ࡱ> _ )bjbj(( B8\B8\!HH$<Y;4(\\\\:::::::$i=@:@:\\{;"\\::R7x:\P~mټ98,:);0Y;8@O@<x:@x:L::Y;@H> : Boise State University-Rocky Mountain High School Concurrent Enrollment Program Math 170: Calculus 1 (4 Credits) 2016-2017 School Year Mr. Dan Drlik  HYPERLINK "mailto:drlik.daniel@westada.org" drlik.daniel@westada.org 208-350-4340 x 1127 Course Overview I cover everything in the Calculus AB topic outline. My main objective is to enable students to appreciate the simplicity and power of calculus and receive a strong foundation in mathematics. I try to improve my students critical thinking skills that will allow them to make the necessary connections needed to be successful on the AP exam. Students know they will work much harder than in any previous math class, but as a result, will gain a tremendous amount of knowledge. Disciplinary Lens Math 170: Calculus I satisfies four credits of the Foundation Program's Disciplinary Lens-Mathematics (DL-M) requirement. It supports the following University Learning Outcomes, along with a variety of other course-specific goals. 7. Apply knowledge and the methods of reasoning characteristic of mathematics, statistics, and other formal systems to solve complex problems. Math 170: Calculus I is designed to introduce students to the principles, techniques and applications of derivatives and integrals. This course helps to achieve the goals of the Foundations program by focusing on the following course learning outcomes. After successful completion of this course, you will be able to: Recognize and illustrate the geometric relationships between the derivative and integral of a function and the graph of the function, and relate this geometric information to solutions derived through formulas. Identify the relevant data contained in problems presented in verbal, tabular and/or graphical formats. Present solutions clearly in logical and mathematically correct terms. Formulate and implement solution strategies for problems drawn from the sciences and engineering, and draw meaningful conclusions from the resulting answers. Recognize that the derivative is a rate of change, and be able to apply this insight to analyze and solve problems. Recognize that the integral can be approximated by finite sums, and be able to apply this insight to analyze and solve problems. Course Planner Below is the sequence of the AP Calculus AB course. Limits and Their Properties A Preview of Calculus Finding Limits Graphically and Numerically Evaluating Limits Analytically Continuity and One-Sided Limits Infinite Limits Differentiation The Derivative and the Tangent Line Problem Basic Differentiation Rules and Rates of Change The Product and Quotient Rules and Higher-Order Derivatives The Chain Rule Implicit Differentiation Related Rates Students will be shown how to use their calculator to evaluate a derivative at a given point. They will then practice using their calculators to answer several AP exam questions. Applications of Differentiation Extrema on an Interval Rolles Theorem and the Mean Value Theorem Increasing and Decreasing Functions and the First Derivative Test Concavity and the Second Derivative Test Limits at Infinity A Summary of Curve Sketching Optimization Problems Newtons Method Integration Antiderivatives and Indefinite Integration Area Riemann Sums and Definite Integrals The Fundamental Theorem of Calculus Integration by Substitution Numerical Integration Students will be shown how to use their calculators to evaluate definite integrals. We will discuss various uses of the Fundamental Theorem of Calculus and work several AP exam problems. Logarithmic, Exponential and other Transcendental Functions The Natural Logarithmic Function: Differentiation The Natural Logarithmic Function: Integration Inverse Functions Exponential Functions: Differentiation and Integration Bases other than e and Applications Inverse Trigonometric Functions: Differentiation Inverse Trigonometric Functions: Integration Differential Equations Slope Fields and Eulers Method Differential Equations: Growth and Decay Separation of Variables and the Logistic Equation Applications of Integration Area of a Region Between Two Curves Volume: The Disk Method Volume: The Shell Method Arc Length and Surfaces of Revolution Work Fluid Pressure and Fluid Force Integration Techniques Integration by Parts Trigonometric Integrals Trigonometric Substitution Partial Fraction Decomposition LHopitals Rule Improper Integrals Preparation for the AP Exam In preparing for the AP Exam, I will do various activities. One of the activities we work on the most is having my students explain the calculus concepts and justify their solutions. This is done both orally and in written sentences. We will discuss various concepts as a class and I will call on individual students to give reasons or explanations for the answers. They will then be given assignments that they can work on individually or as groups that require them to write their justifications of the answers in complete sentences. This way I know they not only understand how to get the answers but that they can back up those answers with correct justifications. Primary Textbook and Tools Larson, Hostetler, Edwards. Calculus of a Single Variable 8th ed. Boston: Houghton Mifflin Company 2006 ISB: 0-618-50304-8 The majority of my students use TI 83 and TI 84, with some TI 89 Calculator Ideas Throughout the year, we will discuss how to use the graphing calculators to solve various types of problems. This includes: finding roots, sketching functions in certain windows, and approximating the derivative at a point and definite integrals using numerical methods. Students will also be asked to make connections between the graphs of functions and their analysis, and conclusions about the behavior of functions when using a graphing calculator. Student Assessment An exam is given after each topic listed above. Most exams have both a non-calculator and calculator section. This ensures that my students have the required calculator skills for the AP exam but at the same time must show proficiency in understanding the concepts without having to rely on the calculator. Grades The course grade will be determined by scores earned on homework, quizzes, projects, tests and the final exam. The weights for each are listed below: Homework 10% A.>90% Quizzes/Projects20% B.80-89% Tests.......50% C.70-79% Final20% D.60-69% F..<60% Extra Help I will make myself available for help outside the class period at specified times. If a student needs extra help, it will be their responsibility to seek me out during one of these times. Homework Policy As with any skill based subject or activity, without perfect practice, perfection cannot be achieved. Homework is the way that you will practice in this class. Without doing the homework, you should not expect to perform well in this class. All homework will be self-assessed. The homework score will be based on a self-assessment (5 points) as well as a one or two question quiz (5 points). Students will be able to make-up homework scores by completing an assignment determined by the instructor prior to taking the test for the chapter. Once the test has been administered, all homework scores are final. Tests and Quizzes Quizzes will be given throughout the course of a chapter. Some will be in-class, while others will be take-home. These will measure your understanding throughout the chapter. Tests will be given upon the completion of a chapter. Reviews will be given for each test. However, the review will simply have topics that have been covered in the chapter and will in no way resemble the format of the test. Solutions for the review will be posted on the class website well in advance of the test. There are NO MAKE-UPS on tests and quizzes. Take-home quizzes will not be accepted after the assigned due date. Class website Visit  HYPERLINK "http://www.westada.org/Domain/2744" http://www.westada.org/Domain/2744 for class documents, notes, and review solutions. Academic Dishonesty The West Ada School District student handbook as well as policies set forth by Boise State University will be followed when it comes to academic dishonesty. 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