway. Instead of first completing a full semester of Pre-calculus, students in Integrated Calculus IA and IB begin to study Calculus topics immediately, and learn the necessary Pre-calculus topics along the way.
Course Content: All MATH 241 topics are developed by the end of the two-semester course sequence, along with the necessary Pre-calculus topics from MATH 117.
Integrated Calculus IA (first semester) – Topics
- Functions and key characteristics of functions
- The limit of a function
- Finding limits graphically and numerically
- Linear and piecewise-defined 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
- 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
Integrated Calculus IB (second semester) – Topics
- 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 Double-Angle 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
- Predator-Prey systems (optional)
Required Math Placement Test Level: S, B, or C. 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. Pre-calculus 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 textbook, and testing
- Integrated Calculus: Stewart Supplement
- 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, Integrated Calculus IA and IB 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.
The first course in this two-course sequence meets four times a week, on a MTWF or MWRF schedule. The second course in this two-course sequence meets three times a week, on a MWF schedule. Typically, there are two out-of-class 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 drop-in site – 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 148-150 South College Avenue, this site provides a number of different course resources for students. Please visit their web site for more information: http://ae.udel.edu/
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.
Note: In the table below, Course 1A refers to Integrated Calculus IA and Course IB refers to Integrated Calculus IB.
|Program requirement/ Situation|
Department of Mathematical Sciences Recommendation – See your advisor or department of your major to verify.
|Requires MATH 117, D- or better|
Course 1B, D- or better
|Requires MATH 117, C- or better|
Course 1B, C- or better
|Requires MATH 117 as a co-requisite||Course 1A as a co-requisite, or Course 1B as a co-requisite, depending on student major's department requirements.|
|Requires MATH 221 as a co-requisite|
Course 1A as a co-requisite
|Requires MATH 241, D- or better||Course 1A and Course 1B, D- or better in both courses|
|Requires MATH 241, C- or better||Course 1A and Course 1B, C- or better in both courses|
|Requires MATH 241 as a co-requisite||Course 1A as a co-requisite, or Course 1B as a co-requisite, depending on student major's department requirements.|
|Requires both MATH 117 and MATH 241 (C- or better in both courses)||Course 1A and Course 1B, C- or better in both courses|
|Requires both MATH 117 and MATH 241 (D- or better in both courses)||Course 1A and Course 1B, D- or better in both courses|
|Students who need to complete MATH 242 in the shortest amount of time||Take Course 1A in the Fall, Course 1B in the Spring, and MATH 242 in subsequent summer session.|
|Pre-med (or other programs) may require two semesters of calculus. Will Course 1A / Course 1B count as one semester or two semesters of calculus?||Course 1A and Course 1B 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 Course 1A. Does Course 1A fulfill a requirement for at least one three-credit math course?||Yes.|
|Are there any restrictions (other than math placement score) to enrolling in Course 1A?||Anyone can enroll, as long as they have completed MATH 010 with a C- or better, or their math placement score is above 65.|
|Can a student receive credit for both Course 1A and MATH 117, MATH 115, MATH 114, MATH 113, MATH 221, and/or MATH 241?||No, there are duplicate credit issues and overlap of topics.|
|Can a student receive credit for both MATH 267B and MATH 117, MATH 115, MATH 114, MATH 113, MATH 221, and/or MATH 241?||No, there are duplicate credit issues and overlap of topics.|
|Can students take Course 1A and/or Course 1B as pass/fail?||Students should follow the guidelines of their major department regarding MATH 241 and the pass/fail grading option.|