ࡱ>  v0bjbj 1rr(H'VVVjjj8djt(sss5t7t7t7t7t7t7t$dvy[tVsQ"sss[t?ptAAAs8V5tAs5tAA l>rP\`jGpb!tt0tp^y_yrr&yV-rssAsssss[t[tMssstssssysssssssss : William Paterson University, NJ College of Science and Health Department of Mathematics Course Outline 1.Title of Course, Course Number and Credits: Calculus I Math 1600 4 credits 2.Description of Course: Limit and continuity of functions, the Intermediate Value Theorem, derivatives, differentiation rules, Rolle's theorem and the Mean Value Theorem, applications of differentiation, antiderivatives, definite integrals and the Fundamental Theorem of Calculus. 3.Course Prerequisites: Placement or Pre-Calculus - Math 1160 or Algebra, Trigonometry and Functions - Math 1350 4.Course Objectives: To study calculus techniques and methods and to teach the use of technology to explore topics related to limits, continuity, differentiation and integration. To illustrate applications of those techniques and technology to problem solving in science, mathematics, business, computer science, and other related areas. 5.Student Learning Outcomes. UCC Area SLOs students will meet upon the completion of this course. Area Three: Ways of Knowing, Quantitative Thinking SLOS Students will be able to: 3e1.Interpret and evaluate quantitative or symbolic models such as graphs, tables, units of measurement, and distributions. In Limits, students learn to read limits from graphs, compute them from tables and from algebraic formulas of functions. Continuity is taught by interpreting graphs of functions and analytically by using limit definition of continuity. The Derivative is introduced as a rate of change and as a graphical representation of the slope of the tangent line of the graph of a function. Derivatives are computed algebraically and using rules of differentiation. The definite integral is interpreted graphically as the area under the curve, evaluated numerically using the limit of a Riemann sum and evaluated analytically using formulas for antiderivatives and integrals. (Meets Program Outcomes (2), (4), (5) and (8)). 3e2.Perform algebraic computations and obtain solutions using equations and formulas. Students continually perform algebraic computations, simplify algebraic expressions and solve structured multi-step problems throughout the course. For instance, students apply derivatives to successively compute position, velocity and acceleration. Differentiating functions typically involves working on their parts and assembling the parts, using rules and formulas. (Meets Program Outcomes (2), (4) and (5)).3e3.Acquire the ability to use multiple approaches - numerical, graphical, symbolic, geometric and statistical - to solve problems. Students learn Limits using graphs of functions and by algebraic computations. Continuity is taught by interpreting graphs of functions and analytically by using limit definitions of continuity. The Derivative is introduced as a rate of change and as a graphical representation of the slope of the tangent line of the graph of a function. Derivatives are computed algebraically and using rules of differentiation. The definite integral is interpreted graphically as the area under the curve, evaluated numerically using the limit of a Riemann sum and evaluated analytically using formulas for antiderivatives and integrals. Students see the main concepts of calculus, namely, Limits, Continuity, Differentiation and Integration using graphical, symbolic and numerical approaches. (Meets Program Outcomes (2), (4), (5) and (8)). 3e4.Develop mathematical thinking and communication skills, including knowledge of a broad range of explanations and examples, good logical and quantitative reasoning skills, and facility in separating and reconnecting the component parts of concepts and methods. Students learn to apply mathematical thinking and techniques to problems such as maximizing the volume of a box or a cone with a fixed surface area. They understand the requirements of a given problem, represent it symbolically, use appropriate geometric formulas, calculus techniques, solve the problem and meaningfully interpret the answer. Another area of such an application is computing velocity and acceleration and using their answers meaningfully to evaluate the maximum height reached by an upward moving object. (Meets Program Outcomes (2), (4), (5) and (8)). Other Course Specific SLOs students will meet upon the completion of this course: Effectively write mathematical solutions in a clear and concise manner. (Meets Program Outcome (1)) Locate and use information to solve calculus problems. (Meets Program Outcome (5)) Demonstrate ability to think critically by interpreting and solving related rate, optimization, and additional application problems. (Meets Program Outcomes (2), (4) and (5)) Demonstrate ability to think critically by recognizing patterns and determining and using appropriate techniques for solving problems involving limits and derivatives. (Meets Program Outcomes (2), (4) and (5)) Work effectively with others to complete homework and class assignments. This will be assessed through graded homework assignments and class discussions. (Meets Program Outcome (1)) Demonstrate the ability to integrate knowledge and ideas of limits and derivatives in a coherent and meaningful manner and use appropriate technique for solving such problems. (Meets Program Outcomes (1), (2), (4) and (5)) Demonstrate intuitive and computational understanding of limits, continuity and differentiation, through calculations and graphing calculators, and usage of web based learning tools. (Meets Program Outcomes (2), (4), (5) and (8)) Demonstrate the ability to integrate knowledge and ideas of definite and indefinite integrals in a coherent and meaningful manner. (Meets Program Outcomes (1), (2), (4) and (5))6.Topical Outline of the Course Content:Limits and Their Properties3 weeksFinding Limits Graphically and Numerically Evaluating Limits Analytically Continuity and One-Sided Limits Infinite Limits Limits at InfinityDifferentiation3.5 weeksThe Derivative and the Tangent Line Problem Limit Definition on the Derivative Basic Differentiation Rules and Rates of Change The Product and Quotient Rules and Higher Order Derivatives The Chain Rule Implicit Differentiation Derivatives of Inverse Functions Applications of Differentiation 3.5 weeksExtrema on an interval Rolle's Theorem and the Mean Value Theorem Increasing and Decreasing Functions and the First Derivative Test Concavity and the Second Derivative Test A Summary of Curve Sketching Optimization Problems or Related RatesIntroduction to Indefinite and Definite Integrals3 weeksAntiderivatives and Indefinite Integrals Basic Rules of Integration The Area Problem Riemann Sums and Definite Integrals The Fundamental Theorem of Calculus 7.Guidelines/Suggestions for Teaching Methods and Student Learning Activities: This course is taught as a lecture course with student participation. Classroom lectures to illustrate concepts. Student assignments to enhance concepts. Web-based assignments to enhance problem solving skills. Web-based resources for independent learning and practice. Math Learning Center available for peer tutoring 8.Guidelines/Suggestions for Methods of Student Assessment (Student Learning Outcomes) Short quizzes, graded homework, graded web-based homework (suggested 10% of final grade) and three in-class examinations are suggested. The common final examination is cumulative. Attendance Policy - More than 5 absences is an automatic F. The UCC Area SLOs will be assessed as follows: 3e1. The methods of evaluation used in this course are primarily homework, class work, quizzes and tests. Online homework is assigned and online learning tools are available. This SLO will be assessed primarily through homework and test questions designed to gauge a students ability to interpret graphs and their relations to symbolic manipulations. 3e2. The methods of evaluation used in this course are primarily homework, class work, quizzes and tests. Online homework is assigned and online learning tools are available. This SLO will be assessed primarily through homework and test questions which gauge the students ability to perform standard algebraic computations necessary for effective problem-solving. The problems will also measure the students ability to use appropriate formulas, including proper identification of the relevant quantities involved. 3e3. The methods of evaluation used in this course are primarily homework, class work, quizzes and tests. Online homework is assigned and online learning tools are available. This SLO will be assessed partly through homework and test questions designed to measure the students proficiency in employing each approach. 3e4. The methods of evaluation used in this course are primarily homework, class work, quizzes and tests. Online homework is assigned and online learning tools are available. This SLO will be assessed primarily through homework and test questions designed to gauge the students proficiency in the problem solving procedure: assembling the relevant information, translating into mathematics, employing a model or formula and interpreting results. 9.Suggested Reading, Texts and Objects of Study: Calculus: Early Transcendental, 2nd Ed. Briggs, Cochran, Gillett, Pearson. 10.Bibliography of Supportive Texts and Other Materials: Calculus: Early Transcendental Functions, Larson/Edwards, Brooks/Cole. Calculus, Early Transcendentals, Edwards and Penney, Prentice Hall. Calculus: Early Transcendentals, James Stewart, Brooks/Cole. 11. Preparers Name and Date: Fall 1979 12.Original Department Approval Date: Fall 1979 13.Revisers Name and Date: Professor P. von Dohlen, Fall 2008 Professor J. Champanerkar, Fall 2010 Professor C. 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