Introduction to differential calculus with the associated analytical geometry. Completion of both MATH 109 and MATH 110 will be equivalent of the completion of MATH 111. Prerequisites: Two years of high school algebra. Meets General Education Mathematical Sciences requirements. (Offered fall semester.)

Larson, Hostetler and Edwards, Calculus with Analytic Geometry, 8^th edition, D. C. Heath, 2006.

Douglas C. Phillippy, Ph.D., Associate Professor of Mathematics

Students majoring in mathematics, computer science, engineering, physics, chemistry, or economics. Intended for students who desire to have the course material for Calculus I presented at a slower pace.

1. To develop a rigorous understanding of the concept of differentiation.
2. To strengthen the student’s mathematics background by reviewing selected precalculus topics as they are needed in the calculus sequence.
3. To enhance learning by examining geometric, numerical, and algebraic aspects of topics taught.
4. To acquire an understanding of the breadth of mathematics by introducing applications in a wide variety of scientific fields.
5. To use the tools of Calculus to formulate and solve multi-step problems and to interpret the numerical results.
6. To develop the student’s ability to communicate mathematical concepts through a series of written laboratory assignments and classroom discussions.
7. To select and use technology when appropriate in problem solving.
8. To develop the process of making appropriate conjectures, finding suitable means to test those conjectures, and drawing conclusions about their validity.

1. Algebraic skills needed to solve inequalities and equations involving rational polynomial expressions.
2. Understanding the use of variables.
3. Basic properties of the real number system, including rational and irrational numbers.
4. The ability to use the Cartesian plane to plot and draw graphs including the conic sections.
5. Understanding exponential, logarithmic and trigonometric functions.
6. Ability to analyze functions and their graphs.

1. Review and further development of precalculus material including analytic geometry, functions, and trigonometry.
2. Limits: A) finite and infinite, B) one-sided limits, C) continuity of functions.
3. The derivative: A) slope of a tangent line, B) difference quotient, C) derivative formulas, D) chain rule, E) implicit differentiation.
4. Applications: A) rectilinear motion, B) optimization, C) related rates, D) differentials, E) Newton’s method, F) curve sketching and relative extrema G) concavity and inflection points.

1. The mathematics reading room (Frey 351).
2. Student math resource people available Monday through Thursday nights in Frey 349 and 351.
3. Messiah College welcomes students with disabilities. If you have a documented disability and wish to discuss academic accommodations for this specific course, please contact me as soon as possible. All disability accommodations must be pre-approved through the Office of Disability Services, Hoffman 101 and 102 (x5358).

1. This class is a lecture and discussion oriented class.
2. There will be a minimum of six computer laboratory projects that include written reports.