**Text:** Larson, Hostetler & Edwards. *Calculus: Early Transcendental Functions*, 6th ed. Cengage Brooks/Cole, 2014, ISBN-10: 1285774779.

**Rationale.** Calculus is an introduction to the branch of mathematics called real analysis. It is the science of change. This change is expressed using two complementary concepts: derivative and integral. These are powerful ideas that underly profound developments in technology and the physical, social, and life sciences of our time. Calculus 1 focuses on differential calculus, Calculus 2 centers on integral calculus, Calculus 3 extends these ideas to functions of several variables, and this study of calculus culminates in Ordinary Differential Equations (MAT 224) where calculus is used to create mathematical models of systems and phenomena. To be conversant, to solve problems, and to investigate things that change requires a knowledge of calculus.

**Catalog Course Description.** http://www.wlc.edu/uploadedFiles/_Site_Assets/Documents/Academics/Catalog-MAT.pdf

**Objectives.** (1) To initiate an understanding of the fundamental definitions and concepts of analysis, (2) To master computational skills in real analysis, (3) To sample some of the many application areas of analysis, (4) To expand personal perspectives on the history and role of mathematics in society, and (5) To inculcate an appreciation of the concepts that form the foundation of science and technology.

**Course Content.** The course will consist of topics chosen from review material and chapters 1 - 5 in the text plus supplementary material as required. On the average one section of the text will be covered each day. Some sections will require two days.

**Labs.** There will be a 1-week (ungraded) tutorial assignment plus 3 (graded) lab assignments which will be done by pairs of students in a computer lab. These will introduce concepts covered in class and enable the discovery of additional ideas. For every lab (not the tutorial) each pair of students will complete and submit a brief written report. There will be approximately one week to complete each lab.

**Methodology.** See your professor's personal syllabus for a description of the manner in which the course will be taught. In particular take note of how the instructor's component of the final grade is determined. WARNING: learning calculus is a cumulative experience. New knowledge depends on understanding previous material. For this course it is imperative that you get your work done on time. If you are unprepared even once, you may never catch up.

**Exams.** There will be three in-class exams plus a final exam. Each exam will cover one or two chapters in the text. The final exam will be cumulative. IMPORTANT: see the Calculus 1 Core Exercises page (http://faculty.wlc.edu/calc/calc1_core_exercises.html) for the kinds of problems you need to be able to do on exams. Also see the Calculus 1 Performance Expectations page (http://faculty.wlc.edu/calc/calc1_performance_expectations.html) which lists the topics and proficiences that will be tested on exams.

Exam policies:

- Calculators may not be used on exams. Mathematics is an exact science. Calculators are used for computational approximation and graphing. You will be tested on the performance expectations for the course. These involve understanding concepts, performing certain mental procedures, analyzing functions, and doing some exact evaluations. For this calculators are unnecessary. They also cause problems with testing: some students may not have calculators, some calculators can perform symbolic manipulations that are on the exam, some can store in memory information that is being tested, and some can communicate with other calculators. You are encouraged, however, to use calculators for your daily work to check approximate answers to homework exercises and for graphing functions. It is not wise to rely on calculators to evaluate trigonometric functions that you need to be able to do mentally. Calculators do have appropriate uses.
- All exams are closed book, closed notebook.

**Grading.** The final average (AVE) is a percentage that will be computed as follows:

- E = Exam average
- F = Final exam score
- L = Lab average
- I = Instructor component
- AVE = .55E + .25F + .10L + .10I

The grade for the course is determined by the value of AVE: A: 100-93, AB: 92-88, B: 87-83, BC: 82-78, C: 77-73, CD: 72-68, D: 67-60, F: below 60. Your professor reserves the right to exercise discretion in raising your grade if he feels that the value of AVE does not properly reflect the quality of your work (e.g. because of one low exam score). This does not imply in any way that the lowest test score necessarily will be dropped. Your professor will not use discretionary judgments to lower your final grade.

**Attendance Policy.** We want you to succeed in this course. Experience shows that cutting calculus can be disastrous. Consequently, any kind of absence is unwise. Unexcused absences will not be permitted. Any student who, in the judgment of the professor, has a pattern of unexcused absences will be cautioned that attendance is required. A student who fails to heed this warning will be reported to the dean of the College of Arts and Sciences for corrective action.

**Late Work.** Submitting late work and taking make-up tests will not be permitted unless, in the judgment of the professor, there are legitimate extenuating circumstances. If you must miss a test, you are expected to notify your professor beforehand by phone, email, or in person. Unacceptable late work or make-up tests will receive a grade of 0.

**Class Atmosphere.** As in all WLC classes you are expected to conduct yourself honorably and considerately.

**Academic Integrity.** You are expected to abide by the WLC Code of Academic Ethics (http://www.wlc.edu/uploadedFiles/Content/Campus_LIfe/Student_Life/Student-Handbook.pdf).

**Accommodations for Students with Disabilities.** In compliance with the WLC policy and equal access laws, your professor is available to discuss appropriate academic accommodations that may be required for students with disabilities. Requests for academic accommodations should be made during the first three weeks of the semester (except for unusual circumstances) so arrangements can be made.

Students with documented disabilities are encouraged to contact the Office of Student Support (http://www.wlc.edu/supportservices/) regarding services including reasonable accommodations. Reasonable accommodations are adjustments to either the College environment or to academic processes in order to assist students with disabilities to succeed. Reasonable accommodations include neither those which require significant difficulty or expense for the College nor personal items such as eyeglasses. In addition to documented disabilities, students facing temporary disabilities such as a surgery or personal/situational crisis are encouraged to contact the Director of Student Support at (414)443-8797 for assistance.

**Subject to Change.** The syllabus and course schedule are subject to change in the event of extenuating circumstances.

Mathworld

Extensive collection of articles on mathematical topics with alphabetical index and search engine.

Wikipedia

Free online encylopedia. Many good articles. However, authors are not necessarily professional experts.

MAA (Mathematical Association of America)

For college students and professors. Special section for students, links to student MAA chapter websites, available REU's (Research Experience Undergraduate), mathematics competitions, schedule of meetings, podcasts, YouTube videos.

AMS (American Mathematical Society)

Geared toward professional researchers. Good starting point for mathematics on the WWW.

SIAM (Society for Industrial and Applied Mathematics)

Links to the world of applied mathematics and computing, professional opportunities.

ASA (American Statistical Association)

Graduate schools in statistics, careers in statistics, and links to other pertinent sites.

INFORMS (Institute for Operations Research and the Management Sciences)

Gateway to OR/MS: Educational and Student Affairs Homepage, educational programs, careers booklet, professional opportunities, job placement, summer internships, on-line publications, news, and links.

SOA (Society of Actuaries)

The leading professionals in the modeling and management of financial risk and contingent events. Publications, education and actuarial exams, research, continuing education, newsroom, special interest groups, and links.

NCTM (National Council of Teachers of Mathematics)

For elementary and high school teachers of mathematics. Curriculum and evaluation standards, news, news service, online jobs.

**What kind of people are mathematicians?**

Albers, Donald J. and Alexanderson, Gerald L., Eds. *Mathematical People: Profiles and Interviews.* 2nd ed., A. K. Peters Ltd, 2008.

Unless your next-door neighbor happens to be a mathematician, you won't find a more human introduction to mathematics than Mathematical People. The book relies on short, lively interviews instead of scholarly biography to dramatize the daily lives, work, and hopes of some 20 modern mathematicians. --Frank Morgan, Technology Review

Albers, Donald J., et al., Eds. *More Mathematical People: Contemporary Conversations.* Harcourt Brace Jovanovich, 1990.

Boyer, Carl B. and Merzbach, Uta C. *A History of Mathematics*, Second Edition. Needham Heights, MA: Allyn and Bacon, 1985; Dubuque, IA: William C. Brown, 1991.

Boyer, Carl B. *The History of Calculus and Its Conceptual Development.* Mineola, NY: Dover, 1959.

Edwards, C.H., Jr. *The Historical Development of the Calculus.* New York, NY: Springer-Verlag, 1979.

Eves, Howard W. *An Introduction to the History of Mathematics with Cultural Connections*, Sixth Edition. New York, NY: Rinehart and Co., 1953; Philadelphia, PA: Saunders College, 1990.

History of Mathematics Archive

Excellent source for biographies of mathematicians, topics in the history of mathematics, chronologies, and historical links. (Award winning site at the University of St. Andrews, Scotland)

Kline, Morris. *Mathematics in Western Culture.* New York, NY: Oxford University Press, 1953, 1971.

Kline, Morris. *Mathematical Thought from Ancient to Modern Times. 3 vols.* New York, NY: Oxford University Press, 1990.

Apostol, Tom M., Ed. *Selected Papers on Calculus.* Washington, DC: Mathematical Association of America, 1969.

Sawyer, W. W. *What is Calculus About?* Washington, DC: Mathematical Association of America, 1975.

Stewart, James. *Calculus: Early Transcendentals* 7th ed., Cengage Brooks/Cole, 2011.