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5040630-250190261938-318687WINDOW ROCK HIGH SCHOOLMATH 162 CALCULUS I Dual Credit Course OutlineNavajo Technical University Course Description:MTH-162 (4) Calculus I This course is designed to develop the analytical ability of students through (1) modeling functions and calculation of its limit, (2) defining and solving derivatives of functions, (3) solving equations of tangent and normal lines, (4) implicit differentiation, (5) chain rule, (6) related rates and optimizations, (7) fundamental theorem of Calculus, (8) volumes of solids of revolution. At times, the learning process relating to the Navajo Culture in the areas of Nitsahakees, Nahat’a, Iina, and Sihasin will be covered as well as other cultures (multi-cultural studies). Prerequisite: A grade of C or better in MTH-123 or an equivalent course or satisfactory placement score. Course ObjectivesIn a calculus course taught using traditional pedagogy, students learn to use calculus to formulate problems, to solve problems, and to communicate their solutions to others.? In addition to these skills, students who successfully complete this course will learn toUse mathematics to structure their understanding of the world around them, and investigate interesting questions in this worldUse technology as an integral part of the process of formulation and solution of problems, and communication of their solutions to othersWork together productively, and learn cooperativelyWeek 1 – Introduction to CalculusActivity/Exercises/Assignment What is Calculus and why do we study it?Research-Computer LabWhat is Calculus used for?Group PresentationHistory of Calculus.Chapter 1 - Limits and Their Properties1.1 An Introduction to Limit.Section Project: Graphs and Limits of Trigonometric Functions1.2 Properties of Limits – Techniques of Limit ComputationAP TEST Prep Exercises, Review Exercises, Problem Solving1.3 Continuity of Functions1.4 Slope of a Curve, Velocity, and Rates of ChangeChapter 2 - Differentiation2.1 The Derivative and the Tangent Line Problem2.2 Basic Differentiation Rules and Rates of ChangeAP TEST Prep Exercises, Review Exercises, Problem Solving2.3 Product and Quotient Rules and Higher-Order Derivatives2.4 The Chain Rule2.5 Implicit DifferentiationSection Project: Optical Illusions2.6 Related RatesChapter 3 – Applications of Differentiation3.1 Extrema on an Interval3.2 Rolle’s Theorem and the Mean Value Theorem3.3 Increasing and Decreasing Functions and the First Derivative TestSection Project: Rainbows3.4 Concavity and the Second Derivative Test3.5 Limits at Infinity3.6 A Summary of Curve Sketching3.7 Optimization ProblemsSection Project: The Connecticut River3.8 Newton’s Method3.9 DifferentialsReview Exercises, Problem Solving, AP Test Prep ExercisesPrerequisites: To be successful in this course, a student should have a strong background in algebra and some familiarity with trigonometry.? Ordinarily this means high school trigonometry and algebra 2, or a course in College Algebra and Trigonometry (Pre-Calculus).Please see the instructor if you have any questions about your preparation for this course.Textbook and required materials:A 3 ring binder to keep and organize your work in this class and a scientific calculator (we have plenty of scientific calculators in class).Loose-leaf paper, which is hole-punched to fit into your ring binder.IMPORTANT REMINDER: When you turn in an assignment, please do not give me pages which have been torn out of a spiral-bound notebook (unless you first trim the edges with scissors). As a matter of courtesy, students are expected to turn off their cell phones during class. You can only use your it if desmos is downloaded on your phone. ................
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