MAT104

MAT104 is the second course of the standard 3-semester calculus sequence. The topics in this course are of fundamental importance in the natural sciences, engineering and finance:

• Techniques and Applications of Integration: Standard techniques for computing integrals including substitution methods, integration by parts, the method of partial fractions are thoroughly developed in the first three weeks of the course, along with techniques for analysis of the behavior of improper integrals. These methods for computing integrals appear again later in the course when we discuss applications of the definite integral to geometry (area, length and volume) and applications of indefinite integrals to modeling techniques.
• Infinite Series and Approximation:  In the second three weeks of the course, the analysis of rates of growth/decay introduced in the discussion of improper integrals are extended to study the convergence and divergence of infinite series, starting from the geometric series and the harmonic series. This leads into a thorough discussion of power series and Taylor's theorem with theoretical applications as well as applications to numerical estimation and approximation (with error analysis) of transcendental quantities or integrals that cannot be computed in closed form using the standard library of functions.
• Introduction to Differential Equations: Starting with first-order separable and linear equations, we move on to discuss complex numbers and polar coordinates as a tool for analyzing second-order differential equations.  

Success in this course requires expert familiarity and fluency in using all the standard algebraic manipulations and the standard library of functions (polynomials, rational and root functions, logarithms and exponentials, trigonometric functions and their inverses). Solving equations with these functions, computing their derivatives and sketching their graphs (without calculators) are common intermediate steps that are assumed to be second-nature, requiring little to no review for most students. 

This course emphasizes the development of mature problem-solving skills, requiring sophisticated pattern-recognition and the ability to plan-out, apply and adapt multiple techniques to solve a single problem. Learning to think independently and creatively in a quantitative setting takes time and lots of practice, and it can be very intimidating at first, but it is worth the effort, and an essential skill for a working scientist or quantitative analyst in any field.

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.
• 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