Introduction to the differential and integral calculus with the associated analytic geometry. Meets General Education Mathematical Sciences requirement. Prerequisite: Two years of high school algebra. (Offered each 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, or any student wanting to take more than one semester of Calculus.

1. To develop a rigorous understanding of functions.
2. To study the concepts of differentiation and integration based upon limits.
3. To enhance learning by presenting each topic geometrically, numerically and algebraically.
4. To give students an understanding of the breadth of mathematics by introducing applications in a wide variety of scientific fields.
5. To use the techniques 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 an ability to recognize calculus concepts in the context of written problems and implement the corresponding processes.
9. To develop the process of making appropriate conjectures, finding suitable means to test those conjectures and drawing valid conclusions.

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.

1. Analytic geometry: a) slopes of lines, b) parallel and perpendicular lines, c) distance formula, d) circles and parabolas.
2. Functions: a) domain and range, b) function composition, c) graphing, including odd, even or periodic functions, d) inverse of a function, e) asymptotes, f) use of functions to model concepts.
3. Limits and Continuity: a) finite and infinite, b) one-sided limits, c) continuity of functions.
4. The derivative: a) slopes revisited, b) difference quotient, c) derivative formulas, d) differentiating composite functions, e) uses of the derivative, including curve sketching and finding relative extrema, f) concavity and inflection points, g) implicit relationships and implicit differentiation.
5. Applications of Differentiation: a) extrema on an interval, b) Rolle's Theorem and the Mean Value Theorem, c) increasing and decreasing functions and the first derivative test, d) concavity and the second derivative test, e) curve sketching, f) optimization problems, g) Newton's Method, h) differentials.
6. Integration: a) antiderivatives and indefinite integration, b) area, c) Riemann Sums and definite integrals, d) the fundamental theorem of calculus, e) integration by substitution, f) numerical integration.
7. Logarithmic, Exponential, and other Transcendental Functions: a) the natural logarithmic function and differentiation, b) the natural logarithmic function and integration, c) inverse functions, d) exponential functions: differentiation and integration, e) bases other than e and applications, f) differential equations: growth and decay, g) inverse trigonometric functions and differentiation, h) inverse trigonometric functions: integration and completing the square, i) hyperbolic functions.

1. Modern classrooms (Frey 343-349) equipped with a teaching station and VCR.
2. Several computer labs (Frey 145, 166, and 245) equipped with appropriate software.
3. The mathematics and engineering reading room (Frey 351).
4. Student math resource people available Monday through Thursday evenings 7 - 9 p.m. in Frey 349 and 351.
5. The Murray Library.
6. Films and videos.

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.