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Techniques of Calculus I

by: Elaina Osinski

Techniques of Calculus I MATH 110

Elaina Osinski
Penn State
GPA 3.88

Ping Xu

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Ping Xu
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This 0 page Class Notes was uploaded by Elaina Osinski on Sunday November 1, 2015. The Class Notes belongs to MATH 110 at Pennsylvania State University taught by Ping Xu in Fall. Since its upload, it has received 12 views. For similar materials see /class/232996/math-110-pennsylvania-state-university in Mathematics (M) at Pennsylvania State University.

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Date Created: 11/01/15
MATH 110 Techniques of Calculus 1 Penn State University Fall Semester 2011 Dr James Hager Coordinator Dr Ping Xu Office 211 McAllister Building Office 329 McAllister Building Phone 863 8753 Phone 865 3517 email hagermathpsuedu jah14psuedu email pingmathpsuedu Office Hours TTH 100 300 Office Hours To be announced during class and By Appointment Textbook Applied Calculus for the Managerial Life and Social Sciences 8th Edition by ST Tan BrooksCole etextbook textbook In addition to the option of purchasing your textbook from the bookstore if you navigate to the cengagebraincom website there are a variety of alternative ways formats for acquiring the textbook materials including renting your textbook purchasing etextbooks or purchasing individual 6 chapters If you plan to take Math 111 you will not need to purchase an additional textbook the same textbook will support both classes All new S T Tan 8th edition copies of your textbook come bundled with the WebAssign learning environment If you choose to purchase a used copy of the textbook you may purchase the WebAssign learning environment directly from the WebAssign website The WebAssign materials include 1 a significant number of homeworkexercise problems from the chapters covered during the lectures 2 instructional videos and 3 stepbystep tutorials Access to these materials is granted by the licensekey included in your textbook Although the completion of WebAssign exercises will not be used directly in the calculation of your grades students are highly encouraged to explore these materials Based on the usefulness of these learning aids a goal during the semester is to integrate some of these materials into the lecture discussions Course Description TECHNIQUES OF CALCULUSI 4 Functions graphs derivatives integrals techniques of differentiation and integration exponentials improper integrals applications Students may take only one course for credit from MATH 110 140 140A and 140B Prerequisite MATH 022 or satisfactory performance on the mathematics proficiency examination Course Coverage The goal for the course is to cover Chapters 26 from the text Chapter 1 is considered review material for the students Each student should confirm that they understand the material in Chapter 1 during the first week of the course Exams Two evening examinations midterms will be given The dates and times of these exams will be as follows Examination 1 Tuesday October 4 2011 630 745 pm Examination 2 Monday November 7 2011 630 745 pm Information on the locations of these exams will be distributed at a future date In addition the math department schedules a con ict exam for each of the midtenns from 505 620 on the same night as the regularly scheduled exam and a makeup exam scheduled on an evening different from the regularly scheduled exam night Signup sheets for the con ict exam or the makeup exam will be available from your lecturers approximately one week before the exam A valid con icUmakeup reason is required to sign up for either of these exams NOTE Ifyou miss an exam Without an of cial excuse such as illness or of cial university business then you may be allowed to take a makeup exam but With an automatic 25 deduction from the grade To avoid this deduction you must notify your lecturer with your of cial excuse before the late and time of the exam This noti cation may be performed in person Via email or by telephone Final Exam The final examination in the course will be comprehensive It will be given during the university s final examination week December 1216 2011 Do not make plans to leave the university before the end of this week Travel plans do not constitute an official university excuse for missing an examination or for obtaining a con ict or makeup examination Con icts for the final exam are determined by scheduling any student with a potential final exam con ict situation should apply online before the final exam con ict application period expires The math department does not offer a makeup exam option for the final exam Readiness Test A Readiness Test is posted under your Lessons tab in your Angel Math 110 workspace Since the purpose of the Readiness Test is to test the basic algebraic skills required to be successful in Math 110 it is critical that everyone take the test during the first week of classes The results of the Readiness Test will not be used in any way during the calculation of your overall course grade Students who score poorly on this test should work the Chapter 1 selfassessment exercises also included on Angel and if still finding difficulty with the preparatory materials strongly consider taking Math 22 before proceeding with Calculus Minimally all students should review the basic algebraic concepts covered by the test questions during the first week of the semester in preparation for the related Calculus materials Chapter 1 of your textbook also provides background materials that may be helpful in preparation for the Calculus concepts discussed in Chapters 2 6 In C l ass Several short quizzes will be given throughout the course of the semester during the recitation class The quiz questions will be similar to the assigned homework problems and the reading done in preparation for class The purpose of the quizzes is to encourage you to keep up with your preparation and reward you for doing so Each quiz will consist of problems based on the materials presented during the previous week s lectures Twelve quizzes are planned for the semester A student s quiz grade will be determined by summing each student s highest ten quiz scores and dropping the remaining ones Each quiz will be worth 10 points Only students with documented universityapproved absences will be allowed to makeup missed quizzes eg university sports participation healthinjury etc Students need to contact their recitation leaders not their lecturers to discuss any issues related to quiz policies The quiz content specific makeup policies partial credit rubric etc are all determined by your individual recitation leader Self Assessment Tests Self Assessment Tests are posted under the Lessons tab at your Math 1 10 Angel website The Self Assessment Tests provide additional problemsexamples that allow you to further explore the key concepts introduced in the lecture classes and assigned homework problems After submitting the tests a numerical score is calculated and feedback provided on the correct approach for solving each problem Each instance of the Self Assessment Test is unique so you may take these tests several times and still benefit from working through the problems Similar to homework problems calculators may be useful to fully explore the problem solutions Although the selfassessment tests are scored their purpose is mainly self diagnostic the numerical results are not included in the determination of your course grades In addition a Collaboration tab is included for you to post questions and responses related to the contenU solutions of these problems to the rest of the class Where helpful I will periodically review these postings and provide additional guidance where necessary Example Practice Exams Models of previous Math 110 exams are included in a folder under the Lessons tab in your Math 110 Angel website Care should be taken in the usage of these models during the preparation for each exam ie students should understand that the exams for this semester are not based strictly on the practice exams Good studypreparation habits include the review of lecture notes completion of assigned homework problems completion of selfassessment exercises and where appropriate attendance at supplemental instruction help sessions Your lecturer will provide specific guidance prior to each exam on the specific topics includedexcluded Sugg ested Homework A list of suggested homework problems appears at the end of this syllabus These homework problems will not be turned in for a grade The purpose of doing the homework is to better understand the material discussed in the lectures and to prepare oneself for the quizzes and exams Since much of this material builds upon previous material you are encouraged to do all of the suggested homework and keep up with the suggested homework even though it will not be collected Solutions to the suggested homework problems are posted in a folder under your Angel Lessons Tab Academic Integrity Academic integrity is the pursuit of scholarly activity in an open honest and responsible manner Academic integrity is a basic guiding principle for all academic activity at The Pennsylvania State University and all members of the University community are expected to act in accordance with this principle Consistent with this expectation the University s Code of Conduct states that all students should act with personal integrity respect other students dignity rights and property and help create and maintain an environment in which all can succeed through the fruits of their efforts Academic integrity includes a commitment not to engage in or tolerate acts of falsification misrepresentation or deception Such acts of dishonesty violate the fundamental ethical principles of the University community and compromise the worth of work completed by others Based on the University s Faculty Senate Policy 4920 a range of academic sanctions may be taken against a student who engages in academic dishonesty Please see the Eberly College of Science Academic Integrity homepage for additional information and procedures Grading Your course grade will be determined by your exam scores and your quiz scores Total possible points follow Examination 1 100 Examination H il 00 Quizzes i 100 EmaliExamination jISO n39rotal Aso M The exact point requirements for each letter grade will be decided at the end of the course General University guidelines follow um B B C D After the second exam and before the latedrop deadline the gradeline cutoffs for the major grades A B C D F will be provided to facilitate your planning for the remainder of the semester The gradelines will be assigned after the final exam The unavoidable consequence is that some students are just a point away from a higher grade For reasons of fairness the policy in this course is to M adjust individual grades in such circumstances Note Your grade will be based exclusively on the midterm examinations final examination and quiz scores There is no extra credit work Students are encouraged to discuss their perfonnance with their lecturers and recitation leaders regularly during the semester and if appropriate work out strategies to improve overall study problem solving and knowledge retention skills Deferred Grades Students who are unable to complete the course because of illness or emergency may be granted a deferred grade which will allow the student to complete the course within the first six weeks of the following semester Note that deferred grades are limited to those students who can verify and document a valid reason for not being able to take the final examination For more information see DF grade Class Attcnrlan cc Although regular classroom attendance will not be used to determine your grade in a tangible way you are strongly encouraged to regularly attend class Attending classes is beneficial to your understanding of the materials described in the text Seeing the material presented in a lecture is extremely helpful as the presentation will often be different than the text in order to clarify and enhance the reading assignments Additionally material not present in the text may be presented in class39 you will be held accountable for this material on quizzes and exams Classroom Protocol Please turn off all cell phones and put away all materials not directly related to the course e g newspapers Since noises are greatly amplified in the lecture halls it is important that nonessential conversations are minimized Finally if you must leave early please notify your lecturer at the beginning of class and sit near an exit to minimize classroom disturbance Calculator Usage A graphicsbusiness calculator is highly recommended but any calculator that can compute quotx to the power yquot is sufficient It may be used as appropriate in the lectures selfassessment tests and homework but will not be allowed on the inclass guizzes two midterms and final examination Obtaining Assistance There are various avenues for obtaining assistance for this course Your lecturer office hours appear above Your recitation instructor they will also hold office hours each week The Math Tutoring Center part of Penn State Learning located on the 2nd floor Boucke building Guided Study Group part of Penn State Learning Times TBA later JAVA Applets The following link wwwmathpsuedudlittlejavacalculusindexhtml provides a set of JAVA utilities that may be helpful in exploring some of the content introduced in this course Hopefully Helpful Hints 0 Learn for the long term Strive to retain the knowledge that you acquire Do not simply try to learn material a couple of days before an exam with the goal of forgetting it right after nals View the learning of the material as an active process not a passive one You are here to learn not to receive grades Learning is a process not an event Strive to know the material to understand it at a very deep level rather than a super cial one Do the homework with as little help solutions manuals friends etc as possible Balance the use of group learning with individual study so you actually know the material Ask questions either in class or during of ce hours Read the textbook before the planned lecture The tentative schedule of classes gives you a guide as to what to read in advance Carefully study and rework the examples in the text Reread and rewrite your notes Study for exams progressively over a long period of time Begin the studying process at least one week prior to the date of the exam Manage your time wisely Plan to spend at least two hours outside of class for every hour in class if not more Take responsibility for your education Work the self assessment tests and learn from the objective feedback 0 O O O O O O O 0 Final Comments It is our hope that your appreciation for mathematics Will grow during this semester Although the applications we cover are limited in scope the application of mathematics extends to many areas in your chosen careers The Calculus skills developed in this class provide a solid foundation for addressing many of the questions that surface during the introduction of standard business models in your future coursework Tentative Class Schedule Lectures Day Date Material Covered Other Information M 822 Course Overview First Day of Classes W 824 21 F 826 22 M 829 23 W 831 2 3 24 F 9 2 24 2 5 No Intermediate Value Theorem Applications M 9 5 Labor Day No Classes W 97 25 9 9 26 912 31 W 914 32 F 916 33 AI 919 34 MarginalRevenue Cost Pro t Marginal Average Revenue Cost Pro t Elasticity Elasticity and Revenue W 921 34 923 35 926 36 Related Rates Basic AlgebraicGeometric Applications Related Rates Business Applications W 928 36 Related Rates Business Applications F 930 41 M 103 41 42 Exam 1 Tuesday Oct 4 6 307 45 Room Assignments Posted under Angel Lessons tab W 10 5 42 Application of Second Derivative Law of Diminishing Returns not included in textbook 107 43 1 10 10 44 W 10 12 45 Absolute Extrema Optimization Business Applications F 10 14 45 Optimization Basic Algebraic Geometric Applications Optimization More Advanced Business Applications M 10 17 51 W 10 19 52 F 10 21 53 Compound Interest Continuous Interest E 39ective Rates of Interest Present Value M 10 24 53 W 10 26 54 F 10 28 54 M 103 1 55 W 1 1 2 55 F 1 14 61 M 117 61 Exam 2 Monday November 7 630745 Room Assignments Posted under Angel Lessons tab W 119 62 F 1111 62 Late Drop Deadline M 11 14 63 W 1 1 16 64 F 1 1 18 65 Thanksgiving Holiday No Classes November 20 26 11 28 65 66 W 1 1 30 66 F 122 67 Consumer Producer Surplus FuturePresent Value of Continuous Income Stream Annuity Amount and Present Last Day of Classes Suggested Homework Problems Section Problems 11 153 odd 6374 7589 odd 12 1 6 723 o dd 2536 4157 odd 5963 13 133 odd 14 1 101145 odd 2 113 odd 2333 3958 22 123 odd 2534 4352 64 65 66 23 17 odd 91417 18 51 53 55 6669 72 74 75 78 24 18 1722 23 39 odd 4966 7380 83 25 114 2135 3944 4555 5760 26 921 odd 23 24 34 35 4752 31 138 4146 32 129 3541 46 48 33 153 odd 6164 34 317 odd 2333 35 119 odd 36 18 929 odd 4147 41 1335 odd 3743 4548 4965 odd 42 18 1114 2365 odd 90 43 110 1127 odd 3743 4953 56 62 44 18 927 odd 40 4653 45 5 8 91017 51 125 odd 52 1720 2128 3542 53 128 54 128 3339 4346 62 63 55 133 odd 4150 5158 61 950 5158 6770 62 143 odd 59 63 35 71315 64 516 1740 41 42 43 65 127 2941 odd 56 59 66 116 1733 odd 6 7 118 Learning Objectives Upon successful completion of Math 110 the student should be able to 1 Identify polynomial rational power exponential and logarithmic functions 2 Calculate the domains of polynomial rational power exponential and logarithmic functions 3 Calculate the sums differences products quotients and compositions of functions 4 Model cost revenue pro t supply and demand business functions 139 Calculate equilibrium points Within supplydemand markets and interpret the results 9 Calculate or estimate nitein nite limits of functions given by formulas graphs or tables gt1 Calculate onesided limits of functions 8 Determine Whether a function given by a graph or formula is continuous at a given point or on a given interval 9 Determine Whether a function given by a graph or formula is differentiable at a given point or on a given interval 10 Distinguish between average and instantaneous rate of change and interpret the de nition of the derivative graphically 11 Determine derivatives of some functions using the de nition of derivative of a function 12 Calculate derivatives of polynomial rational power exponential and logarithmic functions and combinations of these functions 13 Calculate derivatives of implicitly deflned functions 14 Apply the ideas and techniques of derivatives to related rate problems to include basic algebraicgeometric models and costaverage cost revenueaverage revenue profltaverage pro t supply and demand models 15 Apply the ideas and techniques of derivatives to perform marginal analysis of basic economics models 16 Apply the ideas and techniques of derivatives to calculate elasticity of basic economics models 17 Apply the ideas and techniques of derivatives to nding extrema 18 Apply the ideas and techniques of derivatives to graphing functions 19 Apply the ideas and techniques of derivatives to optimization problems to include basic algebraicgeometric models and cost revenue pro t supply and demand models 20 Apply the ideas and techniques of derivatives to solve compound interest continuous interest effective interest rate and present value business models 21 Calculate the Riemann sum for a given function partition and collection of evaluation points 22 Describe a de nite integral as the limit of a Riemann sum 23 Determine antiderivatives of basic algebraic functions 24 Calculate values of de nite integrals using antiderivatives and areas 25 Apply substitution techniques to integrate basic functions 26 Apply the ideas of de nite integrals to solve problems of areas 27 Calculate the average value of business models using the de nite integral 28 Apply the ideas and techniques of the de nite integral to evaluate consumerproducer surplus futurepresent value of income streams and annuity business models


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