MAT100

MAT100 (Foundations of Calculus) is an introduction to the fundamental concepts of limits and derivatives as a preparation for further courses in calculus or to understand mathematical models in other contexts. Over the course of the semester we will review and develop an integrated understanding of 

• standard algebraic tools including the quadratic formula, completing the square, conjugation and factoring techniques, the method of elimination and substitution used to solve (possibly nonlinear) systems of equations and inequalities
• geometric concepts including calculating area and distance in the plane, recognizing symmetry and using it as a simplifying tool, sketching conic sections and understanding the equations that describe them, using trigonometry to work with triangles and circles along with special triangles and identities that arise from this study

Both limits and derivatives will be important tools as we work through the standard library of functions including

• polynomials and roots, 
• rational functions, 
• logarithmic and exponential functions, 
• trigonometric functions and their inverses 

with particular emphasis on understanding the graphical behavior of these functions and of more complex functions we can build by combining these basic ones. Limits will give us a language to discuss and understand the general features of a function's behavior near the boundary of its domain, and we will use derivatives to introduce the geometric notions of tangent and normal lines in order to develop tools for numerical estimation and approximation and to study rates of change.

Note: Although calculators can be an extremely useful analytic tool, they will not be a part of this course. At this level, they can be a hindrance to developing the independence and foundational knowledge that are the main goals of the course.

We will consider problems involving geometry, equations and functions that will often appear in later calculus courses or in other contexts where we study models of dynamic behavior of complicated systems and the emphasis throughout the course will be on developing advanced problem solving skills needed to think independently and creatively in a quantitative setting. This adjustment takes time and lots of practice, and it can be very intimidating at first, but it is worth the effort!  Extending your ability to see connections and combine ideas in a mathematical setting will be a powerful enhancement of your problem-solving potential and it 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: A schedule of office hours will be posted on the course web site and no appointment is needed. If the posted office hours conflict with your schedule, discuss this with your instructor – individual appointments can usually be arranged. Remember vague and ill-posed questions are a normal part of the learning process and are very welcome. (If you knew exactly what you were confused about then you probably would not be confused anymore!)
• 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.