MATH 161 Calculus I 5 units (see credit hour statement below) Fall 2014

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1 Azusa Pacific University Cllege f Liberal Arts and Sciences Department f Mathematics and Physics MATH 161 Calculus I 5 units (see credit hur statement belw) Fall 2014 MTWRF 11:40am 12:35pm Segerstrm 154 Instructr: Dr. Sharn McCathern Phne: (626) x smccathern@apu.edu (***this is my preferred methd f cntact***) Office Fax: (626) Emergency: (626) (department ffice) Office: Segerstrm 106 Office Hurs: Mnday 1:10-2:40 pm Thursday 9:30-11:00 am, 12:50-2:15 pm (and by appintment Tuesday 12:50-2:15 r ther times as needed) Curse Website: (Nte: this is NOT SAKAI) E-bk and Online HW: (see belw fr mre infrmatin) Curse Descriptin (frm APU catalg): This curse is an intrductin t the basic techniques f calculus f ne variable, including limits and cntinuity, differentiatin and integratin, with graphing and applicatins. Textbk: Single Variable Calculus (r the first 5 chapters f Calculus) with WebAssign access, by James Stewart (***see sectin belw fr mre infrmatin n WebAssign***) Hw this Curse Will be Taught: Sme class time will be spent in a traditinal lecture frmat. Hwever, we will ften wrk n prblems tgether, as a class r in small grups. Yu will be expected t read the bk befre class, and ften t watch a shrt vide lecture, s that yu ll be ready t wrk n prblems when yu cme t class. There will be at-hme assignments and in-class quizzes checking t see if yu ve dne this preparatry wrk. Yu are respnsible fr yur wn learning -- I can t help yu if yu dn t d the wrk, and I als can t help yu if yu dn t let me knw when yu have questins r are struggling.

2 APU Department f Mathematics and Physics Fall 2013 Credit Hurs and Out-f-class Wrk: Fllwing the APU Credit Hur plicy, t meet the identified student learning utcmes f this curse, the expectatins are that this 5 hur curse, delivered ver a 14 week term, will apprximate 5 hurs per week classrm f direct faculty instructin. In additin, ut-f-class student wrk will apprximate a minimum f 10 hurs each week. WebAssign Infrmatin Yu will cmplete mst hmewrk assignments using WebAssign, an nline hmewrk site that is crdinated with ur bk. This is als where yu ll access the e-bk, if yu chse nt t buy a hard cpy f the bk. Using WebAssign fr hmewrk lets yu have multiple attempts at slving each prblem, with immediate feedback fr crrect r incrrect answers. Mst students like it, althugh it can be a bit difficult t get started and there are ccasinal technical glitches. I ll help as much as I can as we get ging. Hw t enrll in WebAssign fr this curse: 1) G t and click Enter class key (next t the Lg In buttn) 2) Enter the class key azusa and click Submit 3) If the class lks right, click Yes this is my class 4) If yu ve had a WebAssign accunt befre, select I already have a WebAssign accunt and enter yur infrmatin. Otherwise, select I need t create a WebAssign accunt and cmplete all the fields. Nte that yu get 2 weeks f free trial access, and then yu ll need t pay fr access. If yu purchased a cde at the bkstre r elsewhere, enter it when yu re prmpted. Otherwise when the system asks fr payment and yu re ready t pay, yu can buy access thrugh WebAssign with a credit card r PayPal accunt. Hw t lg in t use WebAssign: 1) G t and enter yur WebAssign username. 2) The Institutin shuld be azusa 3) Enter yur passwrd, and click Lg In. 4) Click n ur curse. Yu shuld see an assignment list and ther items. Yu can view the e-bk by clicking n the link under Abut this curse. 2

3 APU Department f Mathematics and Physics Fall 2013 The Calculus Sequence Calculus is the study f cntinuusly changing quantities. The instantaneus rate f change f a quantity is measured by the derivative. The net change f a quantity is btained by adding tgether infinitely many instantaneus changes using a definite integral. These tw key cncepts are related by the Fundamental Therem f Calculus. Calculus I In Calculus I, yu becme familiar with limits as a language fr discussing the infinite and the infinitesimal. Limits are then used t define the derivative and integral, which yu learn t cmpute and apply in a variety f ways. Calculus I fcuses n pwer, plynmial, ratinal, and trignmetric functins. Calculus II In Calculus II, yu expand yur reach t include the remaining elementary functins: expnential, lgarithmic, inverse trignmetric, and hyperblic. If yu take Differential Equatins, yu will cme t further understand why all f these classes f functins are s fundamental, bth fr the thery and the applicatin f mathematics. Calculus II will equip yu with further integratin techniques. Yu will apply the integral t cmpute arc length and surface area. Yu will learn t wrk with new kinds f graphs, described using parametric equatins and plar crdinates. Finally, yu will study the cnvergence f sequences and series, with an eye tward apprximating functins by infinite pwer series. Multivariable Calculus The first tw semesters f calculus deal with functins f: R R. Here the dmain and cdmain are bth the real number line, which is ne-dimensinal. Since, amng ther reasns, ur wrld cntains (at least) three dimensins, it is desirable t apply calculus t functins whse dmain and/r cdmain is a plane (R 2 ), r a space (R 3 ), etc. This is the task f the third semester f calculus, called Multivariable Calculus r Vectr Calculus. This curse climaxes with a number f beautiful generalizatins f the Fundamental Therem f Calculus in higher dimensins, each f which relates a functin s behavir n the bundary f a regin t the values f its derivative inside the regin. and beynd... In Differential Equatins, yu will apply calculus t dynamical systems f interrelated quantities in bilgy, chemistry, physics, ecnmics, etc. In Real Analysis, yu will learn abut the subtle paradxes which drve mathematicians t refine their understanding f the real numbers and f calculus, and in Cmplex Analysis, yu will behld the beauty that springs frth when calculus meets the cmplex numbers! 3

4 APU Department f Mathematics and Physics Fall 2013 Student Learning Outcmes The fllwing table lists the student learning utcmes alng with the manners in which they will be assessed. Student Learning Outcme: Students will be able t read and cmprehend a mathematical text, and t learn mathematical cncepts n their wn participate actively in small grup mathematical discussins and prblemslving translate between verbal, numerical, visual and algebraic representatins f functins, and apply them t mdel physical and scial phenmena cmpute limits and cnstruct prfs f their existence cmpute derivatives (using difference qutients r differentiatin rules) and apply them t slve prblems cmpute integrals (using Riemann sums r integratin rules) and apply them t slve prblems explain the relatinship between the derivative and the integral captured by the Fundamental Therem f Calculus explre and analyze the use f mathematics in discussins f faith and justice Assessment: Students will demnstrate their learning via Reading/vide questins Hmewrk Grup prjects Hmewrk Prjects Examinatins Hmewrk Examinatins Hmewrk Prjects Examinatins Hmewrk Gini Prject Examinatins Hmewrk Examinatins Gini Prject/Faith Integratin paper COURSE POLICIES: Cllabratin Plicy Yu may nt cllabrate n reading/vide questins, quizzes, r exams. Yu are encuraged t wrk tgether n yur hmewrk and t share ideas, but the written wrk that yu turn in and the nline hmewrk yu submit shuld reflect yur wn understanding f the material. A gd rule f thumb is that yu shuld be able t reprduce fr me any wrk yu submit, and yu shuldn t be lking at anyne else s wrk when yu re writing/entering yur slutins. (Thus, yu have t understand it and be capable f reding the prblem n yur wn.) This als applies t any slutins r ther resurces yu find nline r in a bk use them, but dn t just cpy. Any cpying, cheating, r plagiarism will be treated as a vilatin f the academic integrity plicy, will receive a failing grade, and will be reprted. 4

5 APU Department f Mathematics and Physics Fall 2013 Calculatr Use Graphing r scientific calculatrs will be helpful n many hmewrk prblems and ccasinally in class. (Yur cmputer prbably has a scientific calculatr in its sftware package; it s fine t use that.) Yu shuld bring a scientific (nt graphing) calculatr t class fr sme tests; the calculatr plicy fr each test will be annunced in advance. Classrm Cnduct Please treat me and yur fellw students with respect and civility. In particular, d nt distract yurself r thers with cnversatins r technlgy. I will ask yu t stp if yu are disturbing me r thers. Unless we re ding wrk that requires a cmputer (WebAssign r Mathematica), it is usually a bad idea t have a laptp pen during this class. Hmewrk -- We will have bth nline and n-paper hmewrk. Online hmewrk will be assigned fr each sectin, but usually will nly be due nce a week. (Late hmewrk will nt be accepted.) Yu will d several nline hmewrk assignments each week. Yu must check due dates in WebAssign and make sure yu d all the assigned sectins each week. DO NOT WAIT t start the hmewrk as sn as we ve talked abut a sectin f the bk in class, get started n that sectin s hmewrk. THERE IS TOO MUCH WORK t d it all at the end f the week. Paper hmewrk will ccasinally be assigned, and I ll let yu knw when it s due and cllect it in class. (This is in additin t the vide questins yu ll answer at hme regularly see belw.) Reading and Vide Questins/Quizzes Yu are expected t read the apprpriate sectin f the textbk befre each class, and in sme cases watch a shrt vide lecture. Vides may include questins fr yu t answer and bring t class. On ther ccasins class will start with a shrt questin r quiz designed t make sure yu ve read the bk and/r watched the vide. Gateway Quizzes There will be tw gateway quizzes yu *must* pass in rder t pass this class, regardless f yur scres n ther cmpnents f the curse grade. Yu must scre at least 80% n a trignmetry quiz (withut calculatrs!), and yu must get a perfect scre n a derivative cmputatin quiz. These are designed t make sure yu have a firm fundatin in the cmputatinal skills that will allw yu t succeed in yur wrk with mre cmplicated cncepts in this class and fllwing classes (Math 162, 263, 270). Yu will have multiple chances t pass these quizzes. Exams There will be 4 tests during the semester and ne final exam. The tentative test dates are Sep. 23, Oct. 14, Nv. 4, and Nv. 20. The final exam date and time will be annunced as sn as the Registrar s ffice assigns it keep an eye n yur Student Center nline. Calculatrs will be allwed fr sme parts f sme exams, but yu shuld be prepared t d much f yur wrk withut a calculatr. Faith Integratin A shrt prject and paper will be assigned integrating mathematics with Christian faith. Prjects We will d 2 grup prjects during the semester. These will be started in class, but yur grup will have t cmplete the prject utside f class time and turn it in. Yu will wrk in grups, and all grup members are expected t cntribute. These prjects will invlve bth cnceptual wrk and cmputer wrk fr cmputatins. 5

6 APU Department f Mathematics and Physics Fall 2013 Attendance and Participatin Class attendance and participatin will figure int reslving brderline grades. Make up wrk plicy Except fr university excused absences, n make-up tests r quizzes will be given. Yu must be in class. (I will hwever drp sme scres see the sectin n grading.) If yu miss a prject day, yu will nt have a grup t wrk with, but yu may cmplete the prject n yur wn and submit it n the due date I give yu. I will nt be available t help yu much. It is t yur advantage t be in class n prject days. Grading Online Hmewrk 20% Reading/Vide questins 6% Highest Test Scre 15% 2 nd Highest Test Scre 12% 3 rd Highest Test Scre 9% Lwest Test Scre 6% Grup Prjects 3% each 6% Gini Prject and Paper (faith integratin) 6% Final exam 20% Ntes: 1) Drpping scres: The lwest 4 hmewrk scres and 4 reading/vide quizzes will be drpped. 2) Gateway quizzes: Regardless f the cmputatin abve, n student may pass the class (with D- r better) unless he r she passes bth gateway quizzes as described abve. 3) Minimum exam scres fr C- and D- : Regardless f the cmputatin abve, n student may pass the class (with D- r better) unless he r she has an average f 50% r higher n the 5 tests (including the final), withut weighting. N student may receive a C- r better unless he r she has an average f 60% r higher n the 5 tests, withut weighting. Grading Criteria GRADE LEVEL DESCRIPTION A B C D F Outstanding Abve Average Average Belw Average Nt Acceptable Abve and beynd the requirements f the assignment; utstanding effrt, significant achievement, and persnal imprvement are clearly evident. Sme measure f remarkable skill, creativity, r energy is als evident. Fulfills all aspects f the assignment and ges a bit beynd minimum cmpetence t demnstrate extra effrt, extra achievement, r extra imprvement. Fulfills all aspects f the assignment with bvius cmpetence. Assignments are cmpleted exactly as assigned. Belw average either because sme aspect f the assignment has nt been fulfilled r there are indicatins f a failure t fllw directins, failure t fllw specific recmmendatins, failure t demnstrate adequate understanding f the material, r failure t demnstrate persnal effrt and imprvement. Nt acceptable, either because the assignment was nt cmpleted as directed r because the level f perfrmance was belw an acceptable level fr cllege wrk. 6

7 APU Department f Mathematics and Physics Fall 2013 Math Center The Math Center (in Segerstrm 170) is staffed by experienced math students n Mnday-Thursday frm 2:00-8:00 pm, available fr free, drp-in tutring and hmewrk help. This is als a gd place fr yu t wrk tgether n hmewrk prblems, and it has several cmputers with Mathematica installed. Yu are highly encuraged t frm study grups and wrk tgether. Available Supplemental Resurces Students in MATH 161 are encuraged t use available resurces in additin t the classrm time. These resurces include: 1. individual appintments r ffice hur drp-ins with the instructr; 2. drp in tutring at the Math Center (pen M-Th 2-8 pm), which is staffed by experienced math students 3. many excellent vides and materials nline just Ggle the tpic yu re interested in (and check t see that the materials are frm a university r ther reputable surce) Infrmatin Literacy: Infrmatin literacy is defined as a set f abilities requiring individuals t recgnize when infrmatin is needed and have the ability t lcate, evaluate, and use effectively the needed infrmatin (American Library Assciatin, 1989). In this curse, teaching and learning prcesses will emply the fllwing infrmatin literacy standards, as endrsed by the American Assciatin fr Higher Educatin (1999), the Assciatin f Cllege and Research Libraries (2000), and the Cuncil f Independent Clleges (2004). The students in this curse will: determine the nature and extent f the infrmatin needed. access needed infrmatin effectively and efficiently. individually r as a member f a grup, use infrmatin effectively t accmplish a specific purpse. This curse des nt require students t cmplete curse assignments using resurces available frm the University Libraries. Academic Integrity Plicy: The missin f Azusa Pacific University includes cultivating in each student nt nly the academic skills that are required fr a university degree, but als the characteristics f academic integrity that are integral t a sund Christian educatin. It is therefre part f the missin f the university t nurture in each student a sense f mral respnsibility cnsistent with the biblical teachings f hnesty and accuntability. Furthermre, a breach f academic integrity is viewed nt merely as a private matter between the student and an instructr but rather as an act which is fundamentally incnsistent with the purpse and missin f the entire university. A cmplete cpy f the Academic Integrity Plicy is available in the Office f Student Life, the Office f the Vice Prvst fr Undergraduate Prgrams, and nline. Expectatins regarding academic integrity in this class are cnsistent with thse utlined in the academic integrity plicy. In particular, yu may wrk tgether n hmewrk, but nt n vide questins, quizzes r exams. Althugh yu are wrking tgether, each student must submit hmewrk individually. Cnsequences fr vilatins f academic integrity in this class are cnsistent with thse utlined in the academic integrity plicy. Cpyright Respnsibilities: Materials used in cnnectin with this curse may be subject t cpyright prtectin. Students and faculty are bth authrs and users f cpyrighted materials. As a student yu must knw the rights f bth authrs and users with respect t cpyrighted wrks t ensure cmpliance. It is equally imprtant t be knwledgeable abut legally permitted uses f cpyrighted materials. Infrmatin abut cpyright cmpliance, fair use and websites fr dwnlading infrmatin legally can be fund at University Plicy: All university plicies affecting student wrk, appeals, and grievances, as utlined in the Undergraduate Catalg will apply. 7

8 APU Department f Mathematics and Physics Fall 2013 Azusa Pacific University Missin Statement: Azusa Pacific University is an evangelical Christian cmmunity f disciples and schlars wh seek t advance the wrk f Gd in the wrld thrugh academic excellence in liberal arts and prfessinal prgrams f higher educatin that encurage students t develp a Christian perspective f truth and life. Department Missin Statement: The Department f Mathematics and Physics at Azusa Pacific University: 1) ffers undergraduate degree prgrams in mathematics and physics, a single-subject waiver fr a teaching credential in mathematics, and a pre-degree engineering prgram; 2) prvides general educatin mathematics and science curses cnsistent with the utcmes f a liberal arts educatin; and 3) prepares students fr graduate study r success in their chsen careers. Disability statement: Any student in this curse with a disability preventing a full demnstratin f the student s abilities shuld ntify the instructr and meet with an advisr in the Learning Enrichment Center at the beginning f the semester. Bibligraphy: Calculus, 7 th ed. by James Stewart, Cengage, 2011 (ur textbk) The Hitchhiker s Guide t Calculus by Michael Spivak, MAA, 1995 (a lighter intrductin, with sme gd ways f thinking) A Tur f the Calculus by David Berlinski, Vintage, 1997 (a fun treatment f sme f the basic tpics, with gd expsitin and lts f ideas that make yu g hmmmmmm.) Tpics t be Cvered: (Curse tpics, evaluatin and assignments may be changed at the instructr s discretin) Chapter: 1 Functins and Limits 2 Derivatives 3 Applicatins f Derivatives 4 Integrals 5 Applicatins f Integrals Sectins Assignments: Cvered: , Online and paper hw Reading/vide questins , 2.8 Hmewrk Reading/vide questins Lines f Sight prject , 3.7, 3.9 Hmewrk Reading/vide questins Optimizatin prject Hmewrk Reading/vide questins Gini prject (faith integratin) , 5.5 Hmewrk Reading/vide questins Material Appears n Exams: Test 1, Final Exam Test 2, Final Exam Test 3, Final Exam Test 4, Final Exam Final Exam 8

9 APU Department f Mathematics and Physics Fall 2013 Curse Calendar (*subject t change! All dates are tentative!*) Mnday Tuesday Wednesday Thursday Friday Sep Sep Sep 22 Sep Oct Oct 13 Oct Oct Nv 3 Nv Nv Nv Sep Sep Sep 23 TEST 1 Sep Oct Oct 14 TEST 2 Oct /3.5 Oct 28 Prject 2 Nv 4 TEST 3 Nv Nv Nv *nte that test 4 may be mved here!!* Dec Sep 3 Classes begin Sep Sep /2.1 Sep Oct Oct Oct Oct Oct Nv Nv 12 Gini Prject Nv 19 Nv 26 STUDY DAY N classes meet Sep Sep 11 Wrk n Prblems Sep 18 Wrk n Prblems Sep Oct 2 Wrk n Prblems Oct 9 Wrk n Prblems Oct Oct 23 Wrk n Prblems Oct 30 Wrk n Prblems Nv Nv 13 Wrk n Prblems Nv 20 TEST 4 Nv 27 THANKSGIVING N classes meet Sep Sep *last day t add/drp Sep Sep /Intr t Mathematica Oct 3 Prject 1 Oct Oct Oct Oct Nv Nv *last day t withdraw Nv Nv 28 THANKSGIVING BREAK Dec Dec Dec 4 Dec 8-12 FINAL EXAM WEEK (check yur Student Center nline t find date/time fr ur final exam) Dec 5 9

10 APU Department f Mathematics and Physics Fall