# Math 241

## Math 241 - Analytic Geometry and Calculus A

The information and materials presented here are intended to provide a description of 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. 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.

The purpose of this course is to teach functions, limits, continuity, derivatives, polynomial, rational, exponential, hyperbolic, logarithmic, trigonometric and inverse trigonometric functions. Definite and indefinite integrals and the Fundamental Theorem of Calculus. Simple differential equations (separable ODE, linear ODE). ODE models leading to exponential growth and decay.

**Topics Covered:**

- Chapter 1 Functions and Models
- Exponential Functions (review)
- Inverse Functions and Logarithms (review)

- Chapter 2 Limits and Derivatives
- The Tangent and Velocity Problems
- The Limit of a Function
- Calculating Limits Using the Limit Laws
- Continuity
- Limits at Infinity: Horizontal Asymptotes
- Derivatives and Rates of Change
- The Derivative as a Function

- Chapter 3 Differentiation Rules
- Derivatives of Polynomials and Exponential Functions
- The Product and Quotient Rules
- Derivatives of Trigonometric Functions
- The Chain Rule
- Implicit Differentiation
- Derivatives of Logarithmic Functions
- Exponential Growth and Decay
- Related Rates
- Linear Approximations and Differentials (Do linear approximations)
- Hyperbolic Functions (Don't cover inverse hyperbolic functions)

- Chapter 4 Applicatons of Differentiation
- Maximum and Minimum Values
- The Mean Value Theorem
- How Derivatives Affect the Shape of a Graph
- Optimization Problems
- Antiderivatives

- Chapter 5 Integrals
- Areas and Distances
- The Definite Integral
- The Fundamental Theorem of Calculus
- Indefinite Integrals and the Net Change Theorem
- The Substitution Rule

- Chapter 9 Differential Equations
- Models for Population Growth
- Predator-Prey Systems (optional)

**Text:** Calculus: Early Transcendentals UD Custom pkg by James Stewart, 7th Edition Cengage

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 webpage: 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 website for more information.

Students enrolled at other campuses should contact the math faculty for the specific campus for additional information about this course.

**Dover Campus:**Brad Thompson, bthompso@udel.edu**Georgetown Campus:**Matthew Willis, mjwillis@udel.edu**Wilmington Campus:**Alexia Mintos,