Approved by University Studies Sub-committee 2/21/07. A2C2 action pending. Applied Calculus MATH 140-01 9:30-10:50 a.m., Gild 325 3 credits ~ Spring 2007 This course satisfies the University Studies Mathematics Basic Skills Requirement Instructor: Nicole Williams E-mail: [email protected] Office: Gild 305 Office Phone: 457- 5380 Schedule: Monday Tuesday Wednesday Thursday Friday *** MTED 320 Gild 327 (until 9:20) MTED 421 Gild 161 MTED 320 Gild 327 (until 9:20) MTED 421 Gild 161 8:00-9:00 9:00-10:00 *** 10:00-11:00 Office Hours MATH 140/Gild 325 (9:30-10:50) 11:00-12:00 12:00-1:00 MTED 201 Gild 329 2:00-3:00 Office Hours MATH 140/Gild 325 (9:30-10:50) Office Hours Office Hours Office Hours MTED 201 Gild 329 Office Hours MTED 201 Gild 329 Office Hours Office Hours *** Office Hours *** MTED 201 Gild 329 *** MTED 201 Gild 329 *** *** *** *** 1:00-2:00 MTED 201 Gild 329 Office Hours Text & Calculator The text is Applied Calculus by Hughes-Hallett, Gleason, Lock, Flath, et al, 3rd edition. We will cover several topics from the book but not all. A graphing calculator is required. I will do demonstrations with a TI overhead. Introduction This class will require you to read the entire section before doing the homework. This book is one of the most “readable” math books that I have encountered, so it is possible to do. In order to pass this class you will have to do the homework assignments and ask questions. Almost your entire quiz and test questions will be similar to homework problems. I expect you to be in class. If you miss a class, you are responsible for the material covered and anything else that was stated in class. Quizzes We will have 7 short in class quizzes. Each quiz will count as 10 points. The two lowest quiz scores will be dropped. Quizzes will count toward 25% of your grade. Exams There will be 4 in-class exams and one comprehensive final exam. Exams will consist of multiple-choice questions and/or short-answer. Your exams will count as 45% of your final grade. Your final exam will count as 20% of your final grade. The final exam will be on Wednesday, May 2 from 1:00-3:00 p.m. Homework Daily homework assignments will be collected periodically throughout the semester. Since most of the quizzes and tests are based on homework, it is expected that all homework will be completed. Your homework score will comprise 10% of your final grade. Material Covered Chapter 1 Functions & Change (1.1-1.9, Focus on Theory, Limits)) Chapter 2 Rate of Change: The Derivative (2.1-2.5, Focus on Theory, Definition of the Derivative) Chapter 3 Short-Cuts to Differentiation (3.1-3.4, Focus on Theory, Derivative formulas) Chapter 4 Using the Derivative (4.1-4.5) Chapter 5 Accumulated Change: The Definite Integral (5.1-5.5, Focus on Theory, Theorems) Chapter 6 Using the Definite Integral (6.1-6.4, as time permits) Chapter 7 Antiderivatives (7.1-7.4) Additional topics may be added if time permits and due to time constraints certain elective topics may be deleted. For additional information about the basic skills learning outcomes for this course please see below. Final Grade Homework Quizzes (7 quizzes with two lowest scores dropped) Class Exams (4 exams) Final Exam 10% 25% 45% 20% The grading scale will be 91% for an A, 81% for a B, 71% for a C, 61% for a D, and below 61% will result in an F. Your grades will be posted on D2L as soon as possible after you complete an assignment, test, or quiz. I will e-mail you as soon as I post grades. It is good practice to keep updated on your grade. Here are my expectations for you as a student in my MATH 140 class: I expect you to be in class everyday. Complete all the homework every night, and overall… Extremely enthusiastic about math. Not everyone will meet my expectations but please try to the best of your ability. BASIC SKILLS LEARNING OUTCOMES This course can be used to satisfy the University Studies requirements for Basic Skills in Mathematics. Each of these courses must address at least four of the following outcomes. These courses must include requirements and learning activities that promote students’ abilities to... a. use logical reasoning by studying mathematical patterns and relationships; Studying instantaneous rate of change of certain physical phenomena or processes in this course students learn the mathematical patterns and relationships about changes that happen over the interval of time and with logical reasoning they argue how they can obtain the rate of change at any given instant. Similarly knowing the instantaneous rate of change of a certain physical phenomenon, i.e. the derivative of the function that modeled the phenomenon, students use logical reasoning to find the total change over a period of time. With all derivative and anti-derivative theorems and formulae, students use logical reasoning to simplify and interpret the solutions in a meaningful way in terms of economics and finance. b. use mathematical models to describe real-world phenomena and to solve real-world problems - as well as understand the limitations of models in making predictions and drawing conclusions; Mathematical modeling and solving real-world problems is the primary emphasis of this course. Students learn to find, for example, the price of the tickets which maximizes revenue, how much sales needed to maximize the profit, how much money should be spending on advertising to guarantee maximum sales, what is the time when the concentration of a drug in the blood is maximum and what is the maximum concentration, how to minimize the energy needed to perform a certain job with maximum efficiency, what is the radius of the trachea when a person coughs with a maximum thrust, what should be the shape of a can to minimize the cost of the material use, how to reach a ship in the least amount of time in the middle of the ocean when it calls for help, etc., etc. -- the list is long and strong. All these problems use the knowledge of many functions like linear functions, polynomial functions, exponential functions, logarithm functions and some trig functions; and reasoning and understanding of the problem, limitations of the models, drawing a recent diagram, introducing the variables and notations, making predictions, knowing how to take derivatives and deriving conclusions. Modeling and solving real-world problems are also included in this course via the process of anti-derivative, where students are required to find area, average value of a certain value of a certain function which modeled the changes in price, demand or cost, find consumers and producers’ surplus, find present value or a future value of an estate or a deal in the process of negotiation, finding population of a certain country knowing the relative birth rate, growth rate and death rates etc. etc. c. organize data, communicate the essential features of the data, and interpret the data in a meaningful way; Students need to organize data; learn to read, understand and interpret essential features of the data in this course form the beginning to the end of the course in at least three different ways. First one is from the tables, second one is from the formula of the functions modeling the scenario and third from the graphs that presents the scenario. Without being able to organize, communicate and interpret a data students will not survive in this course. d. extract correct information from tables and common graphical displays, such as line graphs, scatter plots, histograms, and frequency tables; This course requires that students be allowed to use a graphing calculator. They use a graphing calculator to extract correct information from tables and graphs. First they need to understand the story, model with a function, then, use a calculator to analyze the function and finally they extract the meaning information to make a prediction for the story. Students will learn how to connect the mathematics of a function to its appearance. e. express the relationships illustrated in graphical displays and tables clearly and correctly in words; and/or The required efficiency in language skill is extremely high in this course as all students will have to write their answers, interpretations with units in grammatically correct sentences in terms of finance and economics for all the problems they do whether the problems deal with elementary functions, derivatives or anti-derivatives. f. use appropriate technology to describe and solve quantitative problems. Students use a graphing calculator at all times in this course for doing problems as described above.