MAT103 Syllabus

MAT103 (Calculus I) is an introduction to the mathematics of change and a gateway to further study in the natural sciences, engineering, economics and finance.  Its main objectives (continued in MAT104) are

• to develop the technical concepts of limits and continuity, derivatives and integrals in the single variable setting, along with some fundamentally important applications such as
  • related rates
  • extrema and applied optimization,
  • tangent and normal lines (geometry of curves)
  • approximation and error analysis,
  • understanding (counting and estimating) roots ,
  • average behavior and cumulative change,
  • computing area
  • the rudiments of differential equations and modeling, through curve sketching and initial value problems;
• to develop critical reasoning and communication skills in a quantitative setting, to learn how to formulate and test hypotheses independently within a structured mathematical framework, and to practice using calculus to identify key features of a mathematical description of a complex problem.

In MAT103/104, the emphasis is primarily on the first goal above; we focus on concrete examples with the aim of developing the necessary background to pursue the second goal in later courses in mathematics or in other disciplines.

No prior knowledge of calculus is required for MAT103, although a solid background in the main topics from precalculus is absolutely essential. We will emphasize/review the basic toolkit of analytic and algebraic techniques together with the definitions and important properties of the standard functions (polynomials, rational functions, roots, logarithmic and exponential functions, trigonometric functions) that comprise the natural setting for calculus. Although calculators can be an extremely useful analytic tool, they will not be a part of this course. Unfortunately, at this level, they are too frequently a hindrance to developing the independence that is one of the main goals of the course.

The more challenging MAT103 problems require new analytic skills that are not usually taught in typical high school mathematics courses. Learning to think independently and creatively in a mathematical setting takes time and lots of practice. Extending your ability to see connections and combine ideas that originally existed in separate mental compartments to the quantitative realm is a powerful enhancement of your problem-solving potential. Being able to formulate your ideas precisely and test them rigorously in order to refine and deepen your insights through mathematical debate will strengthen your skills as an analyst and as an advocate in your future work, whatever it may be.  

Your job in this course is to work hard and keep an open mind, asking questions and learning from the contradictions and surprises that you encounter as you try to solve the practice problems and struggle with new ideas.  Our job is to make sure you have interesting questions to think about, suitable for your current mathematical level, and access to well-informed guides who can help you get the greatest return on your sustained efforts throughout the semester. Lots of help is available including:

• Instructor Office Hours: You can go to any instructor in the course, and no appointment is needed. A schedule of office hours will be posted on the course web site. If the posted office hours conflict with your schedule, discuss this with your instructor. Individual appointments can usually be arranged.
• Review/Problem Sessions: There will be regular (optional) review/problem sessions with the course instructors/undergraduate course assistants/graduate course assistants. The schedule will be posted on the course web page early in the semester.
• McGraw Tutoring/Study Hall/Workshops: The McGraw Center in Frist offers free (peer) tutoring and a good space for informal work with other students in the class.  We encourage you to work with them this semester.