CENTRAL TEXAS COLLEGE SYLLABUS FOR MATH 2414 CALCULUS II Smstr Hours Crdit: 4 I. INTRODUCTION A. Calculus II is a continuation of Calculus I. This cours mphasizs diffrntial quations; applications of intgration; paramtric quations and polar coordinats; tchniqus of intgration; squncs and sris; and impropr intgrals. B. This is a rquird cours for an Associat in Scinc dgr with a major in Mathmatics or Enginring. C. Prrquisit: A grad of C or highr in Math 2313. II. LEARNING OUTCOMES Upon succssful compltion of this cours, Calculus II, th studnt will: A. Us th concpts of slop filds, Eulr s Mthod, and sparation of variabls to solv diffrntial quations. (F2, F3, F4, F9) B. Us th concpts of dfinit intgrals to solv problms involving ara, volum, work and othr physical applications. (F2, F3, F4, F9) B. Us substitution, intgration by parts, trigonomtric substitution, partial fractions, and tabls of anti-drivativs to valuat dfinit and indfinit intgrals. (F2, F3, F4, F9) C. Dfin an impropr intgral. (F2) D. Apply th concpts of limits, convrgnc, and divrgnc to valuat som classs of impropr intgrals. (F2, F3, F4, F9) E. Dtrmin convrgnc or divrgnc of squncs and sris. F. Us Taylor and MacLaurin sris to rprsnt functions. (F2, F3, F4, F9) G. Us Taylor or MacLaurin sris to intgrat functions not intgrabl by convntional mthods. (F2, F3, F4, F9) H. Us th concpt of polar coordinats to find aras, lngths of curvs, and rprsntations of conic sctions. (F2, F3, F4, F9) I. Us lctronic and othr mdia, such as th computr and DVD, to rinforc and supplmnt th larning procss. (F1, F2, F3, F4, F6) III. INSTRUCTIONAL MATERIAL Th Instructional matrials idntifid for this cours ar viwabl through www.ctcd.du/books
IV. COURSE REQUIREMENTS A. Assignmnts ar givn in WbAssign and ar du as schduld by your instructor. Th instructor will monitor studnts progrss in complting th assignmnts. B. Studnts ar xpctd to attnd vry class, to arriv at ach class on tim, and rmain in class for th ntir priod. Instructors may choos to lowr a studnt's grad bcaus of tardinss. V. EXAMINATIONS A. Examinations will b givn at appropriat intrvals. Each xamination will b announcd at last on wk in advanc. Thr will b two unit xams, and a comprhnsiv final xam. B. Studnts who miss an xam should discuss with th instructor th circumstancs surrounding th absnc. Th instructor will dtrmin whthr a mak-up xam is to b givn. Mak-up xaminations ar givn by appointmnt only. VI. SEMESTER GRADE COMPUTATIONS A. Th smstr avrag is drivd from th homwork, quizzs, unit xams, and REQUIRED comprhnsiv final xam in MyMathLab. You must tak th final xam and scor at last 50% to pass th cours. Final grads will follow th grad dsignation blow: Grad Prformanc A 90-100% and 50% or bttr on th Final Exam. B 80-89% and 50% or bttr on th Final Exam. C 70-79% and 50% or bttr on th Final Exam. D 60-69% and 50% or bttr on th Final Exam. F 0-59% and 50% or bttr on th Final Exam.
VII. NOTES AND ADDITIONAL INSTRUCTIONS A. Withdrawal from Cours: It is th studnt's rsponsibility to officially drop a class if circumstancs prvnt attndanc. Any studnt who dsirs to, or must, officially withdraw from a cours aftr th first schduld class mting must fil an Application for Withdrawal or an Application for Rfund. Th withdrawal form must b signd by th studnt. An Application for withdrawal will b accptd at any tim prior to Friday of th 12th wk of classs during th 16-wk fall and spring smstrs. Th dadlin for sssions of othr lngths is as follows. Sssion Dadlin for Withdrawal 12-wk sssion Friday of th 9 th wk 10-wk sssion Friday of th 7 th wk 8-wk sssion Friday of th 6 th wk 6-wk sssion Friday of th 4 th wk 5-wk sssion Friday of th 3 rd wk Th quivalnt dat (75% of th smstr) will b usd for sssions of othr lngths. Th spcific last day to withdraw is publishd ach smstr in th Schdul Bulltin. Studnts who officially withdraw will b awardd th grad of "W" providd th studnt's attndanc and acadmic prformanc ar satisfactory at th tim of official withdrawal. Studnts must fil a withdrawal application with th collg bfor thy may b considrd for withdrawal. A studnt may not withdraw from a class for which th instructor has prviously issud th studnt a grad of "F". B. An Incomplt Grad: Th Collg catalog stats, "An incomplt grad may b givn in thos cass whr th studnt has compltd th majority of th cours work but, bcaus of prsonal illnss, dath in th immdiat family, or military ordrs, th studnt is unabl to complt th rquirmnts for a cours..." Prior approval from th instructor is rquird bfor th grad of "I" is rcordd. A studnt who mrly fails to show for th final xamination will rciv a zro for th final and an "F" for th cours.
C. Cllular Phons and Bprs: Cllular phons and bprs will b turnd off whil th studnt is in th classroom or laboratory. D. Amricans With Disabilitis Act (ADA): Disability Support Srvics provid srvics to studnts who hav appropriat documntation of a disability. Studnts rquiring accommodations for class ar rsponsibl for contacting th Offic of Disability Support Srvics (DSS) locatd on th cntral campus. This srvic is availabl to all studnts, rgardlss of location. Explor th wbsit at www.ctcd.du/disability-support for furthr information. Rasonabl accommodations will b givn in accordanc with th fdral and stat laws through th DSS offic. E. Civility: Individuals ar xpctd to b cognizant of what a constructiv ducational xprinc is and rspctful of thos participating in a larning nvironmnt. Failur to do so can rsult in disciplinary action up to and including xpulsion. F. Advancd Math Lab: Th Math Dpartmnt oprats an Advancd Mathmatics Lab in Building 152, Room 145. All courss offrd by th Math Dpartmnt ar supportd in th lab with appropriat tutorial softwar. Calculators ar availabl for studnt us in th lab. Studnts ar ncouragd to tak advantag of ths opportunitis. S postd hours for th Advancd Math Lab. G. Offic Hours: Full-tim instructors post offic hours outsid th door of th Mathmatics Dpartmnt (Building 152, Room 223). Part-tim instructors may b availabl by appointmnt. If you hav difficulty with th cours work, plas consult your instructor. VIII. COURSE OUTLINE A. Lsson On: Chaptr 6 Diffrntial Equations will 1. Lsson Objctivs: Upon succssful compltion of this lsson, th studnt b abl to: a. Us initial conditions to find particular solutions of diffrntial quations. b. Us slop filds to approximat solutions of diffrntial quations. c. Us Eulr s Mthod to approximat solutions of diffrntial quations. d. Us sparation of variabls to solv a simpl diffrntial quation.. Us xponntial functions to modl growth and dcay in applications.
f. R c o g n i z a n d s o l v d i f f r n t i a l q u a t i o n s t h a t can b solvd by sparation of variabls. g. Us diffrntial quations to modl and solv applid problms. h. Solv and analyz logistic diffrntial quations.
i. Solv a first-ordr linar diffrntial quation, and us linar diffrntial quations to solv applid problms. 2. Larning Activitis: a. Rad Chaptr 6, Sctions 6.1 through 6.4. b. Work problms assignd by th instructor. c. Complt assignd lab activitis. 3. Lsson Outlin: a. Sction 6.1 Slop Filds and Eulr s Mthod b. Sction 6.2 Diffrntial Equations: Growth and Dcay c. Sction 6.3 Sparation of Variabls and th Logistic Equation d. Sction 6.4 First-ordr Linar Diffrntial Equations B. Lsson Two: Chaptr 7 Applications of Intgration 1. Lsson Objctivs: Upon succssful compltion of this lsson, th studnt will b abl to: a. Find th ara of a rgion btwn two curvs using intgration. b. Find th ara of a rgion btwn two intrscting curvs using intgration. c. Dscrib intgration as an accumulation procss. d. Find th volum of a solid of rvolution using th disk mthod.. Find th volum of a solid of rvolution using th washr mthod. f. Find th volum of a solid with known cross sctions. g. Find th volum of a solid of rvolution using th shll mthod. h. Find th arc lngth of a smooth curv. i. Find th ara of a surfac of rvolution. j. Find th work don by a constant forc. k. Find th work don by a variabl forc. l. Undrstand th dimnsion of mass. m. Find th cntr of mass in a on-dimnsional systm. n. Find th cntr of mass in a two-dimnsional systm. o. Find th cntr of mass of a planar lamina. p. Us th Fundamntal Thorm of Pappus to find th volum of a solid of rvolution. q. Find fluid prssur and fluid forc. 2. Larning Activitis: a. b. c. 3. Lsson Outlin: Rad Chaptr 7, Sctions 7.1 through 7.7. Work problms assignd by th instructor. Complt assignd lab activitis.
a. Sction 7.1 Ara of a Rgion Btwn Two Curvs b. Sction 7.2 Volum: Th Disk Mthod c. Sction 7.3 Volum: Th Shll Mthod d. Sction 7.4 Arc Lngth and Surfacs of Rvolution. Sction 7.5 Work f. Sction 7.6 Momnts, Cntrs of Mass, Cntroids g. Sction 7.7 Fluid Prssur and Fluid Forc C. Lsson Thr: Chaptr 8 Intgration Tchniqus, L Hopital s Rul, and Impropr Intgrals a. Lsson Objctivs: Upon succssful compltion of this lsson, th studnt will b abl to: a. Rviw procdurs for fitting an intgrand to on of th basic intgration ruls. b. Find an antidrivativ using intgration by parts. c. Solv trigonomtric intgrals involving powrs of sin and cosin. d. Solv trigonomtric intgrals involving powrs of scant and tangnt.. Solv trigonomtric intgrals involving sin-cosin products with diffrnt angls. f. Us trigonomtric substitution to solv an intgral. g. Us intgrals to modl and solv ral-lif applications. h. Undrstand th concpt of partial fraction dcomposition. i. Us partial fraction dcomposition with linar factors to intgrat rational functions. j. Us partial fraction dcomposition with quadratic factors to intgrat rational functions. k. Evaluat an indfinit intgral using a tabl of intgrals. l. Evaluat an indfinit intgral using rduction formulas. m. Evaluat an indfinit intgral involving rational functions of sin and cosin. n. Rcogniz limits that produc indtrminat forms. o. Apply L Hopital s Rul to valuat a limit. p. Evaluat an impropr intgral that has an infinit limit of intgration. q. Evaluat an impropr intgral that has an infinit discontinuity. 2. Larning Activitis: a. Rad Chaptr 8, Sctions 8.1 through 8.8. b. Work problms assignd by th instructor. c. Complt assignd lab activitis. 3. Lsson Outlin:
a. Sction 8.1 Basic Intgration Ruls b. Sction 8.2 Intgration by Parts c. Sction 8.3 Trigonomtric Intgrals d. Sction 8.4 Trigonomtric Substitution. Sction 8.5 Partial Fractions f. Sction 8.6 Intgration by Tabls and Othr Intgration Tchniqus g. Sction 8.7 Indtrminat Forms and L Hopital s Rul h. Sction 8.8 Impropr Intgrals D. Lsson Four: Chaptr 9 Infinit Sris 1. Lsson Objctivs: Upon succssful compltion of this lsson, th studnt will b abl to: a. List th trms of a squnc. b. Dtrmin whthr a squnc convrgs or divrgs. c. Writ a formula for th nth trm of a squnc. d. Us proprtis of monotonic squncs and boundd squncs.. Undrstand th dfinition of a convrgnt infinit sris. f. Us proprtis of infinit gomtric sris. g. Us th nth-trm Tst for Divrgnc of an infinit sris. h. Us th Intgral Tst to dtrmin whthr a sris convrgs or divrgs. i. Us proprtis of p-sris and harmonic sris. j. Us th Dirct Comparison Tst to dtrmin whthr a sris convrgs or divrgs. k. Us th Limit Comparison Tst to dtrmin whthr a sris convrgs or divrgs. l. Us th Altrnating Sris Tst to dtrmin whthr an infinit sris convrgs. m. Us th Altrnating Sris Rmaindr to approximat th sum of an altrnating sris. n. Classify a convrgnt sris as absolutly or conditionally convrgnt. o. Rarrang an infinit sris to obtain a sum. p. Us th Ratio Tst to dtrmin whthr a sris convrgs or divrgs. q. Us th Root Tst to dtrmin whthr a sris convrgs or divrgs. r. Rviw th tsts for convrgnc and divrgnc of an infinit sris. s. Find Taylor approximations of lmntary functions and compar thm with lmntary functions. t. Find Taylor and Maclaurin polynomial approximations of lmntary functions. u. Us th rmaindr of a Taylor polynomial.
v. Undrstand th dfinition of a powr sris. w. Find th radius and intrval of convrgnc of a powr sris. x. Dtrmin th ndpoint of convrgnc of a powr sris. y. Diffrntiat and intgrat a powr sris. z. Find a gomtric powr sris that rprsnts a function. aa. Construct a powr sris using sris approximations. bb. Find a Taylor or Maclaurin sris for a function. cc. Find a binomial sris. dd. Us a basic list of Taylor sris to find othr Taylor sris. 2. Larning Activitis: a. Rad Chaptr 9, Sctions 9.1 through 9.10. b. Work problms assignd by th instructor. c. Complt assignd lab activitis. 3. Lsson Outlin: a. Sction 9.1 Squncs b. Sction 9.2 Sris and Convrgnc b. Sction 9.3 Th Intgral Tst and p-sris c. Sction 9.4 Comparisons of Sris d. Sction 9.5 Altrnating Sris. Sction 9.6 Th Ratio and Root Tsts f. Sction 9.7 Taylor Polynomials and Approximations g. Sction 9.8 Powr Sris h. Sction 9.9 Rprsntation of Functions by Powr Sris i. Sction 9.10 Taylor and Maclaurin Sris E. Lsson Fiv: Chaptr 10 Conics, Paramtric Equations, and Polar Coordinats 1. Lsson Objctivs: Upon succssful compltion of this lsson, th studnt will b abl to: a. Undrstand th dfinition of a conic sction. b. Analyz and writ quations of parabolas using proprtis of parabolas. c. Analyz and writ quations of llipss using proprtis of llipss. d. Analyz and writ quations of hyprbolas using proprtis of hyprbolas.. Sktch th graph of a curv givn by a st of paramtric quations. f. Eliminat th paramtr in a st of paramtric quations. g. Find a st of paramtric quations to rprsnt a curv. h. Undrstand two classic calculus problms, th tautochron and brachistochron problms. i. Find th slop of a tangnt lin to a curv givn by a st of
paramtric quations. j. Find th arc lngth of a curv givn by a st of paramtric quations. k. Find th ara of a surfac of rvolution (paramtric form). l. Undrstand th polar coordinat systm. m. Rwrit rctangular coordinats and quations in polar form and vic vrsa. n. Sktch th graph of an quation givn in polar form. o. Find th slop of a tangnt lin to a polar graph. p. Idntify svral typs of spcial polar graphs. q. Find th ara of a rgion boundd by a polar graph. r. Find th points of intrsction of two polar graphs. s. Find th arc lngth of a polar graph. t. Find th ara of a surfac of rvolution (polar form). u. Analyz and writ polar quations of conics. v. Undrstand and us Kplr s Laws of plantary motion. 2. Larning Activitis: a. Rad Chaptr 10, Sctions 10.1 through 10.6. b. Work problms assignd by th instructor. c. Complt assignd lab activitis. 3. Lsson Outlin: a. Sction 10.1 Conics and Calculus b. Sction 10.2 Plan Curvs and Paramtric Equations c. Sction 10.3 Paramtric Equations and Calculus d. Sction 10.4 Polar Coordinats and Polar Graphs. Sction 10.5 Ara and Arc Lngth in Polar Coordinats f. Sction 10.6 Polar Equations of Conics and Kplr s Law