MAT 126 -- Calculus I
Fall 2007

Professor: D. Bradley Phone: (207) 581-3920 Office: 322 Neville Hall Hours: MWF 11 a.m. -- noon*

Teaching Assistant: Zezheng Li Phone: (207) 581-3950 Office: 425 Neville Hall Hours: After 3:00 p.m. Tuesdays and Thursdays

Text: The mathematics department has selected "Calculus: Early Transcendentals" by Jon Rogawski, published by W. H. Freeman and Company, ISBN-13: 978-7167-7267-5, ISBN-10: 0-7167-7267-1. Get the single-variable version unless you intend to take MAT 228 (Calculus III, a.k.a. multi-variable calculus) in the future. Copies should be available at the UM bookstore on the Orono campus.

Lectures: Divisions 7,8 & 9 of MAT 126 meet together Mondays, Wednesdays and Fridays in 102 Murray Hall from 1:10-2:00 p.m. The divisions meet separately on Tuesdays and Thursdays with Mr. Li according to the following schedule: Division 9 meets noon-12:50 p.m. Tuesdays in Barrows 133 and Thursdays in DPC 113; division 7 meets 1:00-1:50 p.m. Tuesdays in Nutting 213 and Thursdays in DPC 113; division 8 meets 2:00-2:50 p.m. Tuesdays in Neville 204 and Thursdays in DPC 113.

Math Help: The Math Lab in 419 Neville Hall will be staffed for the duration of the course from 10 a.m. until 4 p.m. Mondays through Thursdays and from 10 a.m. until 3 p.m. Fridays. Please feel free to contact Mr. Li or Professor Bradley with any course-related issues.

Homework: Assignments will be collected weekly, with classes on Tuesdays and Thursdays devoted to answering questions related to the assignments and working sample problems.

Midterm Exam: Expect an in-class midterm examination to be administered the 3rd or 4th week of October. We'll fix the exact date a week or so in advance.

Final Exam: The final examination schedule is determined university-wide. All final exams are held during the week of Monday December 17 through Friday December 21. When the specific date, time and location of our exam become available, I will convey this information in class.

Grading: Your final grade will be calculated as G=(0.3)F+(0.15)M+(0.55)H, where F, M and H are the respective final exam, midterm exam and homework scores expressed as percentages.

Syllabus:

Background / Preliminaries Multiple representations of functions - table, graph, formula Types of functions Elementary - polynomial, rational, algebraic Transcendental - trigonometric, exponential, logarithmic Piecewise defined Even or Odd Transformations of functions and graphs Translations Reflections Dilations and contractions Operations on funtions Addition, subtraction Multiplication, division Composition Inversion Limits and Continuity Limit concept, motivation, existence Computation of limits Continuity Types of discontinuities Extreme value theorem Intermediate value theorem Differentiation Slopes, rates of change Definition of derivative Mean value theorem Rules for differentiation Sum rule Product rule Quotient rule Chain (composition) rule Rule for differentiating inverse functions Derivatives of trigonometric functions Derivatives of exponential and logarithmic functions Logarithmic differentiaion Implicit differentiation Applications of Derivatives Linear approximations Newton's root-finding method L'Hopital's rule for limits Finding extreme values of functions Determining where a function increases Convextity/concavity and curve sketching Optimization problems Differential equations Introduction to Integration Area under curve Distance vs. displacement Riemann sums Definite Integrals Fundamental Theorem of Calculus Antiderivatives

By the end of the course, you should be able to: represent a "real-life" situation with the graph of a function interpret a graph in "real-world" terms sketch graphs of functions by hand perform algebraic operations on functions decompose a composite function into its component sub-functions determine how transformations of functions affect their graphs recognize whether a function is invertible sketch the graph of f-inverse knowing the graph of f recognize the importance of limits distinguish between limits from the left and the right explain why a limit need not exist determine whether or not a limit exists compute limits that do exist apply limits to graphing, asymptotes determine where a function is and is not continuous find the equation of a secant line find the equation of a tangent line find average and instantaneous velocities differentiate elementary and transcendental functions find the derivative of a function using the definition determine where a function is and is not differentiable deduce properties of a function from its derivative find extreme values of a differentiable function on a closed interval determine the intervals where a function is increasing/decreasing determine the intervals where a function is convex/concave use the above information to sketch an accurate graph set up and solve optimization problems evaluate limits of indeterminate forms solve transcendental equations numerically set up and solve a simple differential equation distinguish between signed and unsigned area calculate areas under curves evaluate limits of Riemann sums express an integral as a limit of sums estimate integrals using upper and lower sums find the distance/displacement given the velocity differentiate a function defined by an integral evaluate an integral by antidifferentiation