MAT135 Course Outline Fall 2019-1 PDF

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Download MAT135 Course Outline Fall 2019-1 PDF

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University of Toronto Mississauga

MAT135H5 Differential Calculus: Fall 2019 Course Description: MAT135H5 is a first year Differential Calculus course with some examples of applications to Physics, Chemistry and other Sciences. Although this course will have a theoretic component, the emphasis will be on concepts, techniques, and applications. Theorems will be stated clearly, but mostly without proof, and many examples will be included in the lectures. New course: This is the first time that MAT135H5 Differential Calculus is offered at UTM. The course MAT135Y5 Calculus has been replaced by MAT135H5 Differential Calculus + MAT136H5 Integral Calculus. In terms of prerequisites and other program planning, MAT135H5 + MAT136H5 = MAT135Y5. Course staff: Section(s): Course coordinator and LEC0107 Assistant coordinator LEC0113

Name: Dr. Maria Wesslén (course coordinator)

Contact: [email protected] Office: DH3048 Phone: 905-828 5323

Office Hours: Tuesdays 3-4 Fridays 1-3

Mike Pitocco

[email protected]

See Quercus

Dr. Nadya Askaripour

LEC0103

Dr. Andie Burazin

Wednesdays 1:30-2:30 Fridays 10-11 Mondays 10-12

LEC0102, LEC0104 LEC0106

Dr. Adina Gamse

LEC0105

Dr. Hossein Lamei Ramandi

LEC0110

Dr. Scott Murray

LEC0109

Dr. Iman Setayesh

LEC0111

Dr. Shiyu Shen

LEC0108

Dr. Daniel Stern

LEC0114

Dr. Xinli Wang

[email protected] Office: DH3097A [email protected] Office: DH3058 [email protected] Office: DH3060 Email - see Quercus Office: DH3021 [email protected] Office: DH3097B [email protected] Office: DH3097C [email protected] Office: DH3097D [email protected] Office: DH3019 [email protected] Office: DH3038 [email protected] Office: DH3060

Dr. Yuri Kudryashov

Mondays and Thursdays 17:15-18:45 Tuesdays 11:00-13:00 See Quercus Tuesdays 3-5 Thursdays 5-6 See Quercus Thursdays 2-4 Tuesdays 2-4 Online: Mondays 11:3012:30 at https://zoom.us/j/9739646 40 In DH3060: Fridays 1:302:30. Book here: wangxinli.youcanbook.me 1

Learning Objectives: On successful completion of MAT135H5, you should be able to solve problems related to differential calculus, which includes limits, derivatives, curve sketching, optimization problems and other related applications. A list of topics can be found below. You should aim for a level of understanding that allows you to: (1) carry out computations with ease; (2) use your conceptual understanding of the material to solve a range of problems, even ones that are different from, or a variation of problems you've seen before; and, (3) give an explanation of your solutions to someone who has not seen the material before (i.e. you should aim to understand the material well enough to be able to explain each step in a calculation, but also the general idea behind the solution). Textbook: Single Variable Calculus: Early Transcendentals, 8th Edition, by James Stewart. You are expected to have access to the textbook throughout the course. Option 1: The UTM bookstore sells a package which includes the textbook, solution manual, and a complementary copy of “Calculus Test and Exam Prep: A Collection of Problems and Worked Solutions”. The extra booklet is not required but you can use it for extra practice. Option 2: If you prefer an online textbook, there are access codes to the eBook (which comes with WebAssign). If you retake the course for any reason in another year, you would need to buy another code. The “multi term” access code gives you access for as long as edition 8 is being used. You can buy the eBook here https://uoftbookstore.com/textbooks/access_codes.asp? Or by going in to the UTM bookstore. Important: A WebAssign access code is NOT required to complete the course. However, WebAssign has many nice help features which you may want to use when studying. If you buy the eBook you will have access to these extra help features. Course Website: You can access the MAT135H course website through the University of Toronto Quercus at https://q.utoronto.ca. After logging in, the course should appear on your Dashboard. All important course information will be posted on Quercus throughout the course. You should therefore log in regularly to check for any updates. You will also be able to see your term marks on Quercus, once they are available. Email announcements will be sent through Quercus - make sure you check your utoronto.ca email regularly. If you want to use another email to receive announcements, you can add it under "account" and "settings". Calculators: Calculators will NOT be allowed during term tests and the final examination. A non-programmable, nongraphing calculator may be used while working on assignments and homework.

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Office Hours and the Math Learning Centre: Please do not hesitate to ask us for help. Both the instructors and TAs of MAT135H are available for extra help outside of class time, during our scheduled office hours. You do not need an appointment to visit office hours. Just show up, but come prepared with questions you have. For example, you can ask questions about a particular concept or something from lectures or the textbook that you want to clarify. Or you can bring a problem you have tried to work on but have questions about (in that case please bring the work that you have done, even if it is not complete). See the course website for any updates on office hour times. The teaching assistants will have office hours in room DH2027 (the Math Learning Centre). A schedule will be posted on the door as well as on Quercus. You can go to any office hour, not only your own TAs. Assessments of Learning Objectives: You will be assessed in several different ways, including written assignments, online work, group work, term tests, and a final examination. Final grades are based on student performance on assessments as stated here. No extra work can be submitted to improve a student’s final grade. Final grades and grade calculations will not be adjusted due to a student’s request. Note: After 4 December 2019, no term work remark requests will be accepted. Final Exam: Tests 1 and 2: Written assignments: Online assignments: Tutorial activities:

40% 40% 6% 8% 6%

(25% for your higher test grade and 15% for your lower grade) (average of all 3 written assignments) (average of best 5 out of 6) (average of best 5 out of 6)

More information about each of these is given below. Additional information will be given on Quercus throughout the course. A schedule of due dates is available in the table on the last page. Final Exam: There will be a final exam during the exam period in December. The exam will be cumulative, i.e. it will include problems from the entire course. The date and time of the exam will be decided by the UTM Exam Office and is usually available in October. Term Tests: The 2 term tests are on the following dates: Test 1: Friday 11 October 2019 at 4:10 to 6pm

Test 2: Friday 15 November 2019 at 4:10 to 6pm

Details such as which sections are covered on each term test and which room to go to will be provided later, on Quercus.

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Missed Term Tests: There will be no make-up term tests. If you miss a term test due to illness or other valid reason, you should declare your absence on ACORN and you must provide written documentation such as for example a doctor’s note written on the Official UTM Verification of Illness or Injury form (available on Quercus under ‘Information and Documents’). You must visit the doctor on the day of the test, or the following day at the very latest. You must submit your documentation both in person and online. (Details available on Quercus.) The deadline to submit the documentation will be posted on Quercus. If these requirements are not met, your test mark will be recorded as zero. If valid documentation is provided, the weights will be shifted as follows: One missed test: The test you write will be worth 30% and the final exam will be worth 50%. We hope that no one will miss both tests. Tutorials: Tutorials start the week of 16th September 2019. All students must enroll in a tutorial section. You should attend only the tutorial that you are enrolled in. It is important to attend your tutorial every week, starting the week of 16th September. Tutorials give you a chance to study with the help of the TA and together with other students. Attending tutorials and actively participating in them will increase your chances of doing well on tests and the exam. A list of which TA is responsible for which tutorial can be found on Quercus under ‘Information and documents; TA and instructor contact info’. Tutorial Activities: In some weeks (see the schedule below), there will be a “Tutorial activity” which will count towards your final grade. Details about the tutorial activities will be posted on Quercus ahead of time. You will get more out of each tutorial activity if you read and go over the relevant material before going to your tutorial. There are 6 tutorial activities and the average of your best 5 will count towards 6% of your final grade. Any student who actively participates in a meaningful way in the tutorial activity will get full marks that week, even if solutions are not completely correct. The purpose of the tutorial activities is to give you a chance to work on problems related to the course, often in groups together with other students and with the guidance of the TA. You will get a chance to discuss your ideas with other students and the TA, which will help you prepare for the tests and the exam. Questions from the tutorial activities may also appear again on tests and/or the final exam. Medical notes will NOT be accepted for missed tutorial activities and there are no make-up tutorial activities. You must attend the tutorial you are registered in to get the grade associated with tutorial activities.

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Online Assignments: This course uses WebWork, which is a FREE online learning and assessment tool. It will be used for online assignments, and you can access it through Quercus. There are 6 online assignments and the average of your best 5 will count for 8% of your final grade. Online assignments will always be due on Sundays at 11:59pm (see the schedule below). No extensions will be given and there will be no make-up assignments. Medical notes will NOT be accepted for missed online assignments. Written Assignments: There will be 3 written assignments for this course. Assignments will be posted on Quercus and it is your responsibility to download/print them in time to complete them by the due date (see the schedule below). The purpose of the written assignments is to give you some practice in writing detailed solutions to mathematical problems, without any time pressure. You will receive feedback on your writing and on your solutions. You are encouraged to take this opportunity to carefully write your solutions and think about how to best present your reasoning behind them. Questions on the assignments may also appear again on tests and/or the final exam. Assignments need to be submitted online by the deadline. To submit, you can scan or take a photo of your work (or write your work electronically). Please make sure that images are clear and easy to read before you submit them. Deadlines to submit assignments are extremely strict. Missing the deadline by even a few minutes will mean that you get 0 for that assignment. Medical notes will NOT be accepted for missed written assignments. Note: It is OK (and you are encouraged) to work together on material related to the course, including discussing the written assignments. HOWEVER, you must write up your own solutions independently. It is an academic offence to copy someone’s solution, or to let someone copy yours. Students are expected to adhere to the Code of Behaviour on Academic Matters: http://www.governingcouncil.lamp4.utoronto.ca/wp-content/uploads/2016/07/p0701-coboam-20152016pol.pdf Also read http://advice.writing.utoronto.ca/using-sources/how-not-to-plagiarize/ Course feedback: A few weeks after the start of term, students will be given the opportunity to provide feedback to the instructor regarding the course and their teaching. Details will be posted on Quercus. You are strongly encouraged to participate and provide your feedback to your instructor. Help and RGASC: If you are finding the course difficult there are many ways in which you can get help. Please ask questions in lectures if something is unclear. Longer questions can be asked in tutorials or during office hours (both the instructors and teaching assistants have office hours). Tutorials are also a great opportunity to work through examples on topics of your choice and ask questions about them. Working in study-groups outside class where you can compare solutions and tackle problems together might also 5

be helpful. The Robert Gillespie Academic Skills Centre (RGASC) provides support and a variety of resources to help students develop their numeracy and scientific literacy skills. The location of the centre is in room MN3251 (3rd floor). Math drop-in sessions give students an opportunity to get more general assistance with the skills they need to succeed in their math courses at UTM. These appointments are generally short and offered on a first come, first served basis. (More information: https://www.utm.utoronto.ca/asc/appointments-undergraduate). As well, Facilitated Study Groups (FSGs) are a great way to help you improve your study skills and meet other students in your courses. Check out the FSGs offered for various courses and other math and science courses get advice on study methods from students who have taken the course, and done well. (More information: https://www.utm.utoronto.ca/asc/facilitated-study-groups-fsgs) . You can also visit the Academic Skills Centre for study tips and other help. Remember that all of these options are there to help you, so please take advantage of them if you need it. Most important of all is to keep up with the homework and to not fall behind. Ask for help early rather than the week of a test! Mathematics is not something you learn overnight, and falling behind is one of the most common causes of not doing well in the course. More information regarding academic resources can be found here: http://www.utm.utoronto.ca/dean/academic-resources

Good luck and welcome to the course!

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MAT135H5 Tentative Course Outline The Sections correspond to Single Variable Calculus: Early Trans c., 8th Edition, by James Stewart.

Week/Date 1

2

3

4

5

6

5 Sept. to 8 Sept. 9 Sept. to 15 Sept.

Sections to be covered

Additional Information

1.1 - Functions PLEASE REVIEW of the following topics independently: Appendix A - Numbers, inequalities, absolute values Appendix B - Coordinate geometry and lines 1.2 - Essential functions 1.3 - New functions from old functions 1.4 - Exponential functions 1.5 - Inverse functions and logarithms

16 Sept. to 22 Sept.

Exponentials and logarithms continued Appendix D - Trigonometry 1.5 cont. (Inverse trigonometric functions)

23 Sept. to 29 Sept. 30 Sept. to 6 Oct. 7 Oct. to 13 Oct.

2.2 - Limits 2.3 - Limit laws 2.5 - Continuity 2.6 - Limits at infinity; horizontal asymptotes 2.7 - Derivative as a rate of change 2.8 - Derivative as a function 3.1 - Derivatives of polynomials and exp. Review if time

A short week! Lectures begin Thursday 5 September No tutorials this week. No tutorials this week. Online assignment 1 is due 15 September at 11:59pm Tutorials start Tutorial activity 1 Online assign. 2 is due 22 Sept. 11:59pm 18 Sept.: Last day to change sections Written assignment 1 is due 29 September at 11:59pm Tutorial activity 2 (a practice test!) Online assignment 3 is due 6 October at 11:59pm 11 October - Term Test 1

Fall Reading Week (14-20 October) 7

8

9

10

11

12

13

21 Oct. to 27 Oct. 28 Oct. to 3 Nov. 4 Nov. to 10 Nov. 11 Nov. to 17 Nov. 18 Nov. to 24 Nov. 25 Nov. to 1 Dec. 2 Dec. to 4 Dec.

3.2 - Product and quotient rules 3.3 - Derivatives of trigonometric functions 3.4 - Chain rule

Tutorial activity 3 Online assignment 4 is due 27 October at 11:59pm

3.5 - Implicit differentiation 3.6 - Derivatives of logarithmic functions

Written assignment 2 is due 3 November at 11:59pm

3.9 - Related rates 4.4 - l’Hopital’s rule

Tutorial activity 4 Online assignment 5 is due 10 November at 11:59pm

4.1 - Max and min values 4.3 - Derivatives and graphs Review if time

15 November - Term Test 2

4.5 - Curve sketching 4.7 - Optimization problems 4.8 - Newton’s method 4.2 - The mean value theorem 4.9 - Antiderivatives Review if time

Tutorial activity 5 Written assignment 3 is due 24 November at 11:59pm. Tutorial activity 6 Online assignment 6 is due 1 December at 11:59pm A short week! Last lectures are on Wednesday 4 Dec. Last tutorials are on Wednesday 4 Dec. 7

Suggested Homework Problems: For each topic covered in this course, you are expected to do homework questions. You are NOT required to hand in your solutions, but it is important that you do all of the questions to prepare for term tests and the final examination. This is a list of the minimum number of problems you should work on. To properly prepare for tests and the final exam you may also want to work on the rest of the problems from the Complete Problem List (posted on Quercus under Course Materials), especially if you are finding a certain topic or a type of question difficult. You may want to start with the Suggested Homework List below, and later work on more problems from the Complete Problem List. Problems refer to: Single Variable Calculus: Early Transcendentals, 8th Edition, by James Stewart. Section: Suggested Homework Problems: Diagnostic Test: Algebra (p. xxvi) Appendix A - Inequalities and Absolute Values Appendix B - Coordinate Geometry and Lines Appendix D - Trigonometry 1.1 - Functions 1.2 - Essential Functions 1.3 - New functions from old functions 1.4 - Exponential functions 1.5 - Inverse functions Chapter 1 Review (p. 68-70) 2.2 - Limits 2.3 - Limit laws 2.5 - Continuity 2.6 - Limits at Infinity 2.7 - Derivative as a rate of change 2.8 - Derivative as a function Chapter 2 Review (p. 165-168) 3.1 - Derivatives of polynomials and exp. 3.2 - Product and quotient rules 3.3 - Derivatives of trig. functions 3.4 - Chain rule 3.5 - Implicit differentiation 3.6 - Derivatives of logarithmic functions 3.9 - Related rates Chapter 3 Review (p. 266-269) 4.1 - Max and min values 4.2 - The mean value theorem 4.3 - Derivatives and graphs 4.4 - l’Hopital’s rule 4.5 - Curve sketching 4.7 - Optimization problems 4.8 - Newton’s method 4.9 - Antiderivatives Chapter 4 Review (p. 358-362)

1-10 9, 11, 23, 29, 37, 39, 49, 51, 53, 55, 59 1, 7, 17, 21, 27, 29, 33, 35, 37, 53* 9, 17, 29, 31, 61, 63, 65, 69, 71, 73, 79 7, 9, 31, 33, 35, 37, 43, 45, 49, 53, 61, 69, 73, 75 3, 5, 15, 19 3, 5, 7, 13, 17, 23, 29, 33, 41, 53, 57, 63* 1, 3, 13, 15, 17, 19, 37* 1, 5, 11, 15, 19, 21, 23, 37, 41, 51, 53, 57, 63, 67, 71 Concept Check: 3, 8, 13; T/F: 1, 5, 7, 11, 14 (F); Ex: 17, 23 1, 3, 5, 7, 17, 31, 33, 35, 37, 39, 41, 43 11, 15, 17, 21-31 (odd), 37, 39, 41, 43*, 51, 59*, 65* 3, 5, 7, 17, 19, 21, 23, 35, 41, 45, 47, 51, 55, 69, 71 3, 9, 19, 21, 23, 27, 31, 33, 35, 39, 49, 55, 57, 65a, 67 5, 7, 11, 13, 17, 21, 25, 35, 37 3, 25, 27, 29, 41, 47, 51 T/F: 1, 7, 13 3-31 (odd), 33, 49, 51, 55, 61, 63, 77, 83 3-27 (odd), 33, 45, 49, 53 1, 5, 13, 15, 21, 31, 33, 51 9-17 (odd), 27, 31-45 (odd), 49, 53, 59, 63, 65 5, 9, 13, 17, 25, 29, 35, 49, 51, 57 2, 7, 11, 17, 19, 25, 33, 41, 4...