Mathematics 10360 - Calculus B for the Life & Social SciencesSpring Semester 2018

Text: Single Variable Calculus (3rd Ed) - Early Transcendentals by Jon Rogawski & Colin AdamsPublisher: W. H. Freeman & Co.

Section Instructor Class Schedule Office email@nd.edu

1 Arthur Lim MWF 8:20 - 9:10 HAYES 127 HAYES 250 arthurlim

2 Priyanka Rajan MWF 9:25 - 10:15 DBRT 131 HAYES 118 prajan

3 Stephan Stolz MWF 10:30 - 11:20 HAYES 117 HURLEY 166A stolz

4 Behrouz Taji MWF 2:00 - 2:50 DBRT 126 HURLEY 278 btaji

5 Anibal Medina MWF 11:30 - 12:20 Jordan 105 HAYES 126 amedinam

6 Joao Santos MWF 12:50 - 1:40 HAGGAR 117 HAYES 219 jsantos3

Section Teaching Assistant Class Schedule Office email@nd.edu

11 Li Ling Ko R 9:30 - 10:20 HAYES 231 HAYES B26 lko

12 Li Ling Ko R 11:00 - 11:50 HAYES 117 HAYES B26 lko

21 Justin Miller R 12:30 - 1:20 DBRT 241 HAYES B26 jmille74

22 Justin Miller R 3:30 - 4:20 DBRT 241 HAYES B26 jmille74

31 Timothy Warner R 11:00 - 11:50 PCTR 112 HAYES B24 twarner

32 Timothy Warner R 9:30 - 10:20 HAYES 229 HAYES B24 twarner

41 Aaron Tyrrell R 12:30 - 1:20 HAYES 229 HAYES B26 atyrrell

42 Aaron Tyrrell R 3:30 - 4:20 HAYES 129 HAYES B26 atyrrell

51 Kostya Timchenko R 11:00 - 11:50 RILEY 200 HAYES 235 ktimchen

52 Kostya Timchenko R 2:00 - 2:50 HAYES 231 HAYES 235 ktimchen

61 Timothy Warner R 2:00 - 2:50 HAYES 129 HAYES B24 twarner

62 Justin Miller R 9:30 - 10:20 HAYES 129 HAYES B26 jmille74

Course Website: http://www.nd.edu/∼m10360Most information for this course is posted on its website. These include instructors and TAs office hours andcontact information, daily homework information, exam dates and venues, practice exams, and etc.

Calculator Policy: Calculators are NOT allowed on any of the exams. You may use your calculators forhomework and assignments, but we strongly recommend that you do not rely on any of its graphing functions.

Course Grade & Breakdown:

Date Day Time Room PointsMidterm 1 Feb. 20 Tuesday 8:00 – 9:15 AM On course website 100Midterm 2 Mar. 27 Tuesday 8:00 – 9:15 AM On course website 100Midterm 3 Apr. 26 Thursday 8:00 – 9:15 AM On course website 100Final May 10 Thursday 1:45 – 3:45 PM On course website 150Differentiation/Integration Gateway Tutorial week 02 (20%), week 03 (30%), & week 04 (50%) 50

Online Hwk & Assignments Submit online or collected in class as scheduled on website 75

Tutorial participation, attendance, activities & quizzes 25

Total points: 600

Cutoffs for major grades (A, B, C, D, F) for each exam will be assigned and announced in class so you have someindication of your level of performance. Your final grade will be based on your total score out of 600.

Missed exams: Note that there will be three Midterm Exams and a Final Exam. A student who misses anexamination will receive zero points for that exam unless he or she has written permission from the Dean of theFirst Year of Studies. Please be aware that travel plans, sleeping in, defective alarm clocks, etc. are not considered

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to be a valid excuse by the Dean of the First year of Studies! If you have a valid excuse (illness, excused athleticabsence, etc.) for missing an exam, please see me ASAP (preferably before the exam) to schedule a makeup exam.

Exam conflicts are governed by Academic code. According to Section 14.2, students with 3 or more finals inone day, or 4 or more finals in a 24 hour period, may negotiate to change the time of one of these finals. If youhave time conflict in your final exam schedule and need to do Math 10360 final at another time, you must informyour instructor by April 21.

Honor Code: Examinations, homework, assignment and quizzes are conducted under the honor code. Whilecollaboration in small groups in doing homework is permitted (and strongly encouraged) in this course, copying isnot. In particular, copying from the Student Solutions Manual is a violation of the Honor Code. Examsare closed book and are to be done completely by yourself with no help from others.

Homework & Assignments: Online Homework and assignment problems are assigned daily. Their scheduleis listed on the course website. Absolutely no late homework or assignment will be accepted. You are encouragedto work on these problems in groups, but all online homework and assignments must be turned in individually.Remember that you will not learn anything by simply copying another student’s work or the StudentSolutions Manual. The main purpose of homework and assignments is to help you learn the material and assessyourself. Experience shows that students who take their homework seriously do very well in the course becausethey have a better understanding of the material. For detailed homework and assignment instructions, please seeattached information.

Class Attendance: A student who accumulates more than 3 unexcused absences may be given an F grade.

Classroom Policies: Please do your best to show up on time and quietly enter the room if you are late. Pleaseremember to respect your peers who are here to learn. Indeed, class disruptions will not be tolerated and offendingparties will be asked to leave. During lectures you are encouraged to actively participate by answering and askingquestions.

Study Tips are posted on the on the course website (http://www.nd.edu/∼m10360). Please print out a copyand review it. The key point is to start early and be consistent.

Getting Help: You can get help for mastering the course material from the following three avenues below.More information can be obtained from the 10360 course website; click on “TUTORING & HELP”.

• Instructor & TA’s Office Hours: The schedule will be posted on Math 10360 website or make an appointmentto meet your instructor or TA. It is important that you see them soon when you have difficulty with the course.The earlier you meet with your instructor and TA, the more we can do to help and advise.

• Learning Resources Center (LRC) Help: You may also obtain valuable assistance from the LRC in theFirst Year of Studies:

Math 10360 Tutoring Program,Math 10360 Collaborative Learning Program,Math 10360 Workshops/Review Sessions.

If you wish to participate in the Tutoring Program or Collaborative Learning Program, you must sign up with MsNahid Erfan, Director of LRC. Regular attendance is required for these programs. Sign-up and regular attendanceare not required for the Math 10360 Workshops/Review Sessions.

• Mathematics Library Tutoring: This is a free tutoring service provided by the Mathematics Library. It isone-on-one and needs sign up. You can find tutoring schedule and the online sign-up sheet at:

http://library.nd.edu/mathematics/

Please note that instructors and tutors are NOT there to do your homework. In fact, tutors are instructed toguide you to the answer and not do your homework. Please do not ask the tutors to grade your homework, andbe specific about what you want to discuss.

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MATH 10360 Course Work Policy

There are both online homework and paper-pencil assignments for this course.

Written Assignments are due in class according to the schedule posted on the Math 10360 website. Thequestions and problems to be turned in are posted on the course website. You are expected to submit your writtenassignment in the following manner:

• Your work has to be clearly and logically written, showing the method of solution, not just a final answer.

• Please staple your work together. It is your responsibility that your work stays stapled together securely.

• Any work falling short of the above expectations may not be graded.

Absolutely no late assignments will be accepted. Exceptions are handled case by case. If you need to attend aschool related event, you may turn in your assignment early or arrange to have your peer turn it in on the day itis due.

Online Homework is assigned daily and is due at the end of the next class day. The online systems we areusing are LaunchPad and Maple T.A. Please follow registration instructions for LaunchPad in the attached flyercarefully.

• Be sure to register your login name on LaunchPad as your ND email address (netID@nd.edu).

• Maple T.A. is accessed through the ND Sakai system.

• The ND e-mail address will be used to make all course related announcements. You must check your e-mailregularly daily.

All online homework should be done using paper and pencil, and be treated the same manner as written assign-ments. We encourage you to keep a record of your work for material submitted online; these are helpful whenyou review for an exam. Usually, you are expected to complete about 5 to 8 problems of your online home-work assigned at the end of each class day. If you have difficulty solving the homework questions please see yourTA/professor or visit the listed the math help resources above.

Absolutely no late homework will be accepted. Register and access the online homework on the LaunchPad webaddress:

http://www.macmillanhighered.com/launchpad/calculuset3eNotreDame

Access Maple T.A. at:http://sakai.nd.edu/

All homework and assignment will be weighted the same. The three lowest of homework/assignment scores willbe dropped. You should bookmark these pages.

Online Homework Submission Policies. All submission deadlines for online homework on LaunchPad are fixed.You are highly encouraged to SUBMIT your homework well ahead of deadlines. We DO NOT accept excuses like:My computer/Webservers shut down just before I could submit my work on time. Save your answers as you enterthem online. This ensures that no work is lost BEFORE the submission deadline. Enough buffer time is givento ensure timely submission of your work. All online homework are due are due at 12:00am (+2 hrs buffer) atthe end of the next class day unless otherwise stated. In addition, after the deadline of a homework, you have 48hours to complete a late homework to obtain up to 80% of the full score.

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Math 10360 (Calculus B) Syllabus Text: Calculus (Early Transcendentals) 2nd Edition – J. Rogawski

3.8

Derivatives of Inverse Functions

5.7 5.8

Further Transcendental Functions Exponential Growth and Decay – Malthusian Growth Model Only

6.1 6.2 6.3 6.4 6.5

Area Between Two Curves Setting Up Integrals: Volumes, Density, Average Value Volumes of Revolution The Method of Cylindrical Shells Work and Energy

7.1 7.2 7.3 7.5 7.6 7.8

Integration by Parts Trigonometric Integrals Trigonometric Substitution The Method of Partial Fractions Improper Integrals Numerical Integration

14.1 15.1 15.2 8.4

Functions of Two or More Variables Setting Up Double Integrals: Volumes, Areas, Density Setting Up Double Integrals: Volumes, Areas, Density Taylor Polynomials

9.1 9.2 9.3 9.4 9.5 14.3 14.6 14.8

Solving Differential Equations Models Involving y’ = k(y-b) Graphical and Numerical Methods The Logistic Equation (including model with harvesting and Birch’s Curve) First-order Linear Equations Partial Derivatives Chain Rule (Appln to Elasticity/Sensitivity) Lagrange Multipliers

Notes 10.1 10.2 10.5 10.6 10.7

Geometric Sequences and Geometric Series (Appln to Medicine and Ecology) Sequences Summing an Infinite Series The Ratio Test (no root test) Power Series (Application of Ratio Test) Taylor Series

Basic Algebra Rules

Exponential Rules:

am · an = am+n (ab)m = ambm am

an= am−n; a 6= 0

a0 = 1 a 6= 0 a1/m = m√

a(a

b

)m

=am

bm; b 6= 0

(am)n = amn

Distribution Law:

a(b + c) = ab + aca + b

c=

a

c+

b

c

a − b

c=

a

c− b

c

Quadratic Factoring:

(a + b)2 = a2 + 2ab + b2 (a − b)2 = a2 − 2ab + b2

a2 − b2 = (a − b)(a + b)

Properties of Logarithm:

loga(MN) = loga M + loga N loga

(M

N

)= loga M − loga N loga(M)t = t loga M

loga a = 1 loga 1 = 0

loga ax = x aloga x = x

Change of Base: loga M =logb M

logb a

ln(MN) = ln M + ln N ln

(M

N

)= ln M − ln N ln(M)t = t ln M

ln e = 1 ln 1 = 0

ln ex = x eln x = x

1

Summary of Differentiation Rules

The following is a list of differentiation formulae and statements that you have to know.

Product Rule:

(f(x)g(x))′ = f(x)g′(x) + f ′(x)g(x)

Quotient Rule: (f(x)

g(x)

)′=

g(x)f ′(x)− g′(x)f(x)

(g(x))2

Chain Rule:

(f(g(x))′ = f ′(g(x))g′(x)

Derivative of Trigonometric Function:

d

dx(sinx) = cos x

d

dx(cosx) = − sinx

d

dx(tanx) = sec2x

d

dx(cscx) = − cscx cotx

d

dx(secx) = secx tanx

d

dx(cotx) = − csc2 x

d

dx(arcsinx) =

1√1− x2

d

dx(arctanx) =

1

1 + x2

Derivative of Exponential and Logarithm Functions:

d

dx(ex) = ex

d

dx(ax) = ax ln(a)

d

dx(lnx) =

1

x

1

Summary of Integration Rules

The following is a list of integral formulae and statements that you have to know.∫xn dx =

xn+1

n + 1+ C; n 6= −1

∫(ax + b)n dx =

(ax + b)n+1

a(n + 1)+ C; n 6= −1

∫x−1 dx =

∫1

xdx = ln |x|+ C

∫1

ax + bdx =

1

aln |ax + b|+ C

∫ex dx = ex + C

∫eax+b dx =

1

aeax+b + C

∫sinx dx = − cosx + C

∫cosx dx = sinx + C

∫sec2x dx = tanx + C

∫secx tanx dx = secx + C

∫cscx cotx dx = − cscx + C

∫csc2 x dx = − cotx + C

∫secx dx = ln |secx + tanx|+ C

∫cscx dx = − ln | cscx + cotx|+ C

∫1

1 + x2dx = arctanx + C

∫1√

1− x2dx = arcsinx + C

Fundamental Theorem of Calculus

Let F an antiderivative of f i.e. F ′(x) = f(x). Then we have:

(1)

∫ b

a

f(x) dx = F (b)− F (a) = [F (x)]ba

(2) Total change in F when x changes from a to b = F (b)− F (a) =

∫ b

a

F ′(x) dx

Integration by Parts:

(1)

∫u dv = uv −

∫v du (2)

∫ b

a

u dv = [uv]ba −∫ b

a

v du

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Math 10360 – Example Set 01A

1. Consider the area function f(x) =

∫ x

1

1

tdt for x > 0. We call f(x) the logarithm function and

denote it by f(x) = ln x.

a. f ′(x) =d

dx[lnx] =

d

dx

[∫ x

1

1

tdt

]?= (x > 0)

b.d

dx[ln |x|] ?

= (x 6= 0)

c. What can you say about ln(1)? Define the value of e using the definition of the natural logarithm.

d. Using the Fundamental Theorem of Calculus, show that ln(ax) = ln(a) + ln(x). Prove further that(i) ln(en) = n where n is an integer and (ii) ln(er) = r where r us any rational number.

Example A. Find the area under the graph of y =−2

4x− 3for 0 ≤ x ≤ 1/2.

e. Give a sketch of the graph of y = lnx. State clearly the domain and range of lnx. What are thevalues of lim

x→0+lnx and lim

x→∞lnx?

f. The inverse g(x) of f(x) = ln x exists. Why? Sketch the graph of g(x) = exp(x). Infer from (d) thatwe may write exp(x) = ex for all real value x.

g. Explain why we may write: (i) ln(ex) = x for all x, and eln y = y for y > 0.

h. Using the fact thatd

dx(ex) = ex, the chain rule and the fact that eln b = b (b > 0), show that

d

dx(bx) = bx ln b.

i. Using the change of base formula logb x =lnx

ln b, show that

d

dx(logb x) =

1

x ln b.

Example B. Find the equation of the tangent line to the curve y = 4−2ex + ln

(1− x2

1 + x2

)at x = 0.

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Review Exercise. Complete the following formulas:

Logarithmic Properties

ln(ab)?= ln(an)

?=

ln(ab

)?=

ln(e)?= ln 1

?=

ln(ex)?= elnx ?

=

Exponential Rules

an · am ?=

an

am?=

an · bn ?=

an

bn?=

Derivative and Anti-derivative Rules

d

dx(lnx)

?=

d

dx(ex)

?=

d

dx(logb x)

?=

d

dx(bx)

?=

∫1

xdx

?=

∫ex dx

?=

∫bx dx

?=

2

Math 10360 – Example Set 01B

1. By restricting the domain of sinx, cosx, and tanx define their inverse functions (arcsinx, arccosx,and arctanx). Sketch the graph of each of the inverse functions stating their range and domain.

2. Using chain rule, obtain the derivative of arcsin(x), arccos(x), and arctan(x).

Key Formulas:

d

dx(arcsinx)

?=

d

dx(arccosx)

?=

d

dx(arctanx)

?=

∫1√

1− x2dx

?=

∫1

1 + x2dx

?=

3. Using the log function, find the derivative of y = (1 + 2x)arctanx.

4a. Find the derivative of arcsin(2x + y2) with respect to x treating y as a constant.

4b. Find the derivative of arcsin(2x + y2) with respect to y treating x as a constant.

5. A population y(t) (in units of millions) of bacteria grows according to the ratedy

dt=

1

1 + 4t2. Find

the total change in the size of the population over the time duration 0 ≤ t ≤ 1/2.

6. (Review) Without using a calculator, find the value of each of the following expressions:

a. arcsin(√

3/2) b. arcsin(−√

3/2) c. arccos(0.5) d. arctan(−1)

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Accessing Your LaunchPad Course Accompanying Calculus by Rogawski & Adams

W.H. Freeman and Company

A. If you are already on LaunchPad, please log in and “Switch Course Enrollment” from the drop-down under your name. If there are issues please contact tech support at 1800-936-6899.

B. First time LaunchPad user follow instructions below: 1. Go to the LaunchPad URL below to register: http://www.macmillanhighered.com/launchpad/calculuset3enotredame/7242489 2. Select “I have a student access code” or “I want to purchase access” 3. Enter your name, and ND e-mail address. You MUST use your netID@nd.edu e-mail address as your username for LaunchPad. If there are issues please contact tech support at 1800-936-6899.