Technical Calculus II Syllabus

Transcription

1 Technical Calculus II Syllabus Table of Contents 1 Basic Information 2 2 Overview 3 3 Syllabus Policy 4 4 Policy 4 5 Calculator Requirement 4 6 Course Components Attenance Homework Homework Policies Homework Process Homework Graing Exams Exam Scheule Preparing for an Exam Exam Policies Make-up Exams Unerstaning Exam Graes Course Grae 11 8 Course Website Homepage Lessons Help Office Hours Brightspace Chat Room Help Help University Tutoring Course Content an Objectives Bulletin Description Course Objectives Course Outline University Policies Unergrauate Bulletin

2 10.2 Attenance Policy Incomplete Policy Withrawal Policy Acaemic Honesty an Stuent Conuct Accessibility, Counseling, an Health Services Title IX at UA Formula Policy 17 1 Basic Information Course: Technical Calculus II, 2030: Course Type: Lecture Course Web Site: Class Location: Polsky 488 Time an Dates: 12:05 1:20 pm, MoWe, 1/17/2018 5/2/2018 Instructor: Dr. Scott Ranby Department: Applie General an Technical Stuies Phone: sranby@uakron.eu Office: Polsky 131F Office Hours Monay: 10:00 11:30 am Tuesay 12:00 2:00 pm Wenesay: 10:00 11:30 am or by appointment Online Office Hours Monay: 10:00 11:30 am Tuesay 12:00 2:00 pm Wenesay: 10:00 11:30 am or by appointment Exam Scheule Exam 1: 2/7 Exam 2: 2/28 Exam 3: 3/21 Exam 4: 4/18 Final: 5/9, 12:15 2:15 pm Optional Text: Technical Calculus with Analytic Geometry. Peter Kuhfittig. Brooks/Cole, Cengage Learning, Fifth Eition,

3 2 Overview Syllabus: Stuents are require to rea an unerstan the entire syllabus. See the Syllabus Policy section for complete information. (1) Stuents are require to check their zips.uakron.eu account at least once each ay. (2) Stuents are require to use their zips.uakron.eu account when they sen to the instructor. See the Policy section for complete information. Calculator: Stuents are require to have a graphing calculator or other evice with minimum functionality equivalent to that of the Texas Instruments TI 83 calculator. See the Calculator Requirement section for complete information. Textbook: No book is use in this class. All course materials (homework assignments, class notes, class auio recorings, hanouts, etc.) are poste on the course website. See the Course Website section for more information. Course content: See the Course Content an Objectives section for complete information about the topics covere in the course. Help: Help is available from Dr. Ranby in person, online an via . See the Help section of this ocument for instructions on obtaining help. Attenance: (1) Stuents are expecte to atten every class, arrive to each class on time, an stay for the entire length of all classes. (2) Stuents who fail to sign the attenance sheet by the en of class are counte as absent. (3) Stuents are expecte to take goo notes uring class, participate in classroom iscussions, an ask questions about material they o not unerstan. (4) Stuents are require to obtain notes an homework ue ate information from the course web site whenever they miss a class. (5) Stuents are also require to complete homework assigne uring a misse class an are expecte to turn in such assignments on time. (6) Stuents are require to know what homework was assigne an what material was covere uring a class whether or not they attene the class. (7) Stuents are permitte to have at most 3 unexcuse absences. See the Attenance section for complete information. Homework: (1) Stuents are require to ownloa the homework assignments from the homepage of the course website. (2) Stuents are require to have access to either a printe or electronic version of the homework assignments uring every class. (3) Stuents are expecte to turn in all homework assignments on time. (4) Each homework assignment is worth 10 points. (5) Electronic submissions of homework are not accepte. (6) Stuents are permitte to have at most 3 unexcuse late homework assignments. (7) For best results, stuents shoul follow the process given in the Homework Process section of this ocument when working on homework assignments. See the Homework section for complete information. Exams: (1) There will be 5 exams. (2) Each exam is worth 100 points an will be base on the material previously covere in class. (3) The ates of the exams are given in the Basic Information an Exam Scheule sections. (4) Early exams will not be given for any reason. (5) Stuents are require to arrange their scheules so that they arrive to all exams on time. (6) For best results, stuents shoul follow the process given in the Preparing for an Exam section of this ocument when stuying for an exam. (7) Make-up exams are given at the iscretion of Dr. Ranby. (8) Requesting a 3

4 make-up exam oes not guarantee that a make-up exam will be grante. (9) A make-up exam is given only when an acceptable make-up exam request has been submitte an circumstances beyon a stuent s control prevente the stuent from taking the exam uring its scheule ate an time. (10) Make-up exam requests for participation in a university-sponsore event, jury uty, or military service require ocumentation. (11) A make-up exam will only be given on campus in the presence of Dr. Ranby. See the Exams section for complete information. Course graes: The formulas use to compute course graes an the course graing scale are given in the Course Grae section. 3 Syllabus Policy Stuents are require to ownloa the syllabus from the homepage of the course website. The syllabus file is a PDF file which shoul be opene using a PDF reaer. It is the responsibility of every stuent to rea an unerstan the syllabus. Failure to rea an unerstan the syllabus oes not exempt the stuent from any course policy or course requirement. 4 Policy All stuents are require to check their zips.uakron.eu account at least once a ay. is not sent out every ay, but stuents are require to check their zips.uakron.eu account anyway. Stuents are require to use their zips.uakron.eu account when they sen to the instructor. from the instructor to a stuent is sent only to the stuent s zips.uakron.eu account. 5 Calculator Requirement All stuents are require to have a graphing calculator or other evice with minimum functionality equivalent to that of the Texas Instruments TI 83 calculator. Every stuent is require to have possession of their calculator or other evice by the en of the first week of classes. Stuents are require to bring the require calculator or other evice to each class. If a stuent has a evice other than a graphing calculator, then the stuent must have the evice approve by Dr. Ranby prior to its use uring an exam. Stuents who o not obtain prior approval for such evices will not be permitte to use those evices on an exam. No exceptions to this policy will be mae by the instructor. 4

5 6 Course Components 6.1 Attenance Attenance will be taken at the beginning of each class. Stuents who arrive late or leave early might be counte as absent. Stuents are expecte to atten every class, arrive to each class on time, an stay for the entire length of all classes. Stuents who have more than 3 unexcuse absences (1) cannot turn in late homework, (2) are not eligible for make-up exams for any reason, an (3) are given no consieration if they have a borerline grae. In aition, stuents who have excessive unexcuse absences may be require to meet with Dr. Ranby outsie of class for a iscussion about attenance. Stuents who fail to respon to an request for such a meeting or who miss such a meeting will receive a 5 point euction from their numerical course grae. Stuents are expecte to take goo notes uring class, participate in classroom iscussions, an ask questions about material they o not unerstan. Stuents shoul not use their electronic evices uring class unless those evices are being use to take notes, to o computations, or to obtain electronic ocuments relevant to the course. Stuents using electronic evices in a manner that isrupts the class or istracts other stuents will be aske to turn off the evices an put them away. Any stuent who fails to comply with such a request will be tol to leave the class an referre to the Stuent Conuct an Community Stanars office. Stuents are require to know what homework was assigne an what material was covere uring a class whether or not they attene the class. Important material is covere in every class. Stuents are require to obtain notes an homework ue ate information from the course web site whenever they miss a class. Stuents are also require to complete homework assigne uring a misse class an are expecte to turn in such assignments on time. Stuents are not permitte to bring chilren, family members, friens, or any other person to class for any reason. 6.2 Homework Homework Policies There will be a grae homework assignment for each section covere in class. 5

6 Each homework assignment is worth 10 points. The ue ate for each grae assignment will be announce in class an poste on the course website. Stuents are require to ownloa the homework assignments from the homepage of the course website. The homework assignments file is a PDF file which shoul be opene using a PDF reaer. Stuents are require to have access to either a printe or electronic version of the homework assignments uring every class. The beginning of each class will be evote to a iscussion of homework problems. During this time, stuents may ask questions about the homework, correct mistakes on their assignments, an supply solutions to help others in the class. Homework will be turne in after the iscussion has ene. Homework Solutions: Solutions to a homework assignment will be poste on the course website after the assignment is collecte. It is the responsibility of the stuent to obtain an review the homework solutions. Stuents are expecte to turn in all homework assignments on time. A homework assignment is counte as late if it is not turne in by the en of class on the ay it is ue. Electronic submissions of homework are not accepte. Unless circumstances beyon a stuent s control prevent the stuent from turning a homework assignment in on time an the instructor agrees to give an extension, the following apply to unexcuse late homework: Maximum number of unexcuse late assignments: 3 1 class ay late: 2 point euction 2 class ays late: 4 point euction 3 class ays late: 8 point euction 4 or more class ays late: 10 point euction Stuents who have more than 3 unexcuse late assignments may be require to meet with Dr. Ranby outsie of class for a iscussion about homework. Stuents who fail to respon to an request for such a meeting or who miss such a meeting will receive a 10 point euction from their numerical course grae. If a stuent has a vali an excusable reason for turning in a homework assignment late an informs the instructor in a timely manner, then the instructor may give an extension at his iscretion. The following reasons are not consiere to be excusable reasons for turning in homework late: oversleeping; technical issues such as (but not limite to) allege computer breakowns, allege lack of computer access, allege inability to access the course materials, an failure to access the course materials in a timely manner; participation in a universitysponsore event without proviing sufficient notice to the instructor an obtaining the instructor s agreement that participating in the event is a legitimate reason for turning in homework late; legal troubles incluing jail time an court summonses; vacations, weings, reunions, grauations, an other types of social or family events; an elective or non-essential meical proceures an non-emergency meical appointments. 6

7 Homework assignments are require to be organize an legible. An assignment is consiere to be organize if the problems an parts of problems are clearly an correctly labele an appear in the correct numerical or alphabetical orer. An assignment is consiere to be legible if the instructor can rea it without ifficulty. If the first submission of an assignment is not organize an legible, then the assignment will be returne with a ealine for submitting an organize an legible version Homework Process In orer to learn the material covere in this course, stuents nee to have goo learning practices while working on homework. Scientific research into learning has shown that stuents who use certain goo practices are more successful than stuents who on t use those practices. The following instructions are meant to encourage stuents to use goo learning practices while working on a homework assignment. 1. View the lessons relevant to the homework on the course website, or ownloa the lessons an work offline. 2. Review the notes relevant to the homework you took in class an compare them to the notes an auio on the course website. Fill in any gaps in your notes. 3. Work through the homework problems referring to your notes an the relevant lessons on the course website when necessary. 4. Once a homework assignment is complete, it shoul be reone at least once (preferably more than once) without using notes. 5. Grae homework assignments shoul be examine for errors an correcte using the solutions poste on the course website. If a grae homework assignment has a low grae, then it shoul be reone correctly at least twice. Do not consier a homework assignment to be complete until you thoroughly unerstan the assignment. If there is something about an assignment you o not unerstan, then obtain help by either asking questions about the assignment when it is iscusse in class, visiting Dr. Ranby in his office uring his office hours, making an appointment to meet with Dr. Ranby in his office an meeting with him uring the appointment s time, visiting the course help room uring Dr. Ranby s online office hours, making an appointment to meet with Dr. Ranby in the course help room an meeting with him in the help room uring the appointment s time, or sening an message to sranby@uakron.eu asking for help Homework Graing Homework Graing Philosophy Stuents nee to figure out what they ve one wrong on a homework assignment. The instructor can only point out an explain errors. Stuents nee to o the har work of unerstaning their errors. Stuies show that oing the har work of fining an fixing errors leas to better comprehension than just looking at errors pointe out by the instructor. Problem Graing Each problem or part of a problem on a homework assignment is grae on a 0 1 7

8 point scale. Problems with incorrect work are marke. If nothing specific is marke on a problem, then it is up to the stuent to etermine what is wrong about the solution by comparing the work to the solution poste on the course website. Sometimes problems with incorrect work will not be marke. Again, it is the responsibility of the stuent to etermine if the work on non-marke problems is correct by comparing the work to the poste solutions. Points Problem not attempte (NA): -1 Problem solution not complete (I): -0.5 Require work missing (RWM): -0.5 or less Assignment Graes The points earne on an assignment s problems are totale, the point total is ivie by the maximum possible point total, the result of the ivision is multiplie by 10, an the result of the multiplication is roune to the nearest 1/10th. The roune number is the grae on the homework assignment. Earning a 10 on an assignment oes not mean that all work is correct. Stuents are responsible for reviewing poste solutions an making sure all of their work is correct even work with no re marks. 6.3 Exams Each exam is worth 100 points an will be base on the material previously covere in class Exam Scheule The ates of the exams appear below. Exam 1: 2/7 Exam 2: 2/28 Exam 3: 3/21 Exam 4: 4/18 Final: 5/9, 12:15 2:15 pm The exam scheule may be altere by the instructor if necessary. Early exams will not be given for any reason Preparing for an Exam Scientific research into learning has shown that stuents who use certain goo practices when preparing for an exam are more successful than stuents who on t use those practices. The following instructions are meant to encourage stuents to use goo practices when preparing for an exam. 8

9 1. Work through each homework assignment one time referring to your grae homework assignments, notes, an the lessons an solutions poste online when necessary. 2. Work through each homework assignment again without referring to any other materials. Once you are finishe, fix any errors by referring to other materials. 3. Repeat step 2 until there are no errors in your work, an you have most or all of the solutions memorize Exam Policies Stuents are require to arrange their scheules so that they arrive to all exams on time. All stuents are require to bring a graphing calculator to the exam. Stuents may not borrow a calculator from another stuent or the instructor uring the exam. Stuents are not permitte to use scrap paper uring an exam. Stuents who use any paper materials other than those supplie by the instructor will will have their exams taken away, will be given a score of zero on the exam, will be tol to leave the class, an will be referre to the Stuent Conuct an Community Stanars office. Stuents are not permitte to write with a re pen or re pencil uring an exam. Except for calculators or evices approve by the instructor prior to the exam, stuents are not permitte to use their electronic evices uring an exam for any reason. Stuents may not leave the class uring an exam to use an electronic evice for any reason. Stuents who use unapprove electronic evices or who leave class to use an electronic evice uring an exam will have their exams taken away, will be given a score of zero on the exam, will be tol to leave the class, an will be referre to the Stuent Conuct an Community Stanars office. Stuents are not permitte to use smartphones, cell phones, heaphones or earbus uring an exam unless the use of such evices meets an accommoation requirement or their use has been approve by the instructor prior to the exam. These evices are not permitte to be visible an they may not make any souns uring an exam (unless their use is permitte of course). A stuent who violates this policy will be given a score of zero on the exam an will be referre to the Stuent Conuct an Community Stanars office. Stuents are require to turn in all materials they have receive from Dr. Ranby after completing an exam. A stuent who fails to o so will be given a score of zero on the exam an will be referre to the Stuent Conuct an Community Stanars office. Stuents are require to finish their exams by the en of the class perio. Stuents who arrive late to an exam will not be given a time extension Make-up Exams Stuents are require to take every exam uring its scheule ate an time unless Dr. Ranby agrees to scheule a make-up exam. It is the responsibility of a stuent to request a make-up exam. A make-up exam request must be submitte via from a zips.uakron.eu account, an it must inclue the full name 9

10 of the stuent, the name of the course the stuent is taking, the number of the exam which will be or was misse, an the reason for missing the exam. If ocumentation is submitte with a make-up exam request, then it must be in PDF format. Dr. Ranby reserves the right to require a stuent to provie aitional information or ocumentation whenever the stuent requests a make-up exam. A make-up exam request must be mae by 11:59 pm on the ay of the exam unless there is an unusual an exceptional circumstance that prevents the stuent from making the request by the ealine. Make-up exams are given at the iscretion of Dr. Ranby. Requesting a make-up exam oes not guarantee that a make-up exam will be grante. A make-up exam is given only when an acceptable make-up exam request has been submitte an circumstances beyon a stuent s control prevente the stuent from taking the exam uring its scheule ate an time. Make-up exam requests for participation in a university-sponsore event, jury uty, or military service require ocumentation. Stuents are require to supply Dr. Ranby with ocumentation in written or PDF form as soon as they are aware of either type of uty. A make-up exam will only be given on campus in the presence of Dr. Ranby Unerstaning Exam Graes Each problem or part of a problem on an exam is grae on a 0 1 point scale in increments of 1/10th of a point. The points are totale, the point total is ivie by the maximum possible point total, the result of the ivision is multiplie by 100, an the result of the multiplication is roune to the nearest 1/10th. The roune number is the grae on the exam. The following questions are aske when an exam problem is grae: 1. Does the solution emonstrate an unerstaning of the concepts an methos covere in class that are relevant to the problem? 2. Does the solution use the require an proper techniques an methos? 3. Is the solution presente in a logical an coherent manner? 4. Does the solution use notation properly an correctly? 5. Are the theoretical an numerical computations that appear in the solution correct? 6. Are the numerical values that appear in the solution correct? 7. Is the solution succinct an to-the-point? 8. Is the solution clear an unambiguous? Problem Graing -0: Perfect work -0.1: A work with minor errors -0.2: B work -0.3: C work -0.4: D work -0.5: F work 10

11 -1.0: No work or require work missing When grae exams are returne to a stuent, only the stuent s grae work is returne. The sheet containing the exam problems is not returne. The reason for this practice is that exams are not learning tools, they are where stuents emonstrate learning. If there appears to be a graing error on an exam or if the graing is not unerstoo, then a stuent shoul meet with Dr. Ranby to iscuss the graing. 7 Course Grae Your numerical course grae G consists of course homework points (H) an course exam points (E). The maximum value of H is 15, the maximum value of E is 85, an the maximum value of G is 100. Use the following to etermine G. hnum = the number of grae homework assignments hmax = the maximum possible points on a homework assignment hsum = the sum of the scores of the grae homework assignments enum = the number of grae exams emax = the maximum possible points on an exam esum = the sum of the scores of the grae exams H = 15 hsum hnum hmax E = 85 esum enum emax G = H + E Use the numerical course grae an the following list to etermine your course letter grae. A if 91 G 100 A if 90 G < 91 B+ if 87 G < 90 B if 81 G < 87 B if 80 G < 81 C+ if 77 G < 80 C if 71 G < 77 C if 70 G < 71 D+ if 67 G < 70 D if 63 G < 67 D if 60 G < 63 F if G < 60 8 Course Website 8.1 Homepage The aress of the homepage of the course website is the following: Homepage: 11

12 The homepage may also be accesse via the learning management system operate by the university. The homepage contains links to the syllabus, homework assignments, an other information about the course. 8.2 Lessons Class notes, auio recore uring class, homework assignment ue ates, an other information relevant to each class are given on the Lessons web page available at the following aress: Lessons page: Stuents are require to obtain notes an homework ue ate information from the Lessons page whenever they miss a class. 8.3 Help Instructions for getting help are given on the Help web page available at the following aress: Help page: The following information is given on the Help page Office Hours Dr. Ranby will be available in Polsky 131F uring the following ays an times: Monay: 10:00 11:30 am Tuesay 12:00 2:00 pm Wenesay: 10:00 11:30 am If Dr. Ranby is not in his office uring one of the above times an he has not previously announce that he will not be there, then stuents shoul assume there is a legitimate reason for his absence. Stuents may either wait to see if Dr. Ranby returns to his office before the en of the help perio, obtain help uring the next scheule help perio, or sen an to sranby@uakron.eu asking for help in Dr. Ranby s office at a ifferent time. If a stuent wishes to meet with the Dr. Ranby at a time not liste above, then that stuent shoul see him in person to arrange a meeting or sen an requesting a meeting to sranby@uakron.eu. Stuents may come to Polsky 131F anytime, not just uring office hours. If Dr. Ranby is in the office when a stuent arrives an he is not working on something urgent, then he will be happy to help the stuent. Please note that office hours are for iscussing homework problems, clarifying concepts iscusse in class, an iscussing general mathematical issues. 12

13 Whenever a stuent goes to Dr. Ranby s office for help, the stuent shoul bring relevant class notes, a copy of any relevant homework assignments, any work the stuent has one, a calculator, a writing instrument, an paper Brightspace Chat Room Help Stuents may communicate in real time with Dr. Ranby in a Brightspace chat room. The following steps explain how to connect to such a room. 1. Log into Brightspace an enter the course s Brightspace site. 2. Click on the Chat link in the navigation bar. 3. Click on the appropriate chat (such as the Online Office Hours chat). The course help room is the Online Office Hours chat room. Dr. Ranby will be available in the course help room uring the following ays an times: Monay: 10:00 11:30 am Tuesay 12:00 2:00 pm Wenesay: 10:00 11:30 am If Dr. Ranby is not in the course help room uring one of the above times an he has not previously announce that he will not be there, then stuents shoul assume there is a legitimate reason for his absence. Stuents may either wait to see if Dr. Ranby enters the course help room before the en of the help perio, obtain help uring the next scheule help perio, or sen an to sranby@uakron.eu asking for help in the course help room at a ifferent time. If a stuent wishes to chat with Dr. Ranby in the course help room at a time not liste above, then that stuent shoul sen an requesting a chat to sranby@uakron.eu Help Stuents may sen questions about the course lessons an homework assignments to Dr. Ranby via . Questions shoul be sent to sranby@uakron.eu from a zips.uakron.eu account. Questions sent from accounts other than zips.uakron.eu accounts will not receive a response. Questions sent via will receive a response within 24 hours after they are sent unless special circumstances prevent Dr. Ranby from replying uring that time perio University Tutoring Information about tutoring services is available at the following link: UA Tutoring Sevices Online tutoring services are available at the following link: Online Tutoring Sevices 13

14 Please note that Dr. Ranby oes not vouch for the quality, knowlege, or ability of any tutor on or off the campus. 9 Course Content an Objectives 9.1 Bulletin Description Prerequisites: 2030:255 or equivalent with a grae of C or better, or placement test. Methos an applications of integration, first an secon orer ifferential equations, series expansion, Laplace transforms, partial erivatives, an ouble integrals. 9.2 Course Objectives After completing this course the stuent shoul have the following competencies: 1. the ability to fin the integral of a function by using partial fractions, integration by parts, or trigonometric substitution; 2. the ability to fin areas an volumes by integration; 3. the ability to fin the solutions of first-orer ifferential equations using separation of variables or integrating factors; 4. the ability to solve secon-orer ifferential equations using stanar methos an Laplace transforms; 5. the ability to use ifferential equations when solving real-worl problems; 6. an unerstaning of the properties of numerical series an series of functions. 9.3 Course Outline 1. Applications of integration (a) Area between curves (b) Volumes of revolution isk metho (c) Volumes of revolution shell metho () Center of mass 2. Methos of integration (a) Partial fractions (b) Integration by parts (c) Trigonometric substitution () Integration using tables (e) Numerical methos 3. First-orer ifferential equations (a) Solutions of ifferential equations (b) Separation of variables (c) Integrating factors () First-orer linear equations 14

15 (e) Applications 4. Secon-orer ifferential equations (a) Linear homogeneous case (b) Linear nonhomogeneous case (c) Applications () Laplace transforms (e) Using Laplace transforms to solve ifferential equations 5. Series (a) Convergence (b) Convergence tests (c) Power series () Maclaurin an Taylor series (e) Approximating series (f) Fourier series 10 University Policies 10.1 Unergrauate Bulletin The university policies that affect stuents are containe in the Unergrauate Bulletin. To view the Unergrauate Bulletin, go to the following aress: Unergrauate Bulletin Attenance Policy The official attenance policy of the university is presente on the Important Policies page of the Unergrauate Bulletin. Important Policies A stuent is expecte to atten all class meetings for which the stuent is registere. A stuent may be roppe from a course in the current term by the ean if absence is repeate an the instructor recommens this action; a stuent can gain re-amission only with permission of both the instructor an the ean. A stuent roppe from a course receives an F which counts as work attempte whenever grae-point ratio calculations are mae Incomplete Policy The official incomplete policy of the university is presente on the Grae Policy an Creit page of the Unergrauate Bulletin. 15

16 Grae Policy an Creit important-policies/grae-policy-an-creit.ot Stuents are expecte to rea an unerstan the official incomplete policy Withrawal Policy The official withrawal policy of the university is presente on the Important Policies page of the Unergrauate Bulletin. Important Policies Stuents are expecte to rea an unerstan the official withrawal policy. The withrawal ealine for this course is Sunay, March Acaemic Honesty an Stuent Conuct Stuents are require to maintain the highest level of acaemic honesty in this course. The university s acaemic honesty expectations are containe in the Grae Policies an Creit page of the Unergrauate Bulletin an in section of the University Rules (see Stuents are require to follow The University of Akron s Coe of Stuent Conuct. The Coe of Stuent Conuct is available on the website of the Stuent Conuct an Community Stanars office. See the following links for more information: Stuent Conuct an Community Stanars Coe of Stuent Conuct 12 Accessibility, Counseling, an Health Services Stuents who require special services an/or accommoations in the course shoul submit a request to the Office of Accessibility (OA) in a timely manner. The OA is locate in Simmons Hall Room 105, an it may be contacte at (v), (t), or access@uakron.eu. See the following link for more information. Office of Accessibility Currently enrolle stuents may obtain free psychological services at the Counseling & Testing Center. See the following link for more information. 16

17 Counseling & Testing Center Currently enrolle stuents may obtain free or low cost health services at Stuent Health Services. See the following link for more information. Stuent Health Services 13 Title IX at UA The University of Akron is committe to proviing an environment free of all forms of iscrimination, incluing sexual violence an sexual harassment. This inclues instances of attempte an/or complete sexual assault, omestic an ating violence, gener-base stalking, an sexual harassment. If you (or someone you know) has experience or experiences sexual violence or sexual harassment, know that you are not alone. Help is available, regarless of when the violence or harassment occurre, an even if the person who i this is not a stuent, faculty or staff member. Confiential help is available. contact: If you wish to speak to a professional, in confience, please University Counseling an Testing Center Website: Phone: University Health Services Website: Phone: Please know the majority of other University of Akron employees, incluing faculty members, are consiere to be responsible employees uner the law an are require to report sexual harassment an sexual violence. If you tell me about a situation, I will be require to report it to the Title IX Coorinator an possibly the police. You will still have options about how your case will be hanle, incluing whether or not you wish to pursue a law enforcement or complaint process. You have a range of options available an we want to ensure you have access to the resources you nee. Aitional information, resources, support an the University of Akron protocols for responing to sexual violence are available at 14 Formula Policy The formulas that stuents are require to know by heart at the beginning of this course are liste below. 17

18 Factoring Formulas a 2 b 2 = (a b)(a + b) x 2 + (a + b)x + ab = (x + a)(x + b) acx 2 + (a + bc)x + b = (ax + b)(cx + ) Quaratic Formula Let ax 2 + bx + c = 0 where a, b, an c are constants with a 0. x = b ± b 2 4ac 2a Equations of Lines Assume a line passes through (x 1, y 1 ) an (x 2, y 2 ) with slope m an y-intercept b. m = y 2 y 1 x 2 x 1 y y 1 = m (x x 1 ) y = mx + b Distance Formula Let be the istance between (x 1, y 1 ) an (x 2, y 2 ). = (x 1 x 2 ) 2 + (y 1 y 2 ) 2 Parallel an Perpenicular Lines Suppose two lines have slopes m 1 an m 2 respectively. If the lines are parallel, then m 1 = m 2. If the lines are perpenicular, then m 2 = 1/m 1. Right Triangle Trigonometry Hypotenuse Opposite of A A Ajacent of A sin(a) = Opposite of A Hypotenuse cos(a) = Ajacent of A Hypotenuse tan(a) = Opposite of A Ajacent of A csc(a) = Hypotenuse Opposite of A sec(a) = Hypotenuse Ajacent of A cot(a) = Ajacent of A Opposite of A 18

19 B c a A a 2 + b 2 = c 2 b C A + B = 90 General Trigonometry sin(a) = a/c cos(a) = b/c tan(a) = a/b csc(a) = c/a sec(a) = c/b cot(a) = b/a sin(b) = b/c cos(b) = a/c tan(b) = b/a csc(b) = c/b sec(b) = c/a cot(b) = a/b A = sin 1 (a/c) = cos 1 (b/c) = tan 1 (a/b) B = sin 1 (b/c) = cos 1 (a/c) = tan 1 (b/a) Angle θ is shown below in stanar position. The initial sie of θ is the positive x-axis, an the vertex of θ is the origin ((0, 0)). Point (x, y) is a point on the terminal sie of θ, an r is the istance from (0, 0) to (x, y). (x, y) r y x r 2 = x 2 + y 2 sin (θ) = y/r csc (θ) = r/y cos (θ) = x/r sec (θ) = r/x tan (θ) = y/x cot (θ) = x/y Raian Measure 180 = π raians Let θ be the raian measure of a central angle of a circle with raius r. Let s be the length of the circular arc intercepte by θ, an A the area of the circular sector mae by θ. s = rθ A = 1 2 r2 θ Factoring Formulas a 3 b 3 = (a b) ( a 2 + ab + b 2) a 3 + b 3 = (a + b) ( a 2 ab + b 2) 19

20 Prouct Formulas Exponents (a ± b) 2 = a 2 ± 2ab + b 2 (a ± b) 3 = a 3 ± 3a 2 b + 3ab 2 ± b 3 a n = 1 a n a m/n = ( n a ) m = n a m Logarithms log b (mn) = log b (m) + log b (n) (m > 0, n > 0) ( m ) log b = log n b (m) log b (n) (m > 0, n > 0) log b (m n ) = n log b (m) (m > 0) log b (b) = 1 log b (1) = 0 log(m) = log 10 (m) ln(m) = log e (m) log b (m) = log a(m) log a (b) Funamental Trigonometric Ientities csc(x) = 1 sin(x) tan(x) = sin(x) cos(x) sec(x) = 1 cos(x) cot(x) = cos(x) sin(x) cot(x) = 1 tan(x) sin 2 (x) + cos 2 (x) = 1 sin 2 (x) = 1 cos(2x) 2 sin(2x) = 2 sin(x) cos(x) cos 2 (x) = 1 + cos(2x) 2 20

21 Differentiation an Integration Formulas x (un n 1 u ) = n u x ( u ) = v u x uv x x v v 2 u (cos(u)) = sin(u) x x u (sec(u)) = sec(u) tan(u) x x x (cot(u)) = csc2 (u) u x x (cos 1 (u)) = x (ln(u)) = 1 u u x 1 1 u 2 u x (uv) = uv x x + v u x u (sin(u)) = cos(u) x x x (tan(u)) = sec2 (u) u x u (csc(u)) = csc(u) cot(u) x x x (sin 1 (u)) = 1 1 u 2 u x x (tan 1 (u)) = 1 u 1 + u 2 x x (eu ) = e u u x u n u = un+1 + C (n 1) n + 1 e u u = e u + C 1 u = ln u + C u sin(u) u = cos(u) + C cos(u) u = sin(u) + C sec 2 (u) u = tan(u) + C csc 2 (u) u = cot(u) + C sec(u) tan(u) u = sec(u) + C csc(u) cot(u) u = csc(u) + C tan(u) u = ln cos(u) + C cot(u) u = ln sin(u) + C sec(u) u = ln sec(u) + tan(u) + C csc(u) u = ln csc(u) cot(u) + C 21