Mathematics Calculus B for the Life & Social Sciences Spring Semester 2018

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1 Mathematics Calculus B for the Life & Social Sciences Spring Semester 208 Text: Single Variable Calculus (3r E) - Early Transcenentals by Jon Rogawski & Colin Aams Publisher: W. H. Freeman & Co. Section Instructor Class Scheule Office @n.eu Arthur Lim MWF 8:20-9:0 HAYES 27 HAYES 250 arthurlim 2 Priyanka Rajan MWF 9:25-0:5 DBRT 3 HAYES 8 prajan 3 Stephan Stolz MWF 0:30 - :20 HAYES 7 HURLEY 66A stolz 4 Behrouz Taji MWF 2:00-2:50 DBRT 26 HURLEY 278 btaji 5 Anibal Meina MWF :30-2:20 Joran 05 HAYES 26 ameinam 6 Joao Santos MWF 2:50 - :40 HAGGAR 7 HAYES 29 jsantos3 Section Teaching Assistant Class Scheule Office @n.eu Li Ling Ko R 9:30-0:20 HAYES 23 HAYES B26 lko 2 Li Ling Ko R :00 - :50 HAYES 7 HAYES B26 lko 2 Justin Miller R 2:30 - :20 DBRT 24 HAYES B26 jmille74 22 Justin Miller R 3:30-4:20 DBRT 24 HAYES B26 jmille74 3 Timothy Warner R :00 - :50 PCTR 2 HAYES B24 twarner 32 Timothy Warner R 9:30-0:20 HAYES 229 HAYES B24 twarner 4 Aaron Tyrrell R 2:30 - :20 HAYES 229 HAYES B26 atyrrell 42 Aaron Tyrrell R 3:30-4:20 HAYES 29 HAYES B26 atyrrell 5 Kostya Timchenko R :00 - :50 RILEY 200 HAYES 235 ktimchen 52 Kostya Timchenko R 2:00-2:50 HAYES 23 HAYES 235 ktimchen 6 Timothy Warner R 2:00-2:50 HAYES 29 HAYES B24 twarner 62 Justin Miller R 9:30-0:20 HAYES 29 HAYES B26 jmille74 Course Website: m0360 Most information for this course is poste on its website. These inclue instructors an TAs office hours an contact information, aily homework information, exam ates an venues, practice exams, an etc. Calculator Policy: Calculators are NOT allowe on any of the exams. You may use your calculators for homework an assignments, but we strongly recommen that you o not rely on any of its graphing functions. Course Grae & Breakown: Date Day Time Room Points Miterm Feb. 20 Tuesay 8:00 9:5 AM On course website 00 Miterm 2 Mar. 27 Tuesay 8:00 9:5 AM On course website 00 Miterm 3 Apr. 26 Thursay 8:00 9:5 AM On course website 00 Final May 0 Thursay :45 3:45 PM On course website 50 Differentiation/Integration Gateway Tutorial week 02 (20%), week 03 (30%), & week 04 (50%) 50 Online Hwk & Assignments Submit online or collecte in class as scheule on website 75 Tutorial participation, attenance, activities & quizzes 25 Total points: 600 Cutoffs for major graes (A, B, C, D, F) for each exam will be assigne an announce in class so you have some inication of your level of performance. Your final grae will be base on your total score out of 600. Misse exams: Note that there will be three Miterm Exams an a Final Exam. A stuent who misses an examination will receive zero points for that exam unless he or she has written permission from the Dean of the First Year of Stuies. Please be aware that travel plans, sleeping in, efective alarm clocks, etc. are not consiere

2 to be a vali excuse by the Dean of the First year of Stuies! If you have a vali excuse (illness, excuse athletic absence, etc.) for missing an exam, please see me ASAP (preferably before the exam) to scheule a makeup exam. Exam conflicts are governe by Acaemic coe. Accoring to Section 4.2, stuents with 3 or more finals in one ay, or 4 or more finals in a 24 hour perio, may negotiate to change the time of one of these finals. If you have time conflict in your final exam scheule an nee to o Math 0360 final at another time, you must inform your instructor by April 2. Honor Coe: Examinations, homework, assignment an quizzes are conucte uner the honor coe. While collaboration in small groups in oing homework is permitte (an strongly encourage) in this course, copying is not. In particular, copying from the Stuent Solutions Manual is a violation of the Honor Coe. Exams are close book an are to be one completely by yourself with no help from others. Homework & Assignments: Online Homework an assignment problems are assigne aily. Their scheule is liste on the course website. Absolutely no late homework or assignment will be accepte. You are encourage to work on these problems in groups, but all online homework an assignments must be turne in iniviually. Remember that you will not learn anything by simply copying another stuent s work or the Stuent Solutions Manual. The main purpose of homework an assignments is to help you learn the material an assess yourself. Experience shows that stuents who take their homework seriously o very well in the course because they have a better unerstaning of the material. For etaile homework an assignment instructions, please see attache information. Class Attenance: A stuent who accumulates more than 3 unexcuse absences may be given an F grae. Classroom Policies: Please o your best to show up on time an quietly enter the room if you are late. Please remember to respect your peers who are here to learn. Inee, class isruptions will not be tolerate an offening parties will be aske to leave. During lectures you are encourage to actively participate by answering an asking questions. Stuy Tips are poste on the on the course website ( m0360). Please print out a copy an review it. The key point is to start early an be consistent. Getting Help: You can get help for mastering the course material from the following three avenues below. More information can be obtaine from the 0360 course website; click on TUTORING & HELP. Instructor & TA s Office Hours: The scheule will be poste on Math 0360 website or make an appointment to meet your instructor or TA. It is important that you see them soon when you have ifficulty with the course. The earlier you meet with your instructor an TA, the more we can o to help an avise. Learning Resources Center (LRC) Help: You may also obtain valuable assistance from the LRC in the First Year of Stuies: Math 0360 Tutoring Program, Math 0360 Collaborative Learning Program, Math 0360 Workshops/Review Sessions. If you wish to participate in the Tutoring Program or Collaborative Learning Program, you must sign up with Ms Nahi Erfan, Director of LRC. Regular attenance is require for these programs. Sign-up an regular attenance are not require for the Math 0360 Workshops/Review Sessions. Mathematics Library Tutoring: This is a free tutoring service provie by the Mathematics Library. It is one-on-one an nees sign up. You can fin tutoring scheule an the online sign-up sheet at: Please note that instructors an tutors are NOT there to o your homework. In fact, tutors are instructe to guie you to the answer an not o your homework. Please o not ask the tutors to grae your homework, an be specific about what you want to iscuss. 2

3 MATH 0360 Course Work Policy There are both online homework an paper-pencil assignments for this course. Written Assignments are ue in class accoring to the scheule poste on the Math 0360 website. The questions an problems to be turne in are poste on the course website. You are expecte to submit your written assignment in the following manner: Your work has to be clearly an logically written, showing the metho of solution, not just a final answer. Please staple your work together. It is your responsibility that your work stays staple together securely. Any work falling short of the above expectations may not be grae. Absolutely no late assignments will be accepte. Exceptions are hanle case by case. If you nee to atten a school relate event, you may turn in your assignment early or arrange to have your peer turn it in on the ay it is ue. Online Homework is assigne aily an is ue at the en of the next class ay. The online systems we are using are LaunchPa an Maple T.A. Please follow registration instructions for LaunchPa in the attache flyer carefully. Be sure to register your login name on LaunchPa as your ND aress (netid@n.eu). Maple T.A. is accesse through the ND Sakai system. The ND aress will be use to make all course relate announcements. You must check your regularly aily. All online homework shoul be one using paper an pencil, an be treate the same manner as written assignments. We encourage you to keep a recor of your work for material submitte online; these are helpful when you review for an exam. Usually, you are expecte to complete about 5 to 8 problems of your online homework assigne at the en of each class ay. If you have ifficulty solving the homework questions please see your TA/professor or visit the liste the math help resources above. Absolutely no late homework will be accepte. Register an access the online homework on the LaunchPa web aress: Access Maple T.A. at: All homework an assignment will be weighte the same. The three lowest of homework/assignment scores will be roppe. You shoul bookmark these pages. Online Homework Submission Policies. All submission ealines for online homework on LaunchPa are fixe. You are highly encourage to SUBMIT your homework well ahea of ealines. We DO NOT accept excuses like: My computer/webservers shut own just before I coul submit my work on time. Save your answers as you enter them online. This ensures that no work is lost BEFORE the submission ealine. Enough buffer time is given to ensure timely submission of your work. All online homework are ue are ue at 2:00am (+2 hrs buffer) at the en of the next class ay unless otherwise state. In aition, after the ealine of a homework, you have 48 hours to complete a late homework to obtain up to 80% of the full score. 3

4 Math 0360 (Calculus B) Syllabus Text: Calculus (Early Transcenentals) 2n Eition J. Rogawski 3.8 Derivatives of Inverse Functions Notes Further Transcenental Functions Exponential Growth an Decay Malthusian Growth Moel Only Area Between Two Curves Setting Up Integrals: Volumes, Density, Average Value Volumes of Revolution The Metho of Cylinrical Shells Work an Energy Integration by Parts Trigonometric Integrals Trigonometric Substitution The Metho of Partial Fractions Improper Integrals Numerical Integration Functions of Two or More Variables Setting Up Double Integrals: Volumes, Areas, Density Setting Up Double Integrals: Volumes, Areas, Density Taylor Polynomials Solving Differential Equations Moels Involving y = k(y-b) Graphical an Numerical Methos The Logistic Equation (incluing moel with harvesting an Birch s Curve) First-orer Linear Equations Partial Derivatives Chain Rule (Appln to Elasticity/Sensitivity) Lagrange Multipliers Geometric Sequences an Geometric Series (Appln to Meicine an Ecology) Sequences Summing an Infinite Series The Ratio Test (no root test) Power Series (Application of Ratio Test) Taylor Series

5 Basic Algebra Rules Exponential Rules: a m a n = a m+n (ab) m = a m b m a m a n = am n ; a 0 a 0 = a 0 a /m = m a ( a b ) m = a m b m ; b 0 (a m ) n = a mn Distribution Law: a(b + c) = ab + ac a + b c = a c + b c a b c = a c b c Quaratic Factoring: (a + b) 2 = a 2 + 2ab + b 2 (a b) 2 = a 2 2ab + b 2 a 2 b 2 = (a b)(a + b) Properties of Logarithm: log a (MN) = log a M + log a N ( ) M log a = log N a M log a N log a (M) t = t log a M log a a = log a = 0 log a a x = x a log a x = x Change of Base: ln(mn) = ln M + ln N log a M = log b M log b a ln ( ) M = ln M ln N ln(m) t = t ln M N ln e = ln = 0 ln e x = x e ln x = x

6 Summary of Differentiation Rules The following is a list of ifferentiation formulae an statements that you have to know. Prouct Rule: (f(x)g(x)) = f(x)g (x) + f (x)g(x) Quotient Rule: Chain Rule: ( ) f(x) = g(x)f (x) g (x)f(x) g(x) (g(x)) 2 (f(g(x)) = f (g(x))g (x) Derivative of Trigonometric Function: (sin x) = cos x x (cos x) = sin x x x (tan x) = sec2 x (csc x) = csc x cot x x (secx) = secx tan x x x (cot x) = csc2 x x (arcsin x) = x 2 (arctan x) = x + x 2 Derivative of Exponential an Logarithm Functions: x (ex ) = e x x (ax ) = a x ln(a) x (ln x) = x

7 Summary of Integration Rules The following is a list of integral formulae an statements that you have to know. x n x = xn+ n + + C; n (ax + b) n (ax + b)n+ x = + C; n a(n + ) x x = x = ln x + C x ax + b x = ln ax + b + C a e x x = e x + C e ax+b x = a eax+b + C sin x x = cos x + C cos x x = sin x + C sec 2 x x = tan x + C secx tan x x = secx + C csc x cot x x = csc x + C csc 2 x x = cot x + C secx x = ln secx + tan x + C csc x x = ln csc x + cot x + C x = arctan x + C + x2 x = arcsin x + C x 2 Funamental Theorem of Calculus Let F an antierivative of f i.e. F (x) = f(x). Then we have: () b a f(x) x = F (b) F (a) = [F (x)] b a (2) Total change in F when x changes from a to b = F (b) F (a) = Integration by Parts: b b () u v = uv v u (2) u v = [uv] b a v u a a b a F (x) x 2

8 . Consier the area function f(x) = enote it by f(x) = ln x. a. f (x) = [ x [ln x] = x x b. Math 0360 Example Set 0A ] t t x [ln x ]? = (x 0) x t for x > 0. We call f(x) the logarithm function an t? = (x > 0) c. What can you say about ln()? Define the value of e using the efinition of the natural logarithm.. Using the Funamental Theorem of Calculus, show that ln(ax) = ln(a) + ln(x). Prove further that (i) ln(e n ) = n where n is an integer an (ii) ln(e r ) = r where r us any rational number. Example A. Fin the area uner the graph of y = 2 4x 3 for 0 x /2. e. Give a sketch of the graph of y = ln x. State clearly the omain an range of ln x. What are the values of lim ln x an lim ln x? x 0 + x f. The inverse g(x) of f(x) = ln x exists. Why? Sketch the graph of g(x) = exp(x). Infer from () that we may write exp(x) = e x for all real value x. g. Explain why we may write: (i) ln(e x ) = x for all x, an e ln y = y for y > 0. h. Using the fact that x (bx ) = b x ln b. x (ex ) = e x, the chain rule an the fact that e ln b = b (b > 0), show that i. Using the change of base formula log b x = ln x, show that ln b x (log b x) = x ln b. ( ) x 2 Example B. Fin the equation of the tangent line to the curve y = 4 2e x + ln at x = 0. + x 2

9 Review Exercise. Complete the following formulas: Logarithmic Properties ln(ab)? = ln(a n )? = ( a )? ln = b ln(e)? = ln? = ln(e x )? = e ln x? = Exponential Rules a n a m? = a n b n? = a n a m? = a n b n? = Derivative an Anti-erivative Rules x (ln x)? = x (log b x)? = x (ex )? = x (bx )? = x x? = e x x? = b x x? = 2

10 Math 0360 Example Set 0B. By restricting the omain of sin x, cos x, an tan x efine their inverse functions (arcsin x, arccos x, an arctan x). Sketch the graph of each of the inverse functions stating their range an omain. 2. Using chain rule, obtain the erivative of arcsin(x), arccos(x), an arctan(x). Key Formulas: x (arcsin x)? = x (arccos x)? = x (arctan x)? = x 2 x? = + x 2 x? = 3. Using the log function, fin the erivative of y = ( + 2x) arctan x. 4a. Fin the erivative of arcsin(2x + y 2 ) with respect to x treating y as a constant. 4b. Fin the erivative of arcsin(2x + y 2 ) with respect to y treating x as a constant. 5. A population y(t) (in units of millions) of bacteria grows accoring to the rate y t = + 4t. Fin 2 the total change in the size of the population over the time uration 0 t /2. 6. (Review) Without using a calculator, fin the value of each of the following expressions: a. arcsin( 3/2) b. arcsin( 3/2) c. arccos(0.5). arctan( ) 3

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B. First time LaunchPa user follow instructions below:. Go to the LaunchPa URL below to register: http://www.macmillanhighere.com/launchpa/calculuset3enotreame/7242489 2.

12 Accessing Your LaunchPa Course Accompanying Calculus by Rogawski & Aams W.H. Freeman an Company A. If you are alreay on LaunchPa, please log in an Switch Course Enrollment from the rop-own uner your name. If there are issues please contact tech support at B. First time LaunchPa user follow instructions below:. Go to the LaunchPa URL below to register: 2. Select I have a stuent access coe or I want to purchase access 3. Enter your name, an ND aress. You MUST use your netid@n.eu aress as your username for LaunchPa. If there are issues please contact tech support at

MATH , 06 Differential Equations Section 03: MWF 1:00pm-1:50pm McLaury 306 Section 06: MWF 3:00pm-3:50pm EEP 208

MATH , 06 Differential Equations Section 03: MWF 1:00pm-1:50pm McLaury 306 Section 06: MWF 3:00pm-3:50pm EEP 208 MATH 321-03, 06 Differential Equations Section 03: MWF 1:00pm-1:50pm McLaury 306 Section 06: MWF 3:00pm-3:50pm EEP 208 Instructor: Brent Deschamp Email: brent.eschamp@ssmt.eu Office: McLaury 316B Phone: