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MAC 2312 Syllabus FALL 2016 LECTURE: MWF 7 & 8, (NRN137): Chui (coordinator) LIT 376, office hours: Tu/1:20-4:20pm, Email: Use Mail tool in Canvas LECTURE: MWF 5 (CAR100): Mahoney LIT467, office hours: MWF 3rd period, Email: Use Mail tool in Canvas My Lecturer Name: Lecture Time & Location: Office & Office Hours: My Discussion Leader (TA) Name: Discussion Time & Location: Office & Office Hours: Email: TEXT: This course will be participating in the UF All Access program. The e-textbook, Calculus Early Transcendental by Stewart, is included in the required WebAssign access code. See Online Homework for an option with reduced price. Do not get the code directly from WebAssign.

MAC 2312 Syllabus FALL 2016 - University of Florida...MAC 2312 Syllabus FALL 2016 LECTURE: MWF 7 & 8, (NRN137): Chui (coordinator) LIT 376, o ce hours: Tu/1:20 4:20pm, Email: Use Mail

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Page 1: MAC 2312 Syllabus FALL 2016 - University of Florida...MAC 2312 Syllabus FALL 2016 LECTURE: MWF 7 & 8, (NRN137): Chui (coordinator) LIT 376, o ce hours: Tu/1:20 4:20pm, Email: Use Mail

MAC 2312 SyllabusFALL 2016

LECTURE: MWF 7 & 8, (NRN137): Chui (coordinator)

LIT 376, office hours: Tu/1:20−4:20pm, Email: Use Mail tool in Canvas

LECTURE: MWF 5 (CAR100): Mahoney

LIT467, office hours: MWF 3rd period, Email: Use Mail tool in Canvas

My Lecturer

Name:

Lecture Time & Location:

Office & Office Hours:

My Discussion Leader (TA)

Name:

Discussion Time & Location:

Office & Office Hours:

Email:

TEXT: This course will be participating in the UF All Access program.The e-textbook, Calculus Early Transcendental by Stewart, is included inthe required WebAssign access code. See Online Homework for an optionwith reduced price. Do not get the code directly from WebAssign.

Page 2: MAC 2312 Syllabus FALL 2016 - University of Florida...MAC 2312 Syllabus FALL 2016 LECTURE: MWF 7 & 8, (NRN137): Chui (coordinator) LIT 376, o ce hours: Tu/1:20 4:20pm, Email: Use Mail

MAC2312 FALL 2016 COURSE CALENDAR

Sunday Monday Tuesday Discussion Day

Wednesday Thursday Discussion Day

Friday Saturday

21 AUG Week 1

22 L1(7.1) Class Begin

23 First Discussion

24 L2(7.1)

25 First Discussion

26 L3(7.2) Drop/Add

27

28 Week 2

29 L4(7.2)

30

31 L5(7.3)

Sep 1

2 L6(7.3)

3

4 SEPT Week 3

5 Labor Day

6 Quiz1 (L1-L5)

7 L7(7.4)

8 Quiz (L1-L6)

9 L8(7.4)

10

11 Week 4

12 L9(7.4)

13 Quiz2 (L6-L8)

14 L11(limit)

15 Quiz2 (L7-L9)

16 L12(L’H)

17

18 Week 5

19 L13(7.8)

20 Quiz3 (L9-L12)

21 L14(11.1)

22 Quiz3 (L10-13)

23 L10(7.5)

24

25 Week 6

26 ExamReview

27 EXAM1(L1-13)

28 L15(11.1)

29

30 L16(11.2)

Oct 1

2 OCT Week 7

3 L17(11.2)

4 Quiz4 (L13-16)

5 L18(11.3)

6 Quiz4 (L14-17)

7 L19(11.4)

8

9 Week 8

10 L20(11.5)

11

12 L21(11.6)

13

14 Home Coming

15

16 Week 9

17 L22(11.6)

18 Quiz5 (L17-21)

19 L24(11.8)

20 Quiz5 (L18-22)

21 L23(11.7)

22

23 Week 10

24 ExamReview

25 EXAM2(L14-23)

26 L25(11.9)

27

28 L26(11.9)

29

30 Week 11

31 L27(11.10)

1 Nov Quiz6 (L22-26)

2 L28(11.10)

3 Quiz6 (L23-27)

4 L29 (11.10-11)

5

6 NOV Week 12

7 L30 (10.1)

8 Quiz7 (L27-29)

9 L31(10.2)

10 Quiz7 (L28-30)

11 Veterans Day

12

13 Week 13

14 L32(10.3)

15 16 L33(10.4)

17

18 L34(10.4)

19

20 Week 14

21 L35

22 No Discussion

23 THANKS

24 GIVING

25 HOLIDAY

26

27 Week 15

28 L36(6.2)

29 Quiz8 (L30-35)

30 ExamRvw EXAM3(24-35)

1 Dec Quiz8 (L31-36)

2 L37(6.3)

3

4 DEC Week 16

5 L37(6.3)

6

7 ExamReview

8 9

10 (L1-37) FINALEXAM

Exam 1~3 evening testing time: 8:20 - 10PM; Cumulative Final exam on Saturday: 12:30 -2:30PM.

Be at exam early. Late comers (10 minutes or more) are not allowed to participate in the exam.

Exam location will be posted in Canvas a week prior to the exam. Written Homework due on the week after the Exams except for HW3 due 12/1 for Thursday sections.

2

Page 3: MAC 2312 Syllabus FALL 2016 - University of Florida...MAC 2312 Syllabus FALL 2016 LECTURE: MWF 7 & 8, (NRN137): Chui (coordinator) LIT 376, o ce hours: Tu/1:20 4:20pm, Email: Use Mail

MAC2312 FALL 2016 WebAssign CALENDAR

Sunday Monday Tuesday Discussion Day

Wednesday Thursday Discussion Day

Friday SAT

21 August

22 L1(7.1) Class Begin

23 First Discussion

24 L2(7.1)

25 First Discussion

26 L3(7.2) D/A d-line

27

28 29 L4(7.2) 30 Diag Quiz 7.1P, 7.1C 7.2P, 7.2C

31 L5(7.3)

Sep 1 7.3P

2 L6(7.3)

3

4 SEPT 7.1M 7.2M

5 Labor Day

6 7.4P

7 L7(7.4)

8 7.3C

9 L8(7.4)

10

11 7.3M 7.4aC

12 L9(7.4)

13 7.4aM 7.4bC

14 L11(limit)

15 7.4bM 7.4cC

16 L12(L’H)

17

18 7.4cM 7.8P

19 L13(7.8)

20 11.1P LimitR

21 L14(11.1)

22 7.8C L’HR

23 L10(7.5)

24

25 7.8M 7.5R

26 ExamReview

27 Exam1R EXAM1

28 L15(11.1)

29 11.1C

30 L16(11.2)

Oct 1

2 OCT 11.1M

3 L17(11.2)

4 11.2aC 5 L18(11.3)

6 11.2aM 11.2bC

7 L19(11.4)

8

9 11.2bM 11.3C

10 L20(11.5)

11 11.3M 11.4C

12 L21(11.6)

13 11.4M 11.5C

14 Home Coming

15

16 11.5M 11.6aC

17 L22(11.6)

18 11.8P 11.6aM

19 L24(11.8)

20 11.6bC

21 L23(11.7)

22

23 11.6bM 11.7R

24 ExamReview

25 Exam2R EXAM2

26 L25(11.9)

27 11.8C 11.9aC

28 L26(11.9)

29

30 11.8M 11.9aM

31 L27(11.10)

1 Nov 11.9bC

2 L28(11.10)

3 11.9bM 11.10aC

4 L29(11.10- 11.11)

5

6 NOV 11.10aM 10.1-4P

7 L30 (10.1)

8 11.10bC

9 L31(10.2)

10 11.10bM

11 Veterans Day

12

13 10.1-10.2C

14 L32(10.3)

15 Exam3R-I

16 L33(10.4)

17 10.3C 10.1-10.2M

18 L34(10.4)

19

20 10.3M 10.4aC

21 L35

22 10.4aM No Discussion

23 THANKS

24 GIVING

25 HOLIDAY

26

27 10.4bC 6.2P

28 L36(6.2)

29 10.4bM Exam3R-II

30 ExamRvw EXAM3

1 Dec

2 L37(6.3)

3

4 DEC 6.2C

5 L37(6.3)

6 6.2M 6.3C

7 ExamReview

8 6.3M FinalR

9

10 FINAL

Blue color ExamR indicates optional exam review assignments. (in WebAssign, Exam Bonus Points) Red color indicates a required graded assignment (in WebAssign). Green color indicates exam dates. Exam 1~3 at 8:20PM; Final exam at 12:30PM. Written Homework due on the week after Exams except HW3 on 12/1 for Thursday Discussion sections.

3

Page 4: MAC 2312 Syllabus FALL 2016 - University of Florida...MAC 2312 Syllabus FALL 2016 LECTURE: MWF 7 & 8, (NRN137): Chui (coordinator) LIT 376, o ce hours: Tu/1:20 4:20pm, Email: Use Mail

COURSE GRADE: A student’s grade will be based on 400 pointsaccumulated as follows:

Lecture Participation (HITT clickers) 35Online Homework (in WebAssign)(out of 54.5) 50Written Homework (5 points × 3=15) 15Discussion Quizzes (best 6 of 8, 6 points × 6=36) 36Discussion Participation 4Semester Exams (60 points × 3=180) 180Cumulative Final Exam 80

400

There will be NO DROP or adjustment on exam grades andNO additional curve in this course. Extra assignments for in-dividual students to improve a grade are NOT possible.

The course grade is determined by the number of points youearn, not by the percentage. A student’s course letter grade is basedon the grading scale below:

A 360 − 400 pts C 280 − 293 pts

A− 348 − 359 pts C−∗ 268 − 279 pts

B+ 334 − 347 pts D+ 254 − 267 pts

B 320 − 333 pts D 240 − 253 pts

B− 308 − 319 pts D− 228 − 239 pts

C+ 294 − 307 pts E 0 − 227 pts

Lecture Participation:

Attendance in lecture and in discussion are required. In lectures,students are required to have a working H-ITT clicker. You may also usesoftclick. Detailed information about using the clicker/softclick is located inthe resources section of the Module tab in Canvas.

Starting approximately the second week of the semester, students will berequired to have their clickers in class in order to participate in lectures.Students will be asked questions to test their understanding of class materialsand their responses will be graded and recorded immediately. A weekly reportwill be sent to students. It’s students responsibility to verify the scoresand fix any problems immediately.

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Page 5: MAC 2312 Syllabus FALL 2016 - University of Florida...MAC 2312 Syllabus FALL 2016 LECTURE: MWF 7 & 8, (NRN137): Chui (coordinator) LIT 376, o ce hours: Tu/1:20 4:20pm, Email: Use Mail

There are NO MAKEUPS, however there will be a small excess of clickerpoints given over the course of the semester to compensate for occasionalabsence, mechanical failures, forget to bring the clicker, etc.

A students is not allowed to respond in class for anyone else but himself; aviolation of this policy is considered cheating and will be handled accordingto standard University policies.

Your instructor will use a LECTURE OUTLINE (may be purchased atTarget Copy on University Ave or, printed online in Canvas). Bring it toeach lecture.

Online Homework:

Students must purchase an access code for WebAssign (WA), which includesthe text as an ebook and the online homework assignments. You have limitedtime (by 9/9/16) to ’opt-in’ to WA access and the ebook through Canvas onceclasses begin for a reduced price of $62.50 and pay for these materials throughyour student account. A print copy of the text is not required.

During the course of the semester, online assignments will be assigned on aroutine basis and must be completed within the given time interval. Studentsare responsible for having access to a working computer and have your workcompleted on time. Start early to avoid any last minutes issues. Always click’SAVE’ as you enter answers in WA. There will be NO MAKEUPS. How-ever, there will be few excess points given to compensate for any difficultiesyou may encounter.

You can request an extension on WA homework within 2 days after thedeadline and you will have 48 hours to complete it after extension request.There will be 20% grade penalty for those problems completed after theoriginal due date.

NOTE: The extension is submitted in WA directly and you must NOT selectto view the answers before the extension request.

Any WA questions must be directed to your TA and/or WA student sup-port, https://webassign.com/support/student-support/ . Always readthe Description and Instruction in each assignment and pay attention to thenumber of submissions allowed in each question since they are different de-

5

Page 6: MAC 2312 Syllabus FALL 2016 - University of Florida...MAC 2312 Syllabus FALL 2016 LECTURE: MWF 7 & 8, (NRN137): Chui (coordinator) LIT 376, o ce hours: Tu/1:20 4:20pm, Email: Use Mail

pending on the types of the questions. True/False question had only onesubmission. You should always click the ’SAVE’ button each time you en-ter an answer. The ’SAVE’ does not reduce your number of submissions, itmerely saves your answer in case any glitches happen, your last saved answeris kept in the system, submitted or not, and can be retrieved by your TA.

Discussion Quizzess:

Every student is registered to attend a weekly discussion session. You mustnotify your TA within the first three weeks of class if you will be missingdiscussion class due to religious observance or participating in UF activities.See your TA if you have court ordered obligation and other UF approvedabsence before you miss the discussion.

8 quizzes will be administered in discussion during the course of the semesterto insure that the student is keeping current with lecture topics. You mustbe present at the beginning of the class and stay the entire period in orderto take the quiz. There will be NO MAKEUPS. However a couple of quizgrades will be dropped at the end of the semester to compensate for anyabsences including UF excused absences.

Written Homework:

As you work out your online assignments, you have the opportunity to prac-tice writing down your solutions algebraically, logically and thoroughly be-fore you have to take quizzes and exams. You may ask TAs for help needed.Rewrite your work neatly if needed to be turned in for written homeworkgrade. They are collected by your TA three times in discussion, there willbe no drops and students have to be present at the beginning of the classand stay the entire period in order to submit your homework. The workmust be your own and not taken from any other sources and it is graded forcompleteness and accuracy. This is a good time to visit office hours and getthe help you may need to master the material.

If you are present in discussion on the day of the collection but forget to bringyour homework, make arrangement with your TA before you leave the dis-cussion. You have 24 hours to turn in your ENTIRE homework with 1 pointpenalty. There are NO MAKEUPS. If you know you must be absent, con-

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Page 7: MAC 2312 Syllabus FALL 2016 - University of Florida...MAC 2312 Syllabus FALL 2016 LECTURE: MWF 7 & 8, (NRN137): Chui (coordinator) LIT 376, o ce hours: Tu/1:20 4:20pm, Email: Use Mail

tact your TA immediately to make prior arrangement to turn it in early, not late.

Exams:

During the semester we will have three mid−terms and a cumulative final,all mandatory. The mid−term exams are assembly exams which begins at8:20PM, consist of multiple choice and free-response questions; the final examtime may change each term, consists solely of multiple choice questions. Allexam dates and time are specified in the course calendar and they mustbe taken at the assigned date and time. If you have class or other examconflict, please see UF during Term Assembly Exam Policy https:

//catalog.ufl.edu/ugrad/current/regulations/info/exams.aspx.You must sign up with your instructor by the end of the third week toavoid 10-point penalty, if MAC 2312 is the course to give the conflict exam.

If you are participating in a UF sponsored event, religious observance or court-ordered obligation, you may make up an exam if you make arrangements withyour instructor the first 3 weeks with valid documentation, same penaltyapplies otherwise.

If illness or other extenuating circumstances causes you to miss an exam, youmust contact your instructor no later than 24 hours after the exam by email,then as soon as you return to campus, bring the appropriate document.

The conflict exam will be offered from 6:40−8:20pm on the same night asthe regular exam. You will not be permitted to leave the exam room be-fore 8:20pm. All makeup exams will be given on the last Wednesday of thesemester at 8:20PM. It is the responsibility of the student to be present duringexaminations with your valid UF Gator I card.

Bubble your scantron carefully, there are 3 points penalty for incorrect UFIDor Form Code. There are 3-point penalty if you do not take your exam inthe assigned room for your section.

ADDITIONAL TOPICS:

All course information will be posted on Canvas which can be ac-cessed using the link http://elearning.ufl.edu . Use your Gator-link credential to login to this site.

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Page 8: MAC 2312 Syllabus FALL 2016 - University of Florida...MAC 2312 Syllabus FALL 2016 LECTURE: MWF 7 & 8, (NRN137): Chui (coordinator) LIT 376, o ce hours: Tu/1:20 4:20pm, Email: Use Mail

One Week Policy: All grades are posted in the Canvas gradebook (exceptindividual WA and H-ITT points which are accessed through those programsdirectly). You are responsible for verifying all grades are accurate. You haveone week after a score is available to discuss any grade concerns with yourTA. There is no grades dispute after one week.

10−Minutes Policy: Only students who are present in the first 10 minutesand stay for the entire period are allowed to participate in class activities(including submitting clicker questions, taking discussion quizzes and turn inhomework assignments). Go to the exams early since you will not be allowedinto the exam if you are 10 minutes late, and no one is allowed to leave examwithin the first 30 minutes.

During the course of the semester we will cover material from chapter 7, 10,11 and 6. After the first week, all TAs and instructors’ office hours will beposted in Canvas. You may go to anyone’s office hours that fit your schedule.We encourage you to use this valuable resource to help you stay on track andsucceed. Both instructors’ LECTURES ARE TAPED, you access themin Canvas. (Chrome is known to have problem sometimes, try use otherbrowsers if needed).

Attendance is mandatory if a student wishes to master the subject. A stu-dents is responsible for all announcements and lecture material covered inclass and/or posted in Canvas. ra (1)

Academic dishonesty in any form will not be tolerated and will be treated inaccordance with the policies of the University of Florida.

Your TA is your first contact if you have any questions. In orderto minimize the volume of mail correspondence in the large assembly class,students are highly encouraged communicate with the instructors after classand during office hours. If you have personal/private issues and you can notmake to office hours to discuss, you may send emails. Your coordinator hasaccess to multiple courses. In order to put your email in the right context,when email the course coordinator, you need to use the Mail tool in thecourse Canvas, write in the subject line your lecture period, TA’sname and section numbers.

Students requesting classroom and exam accommodation must first register

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Page 9: MAC 2312 Syllabus FALL 2016 - University of Florida...MAC 2312 Syllabus FALL 2016 LECTURE: MWF 7 & 8, (NRN137): Chui (coordinator) LIT 376, o ce hours: Tu/1:20 4:20pm, Email: Use Mail

with the Dean of Students Office. The Dean of Students Office will provideinformation to the student who must then see coordinator during office hourswhen requesting accommodation. This should be done at the earliest possibledate.

All students have the extra credit opportunities. There is no makeup on theseopportunities. Please do not ask for special treatment since there will be noextra credit opportunities of any kind grant to individuals without havingthem available to the entire class.

ABOUT THE ONLINE ASSIGNMENTS:

The entire course is organized around a list of Learning Objectives thatdemonstrates mastery of various topics in the course. These objectives fallinto three categories:

• Prelecture (P) objectives in which you will watch video, read from thetextbook and work exercises to review algebraic skills, expose to the newmaterial and to prepare yourself for the sections to come.

• Concept Check (CC) objectives that address basic terminology and com-putations based directly on theorems, definitions and examples of thesection.

• More Practice (MC) objectives address higher-level tasks such as syn-thesis of multiple techniques and creative work through application.

HOW TO BE SUCCESSFUL IN MAC2312

I want you to be successful in this class, I am on your side and will be workinghard to make sure you always have the resources to have a clear path tosuccess. But I cannot walk that path for you! It will take considerable efforton your part. To do this and be successful, you will need to do the following:

1. Prepare diligently outside of class and come to class ready towork from the get-go.

(a) Get an early start on all assignments.

9

Page 10: MAC 2312 Syllabus FALL 2016 - University of Florida...MAC 2312 Syllabus FALL 2016 LECTURE: MWF 7 & 8, (NRN137): Chui (coordinator) LIT 376, o ce hours: Tu/1:20 4:20pm, Email: Use Mail

(b) Do Not Procrastinate on assignments by waiting until the day beforethey are due. (internet is known to be down sometimes)

(c) Work hard, work whole heartily.

(d) Review and master your assignments and lecture notes before arriv-ing at the next class.

(e) If you get stuck, watch the taped lecture again and/or find officehours for timely help. Do not let questions go unanswered.

2. Actually come to class and actively engaged in your learning.

(a) Pay attention and answer questions, at least mentally, posed by yourinstructor in lecture.

(b) Avoid inappropriate distractions in class such as Facebook textingor talking.

3. Engaged and be active in your learning after class.

(a) Watch the lecture video again, go to office hours whenever you getstuck on a problem.

(b) Spend at least 3 hours outside of class for every hour you spend inclass. So 12 hours a week just on MAC2312.

(c) The time you spend on MAC2312 is to spent purposefully, with aplan for what you will master and when you will do it as well as aplan for getting help if you get stuck.

(d) Believe that your mathematical skills can be improved through ded-ication and hard work, and when you fail at something, take it as alearning opportunity and get better by learning from your mistakes.

4. Practice self-guided learning. Pay attention not only to what youare learning but how you are learning it, and you are not dependingupon the instructor or anyone else to learn things. In particular:

(a) Be aware at all times of what you are supposed to be learning.

(b) When you work, work purposefully. Some of the activities are onesthat you make up yourself, such as study guides, even if no grade isinvolved.

(c) If you see there is a gap between your abilities and the topics coveredin lectures, take initiative to find things that will help you close it.

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Page 11: MAC 2312 Syllabus FALL 2016 - University of Florida...MAC 2312 Syllabus FALL 2016 LECTURE: MWF 7 & 8, (NRN137): Chui (coordinator) LIT 376, o ce hours: Tu/1:20 4:20pm, Email: Use Mail

I want you to be successful! It is very easy in MAC2312 to cooperatewith me on this by doing these things. Remember that you are the onlyperson who can walk the path to your success. Your TA and I are there foryou, but you need to stay on top of what’s going on in class and take theinitiative to reach out when you need help.

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Page 12: MAC 2312 Syllabus FALL 2016 - University of Florida...MAC 2312 Syllabus FALL 2016 LECTURE: MWF 7 & 8, (NRN137): Chui (coordinator) LIT 376, o ce hours: Tu/1:20 4:20pm, Email: Use Mail

PREREQUISITES MATERIAL FOR MAC2311, 2312

This course assumes that you have a sound precalculus background. Thefollowing is a summary of some important concepts used in solving calculusproblems. The textbook provides a more complete review of these essentialtopics.

ALGEBRA

1. Basic Geometric Formulas: (b = base, l = length, h = height, w = width)

Triangle: area =1

2bh

Circle: area = πr2; circumference = 2πr

Parallelogram: area = bh

Rectangular box: volume = lwh

Sphere: volume =4

3πr3; surface area = 4πr2

Right circular cylinder: volume = πr2h; surface area = 2πrh+ 2πr2

Right circular cone: volume =1

3πr2h; surface area = πr

√r2 + h2

Facts about similar triangles

Pythagorean theorem: x2 + y2 = z2

x

yz

12

Page 13: MAC 2312 Syllabus FALL 2016 - University of Florida...MAC 2312 Syllabus FALL 2016 LECTURE: MWF 7 & 8, (NRN137): Chui (coordinator) LIT 376, o ce hours: Tu/1:20 4:20pm, Email: Use Mail

2. Basic Functions and their graphs

f(x) = x; f(x) = x2; f(x) = x3; f(x) = |x|; f(x) =√x; f(x) = 1/x;

f(x) = bx, b > 0 and b 6= 1, such as f(x) = 2x

3. Factoring

x3 + y3 = (x+ y) (x2 − xy + y2); x3 − y3 = (x− y) (x2 + xy + y2); etc.

4. Completing the square x2 + ax+ b =(x+

a

2

)2+

(b−

(a2

)2)

5. Law of exponents xnyn = (xy)n; xnxm = xn+m;

xn

xm= xn−m; (xn)m = xnm

6. Roots

n√x = x

1n ; x−n =

1

xn, etc.

7. Inequalities and absolute values

|x| ≤ a − a ≤ x ≤ a; |x| > a x > a or x < −a

8. Properties of logarithms If x > 0, loga x = y if and only if x = ay

If m > 0 and n > 0, then

log (nm) = log (n) + log (m) log( nm

)= log (n)− log (m)

log (nc) = c log (n) logb (x) =ln(x)

ln b

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Page 14: MAC 2312 Syllabus FALL 2016 - University of Florida...MAC 2312 Syllabus FALL 2016 LECTURE: MWF 7 & 8, (NRN137): Chui (coordinator) LIT 376, o ce hours: Tu/1:20 4:20pm, Email: Use Mail

TRIGONOMETRY

1. Identities:

sin(−θ) = − sin θ cos(−θ) = cos θ tan(−θ) = − tan θ

sin(π

2− θ)

= cos θ cos(π

2− θ)

= sin θ tan(π

2− θ)

= cot θ

sin2 θ + cos2 θ = 1 sec2 θ = 1 + tan2 θ csc2 θ = 1 + cot2 θ

2. Sum and Difference Formulas:

sin(A±B) = sinA cosB ± cosA sinB

cos(A±B) = cosA cosB ∓ sinA sinB

tan(A±B) =tanA± tanB

1∓ tanA tanB

3. Double Angle Formulas:

sin 2θ = 2 sin θ cos θ

cos 2θ = cos2 θ − sin2 θ = 2 cos2 θ − 1 = 1− 2 sin2 θ

4. Half-Angle Formulas:

sin2 θ =1− cos 2θ

2cos2 θ =

1 + cos 2θ

2

5. Trigonometric Values:

θ 0 π/6 π/4 π/3 π/2

sin θ 0 1/2√

2/2√

3/2 1

cos θ 1√

3/2√

2/2 1/2 0

tan θ 0√

3/3 1√

3 undef

6. arctanx = at x = 0, 1,√

3,1√3

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Page 15: MAC 2312 Syllabus FALL 2016 - University of Florida...MAC 2312 Syllabus FALL 2016 LECTURE: MWF 7 & 8, (NRN137): Chui (coordinator) LIT 376, o ce hours: Tu/1:20 4:20pm, Email: Use Mail

PREREQUISITES MATERIAL FOR MAC2312

This course assumes that you have a sound calculus 1 background. Thefollowing is a summary of some important concepts and formulas used insolving calculus problems. The textbook provides a more complete review ofthese essential topics.

FORMULAS YOU ARE EXPECTED TO KNOW

1. COMPLETING THE SQUARE:

x2 + ax+ b =(x+

a

2

)2+

(b−

(a2

)2)2. PARABOLA:

y = f(x) = ax2+bx+c, vertex (h, k), where h = − b

2a, and k = f

(− b

2a

)3. CIRCLES:

(x− a)2 + (y − b)2 = r2, Center at (a, b), radius = r

4. DERIVATIVES OF AN INVERSE FUNCTION:

If g = f−1, then g′(x) =1

f ′(g(x))

5. DIFFERENTIATION/INTEGRATION FORMULAS:

CHAIN RULE (f(g(x)))′ = f ′(g(x))g′(x)

PRODUCT RULE (f(x)g(x))′ = f(x)g′(x) + g(x)f ′(x)

QUOTIENT RULE

(f(x)

g(x)

)′=g(x)f ′(x)− f(x)g′(x)

(g(x))2

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d

dx(xn) = nxn−1

∫xn dx =

xn+1

n+ 1+ C

d

dx(lnx) =

1

x

∫1

xdx = ln |x|+ C

d

dx(ex) = ex

∫ex dx = ex + C

d

dx(ax) = (ln a)ax

∫ax dx =

ax

ln a+ C

d

dx(sinx) = cos x

∫cosx dx = sinx+ C

d

dx(cosx) = − sinx

∫sinx dx = − cosx+ C

d

dx(tanx) = sec2 x

∫sec2 x dx = tanx+ C

d

dx(cotx) = − csc2 x

∫csc2 x dx = − cotx+ C

d

dx(secx) = tan x secx

∫tanx secx dx = secx+ C

d

dx(cscx) = − cotx cscx

∫cotx cscx dx = − cscx+ C

d

dx(arcsinx) =

1√1− x2

∫1√

1− x2dx = arcsinx+ C

d

dx(arctanx) =

1

1 + x2

∫1

1 + x2dx = arctanx+ C

d

dx[f(g(x))] = f ′(g(x))g′(x)

∫f ′(g(x))g′(x) dx =

∫f(u) du∫

tanx dx = ln | secx|+ C or, − ln | cosx|+ c

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