ONU Calculus I Math 1631

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1 ONU Clculus I Mth Syllus Mrs. Trudy Thompson tthompson@lcchs.edu Text: Clculus 8 th Edition, Anton, Bivens nd Dvis Prerequisites: C or etter in Pre-Clc nd techer s permission This course is not intended to mke college clculus esier. This course IS college clculus. You will e expected to enroll for college credit through Ohio Northern University. A few students my choose to tke the College Bord AP Test in My. Grding: Grdes will e sed on totl-point system. Grdes my e suject to modified curve (suject to techer s discretion). This is pproximtely wht the grdes will look like: Tests (100 points ech) NO mkeup test if sence is unexcused. Tke home quizzes (pprox. 20 points ech) NO lte work ccepted!!! In-clss homework quizzes NO mkeups. These quizzes re UNANNOUNCED!!! Extr credit, for the most prt, will not e given. Some points my e wrded for mth contests nd for unused hll psses. Pssing this course is no gurntee tht you will pss the AP test should you tke it, ut grde of C or etter will qulify you for credit from ONU. Success in this course depends gretly on your effort. You cnnot expect to succeed in college course using high school effort. Also, e wre tht dvnced credit, s well s trnsfer nd plcement policies do vry mong colleges, nd you re encourged to investigte such policies t the college of your choice. Plese keep copy of the syllus to give to your college dvisor. Generl Clss Rules: 1. Come to clss on time. You re required to hve textook, pencil, ipd nd grphing clcultor EVERYDAY (TI-83 or TI-84). Plese see me if this is n issue. 2. This is college clss nd will e treted s such. If you re not prepred, you will e sked to leve. 3. Cheting of ny kind will not e tolerted nd will e delt with severely. This will include, ut my not e limited to, n utomtic zero on ny ssignment, quiz, or test where cheting hs occurred. Prents will e notified. Students my e removed from the clss (see cdemic dishonesty in hndook). Course Content: Limit of function, continuity, the derivtive, extrem, Men Vlue Theorem, curve plotting, ppliction of the derivtive, introduction to integrtion nd its pplictions. We will lso e reviewing pre-clculus concepts s needed (see ch. 1 in ook)

2 2 ONU Clculus Dy-to-dy syllus * This my e modified t times. Section(s) 2.1 Limits n intuitive pproch Tngent line, re, velocity Informl definition p. 104 One-sided vs. two-sided limits Infinite limits nd symptotes Assignment: p. 110 # Limits computtionl techniques Simple limits, properties, polynomil nd rtionl functions Rdicls nd piecewise functions Assignment: p. 121 # 1, 2, 3-33 odd, Limits t infinity; end ehvior of function Assignment: p. 131 # 1-6 ll, 7-35 odd, odd, odd 2.4 More rigorous tretment: ε-δ definitions Assignment: p. 140 # 1-4, 9,12,15, Continuity: t point, on n intervl Note continuity in pplictions, p. 150 Continuity of polynomil nd rtionl functions Continuity of composite functions One-sided continuity Intermedite Vlue Theorem, p. 154 Approximting roots using the Intermedite Vlue Theorem Approximting roots using the grphing clcultor Assignment: p. 152 # 1-23, 27, Limits nd continuity of trigonometric functions Squeeze Theorem Are of sector of circle Two fundmentl limits involving sine nd cosine Assignment: p. 160 # 1-10, odd, 36,39,51, Tngent lines nd rtes of chnge Precise definition of tngent line Slope of tngent line s limit Averge vs. instntneous velocity, geometric representtions Assignment: p. 176 # 1-9, 13, 17, The Derivtive Definition of the derivtive function Differentiility t point nd over n intervl

3 Differentiility nd continuity Nottion for the derivtive Assignment: p. 187 # 1-4, 7-11,15-18,23,25,26,35,36,38,43, Techniques of differentition y = c, y = x n, y = c f(x), sum nd difference formuls Higher order derivtives Assignment: p. 197 # 1-65 odd, 66, 68, 73, The Product nd Quotient Rules (nd continution of section 3.3) Assignment: p. 202 # 1-13, 19-24, Derivtives of Trigonometric functions Use fundmentl limits to get derivtives of sine nd cosine Derivtives of other trigonometric functions will follow from these Assignment: p. 207 # 1-21, 31,32,34 36, 39 A-F 3.6 The Chin Rule The Most Importnt Topic in Clculus Generliztion of derivtive formuls Alterntive pproch, p. 210 Assignment: p. 214 # 1-3, 7, 9-25 odd, odd, Relted Rtes simple ppliction of the Chin Rule. Assignment: p. 221 # 1,2, 5-9, odd, Differentils Δx = chnge in x; Δy = chnge in y Δy = f(x + Δx) f(x) Then tret dy/dx s lim Δy/Δx s Δx 0 Define the differentils: dy = f (x) dx where dx is just nother independent vrile Locl liner pproximtions: f(x o + Δx) f(x o ) + f (x o ) Δx Error propgtion See p. 215 Assignment: p. 229 # 1,2,5,9,19,20, odd, 41, 42,49,52, Implicit differentition definition of implicit function p. 246 Note tht implicit differentition is specil ppliction of the chin rule Derivtives of rtionl powers of x. Derivtives of inverse functions Assignment: p. 241 # 1-35 odd 4.2 Derivtives of logrithmic functions Use definition of derivtive for d/dx (log x) = 1/(x ln ) Then d/dx (lnx) = 1/x, etc. Logrithmic differentition nd irrtionl powers of x Assignment: p. 247 # 1-41 odd 4.3 Derivtives of exponentil nd inverse trig functions Differentiility of inverse functions

4 Derivtives of exponentil functions Derivtives of inverse trig functions Assignment: p. 254 # 7-47 odd, L Hopitl s Rule for indeterminte forms 0/0, /, 0 *, - cn sometimes e comined into single term (cont. next pge) 0 0, 0, 1 cn sometimes e conquered using log. differentition Assignment: p. 263 # 1-33 odd, ll, 49, Anlysis of Functions: Increse/decrese, concvity Definitions of incresing, decresing, constnt functions Theorem relting these to signs of the derivtive Concvity s relted to the sign of 2 nd derivtive Inflection points = chnge in concvity Assignment: p. 275 # 1-10 ll, odd, odd,40, 57, 63, Anlysis of Functions: reltive extrem Definitions of reltive (locl) mxim/minim Reltive extrem t criticl points Criticl points vs. sttionry points First- nd second-derivtive tests Assignment: p. 287 # 1-6 ll, 7-13 odd, ll, odd, ll 5.3 More on curve sketching: rtionl functions, cusps, verticl tngents, uses of technology Procedure for nlyzing grphs p. 290 Geometric interprettions of multiple roots Grphs of rtionl functions Verticl tngents nd cusps Assignment: p. 299 # 1-17 odd, 20,22,23,25,26,33,35,39-53 odd, 57, Asolute mxim nd minim Definition of solute extrem Extreme Vlue Theorem n existence theorem Asolute extrem on n open intervl must occur t criticl point Procedure for finding solute extrem, p. 332 Severl exmples, pp Assignment: p. 307 # 1, 2, 7-21 odd,27-33 odd, ll, 51, Applied mximum nd minimum prolems Two types of such prolems sed on type of intervl My or my not hve solutions Five-step procedure, p. 311 Discuss ll exmples in text Assignment: p. 318 # 1-67 odd 5.6 Newton s Method Summrize ut do not develop Assignment: Pg. 327 # 1, 5, 7, 9, 15, 19, 23, 27, 29

5 5 5.7 Rolle s Theorem nd The Men Vlue Theorem Consequences of the Men Vlue Theorem Constnt Difference Theorem Assignment: p. 334 # 1-13 odd, 14-16, 19-22, 36-38, Rectiliner motion position function s = f(t) Velocity nd speed Instntneous velocity nd ccelertion Anlyzing the position vs. time curve Speeding up nd slowing down Assignment: p. 342 # 1-18 ll, 21-26, Overview of the Are Prolem Antiderivtive Method for finding re Assignment: p. 354 # 1-21 odd 6.2 The indefinite integrl s n ntiderivtive Antiderivtive is not unique Integrtion formuls Properties of the indefinite integrl Integrl curves Differentil eqution viewpoint; initil conditions Direction (slope) fields Assignment: p. 363 # 1-8 ll, 9-29 odd, 41,43, 47, Integrtion y u-sustitution Procedure outlined, p. 392 Do ll exmples in text Assignment: p. 371 # 1-6 ll, 9-41 odd, ll, Sigm Nottion Index of summtion, upper nd lower limits Chnging the index Net signed re Assignment: p. 383 # # 1-3, 7, 13, 23, 39, The Definite Integrl Rectngulr method for res left, right endpoints, midpoint Definite integrl vs. ctul re Riemnn integrl prtition, mesh Properties of the definite integrl pp Conditions for integrility Assignment: p. 393 # 1,14, 17, 19, 24, 26, The Fundmentl Theorem of Clculus Prt 1: f ( x) dx = F() F(), where F'(x) Men Vlue Theorem for integrls, nd verge vlue of function FTC Prt 2: d dx x f ( t) dt = f(x)

6 Assignment: p. 406 # 1, 3-11, 13, 15-19, 21,27,29,41-47 odd, Rectiliner Motion Revisited Uniformly ccelerted motion, initil conditions Free-fll Integrting rte of chnge Displcement vs. distnce trveled Assignment: p. 416 # 1-7, 9, 11, 16,20,21,23, 25,30, 31, 37, Evluting definite integrls y sustitution Chnging nd not chnging limits of integrtion Assignment: p. 423 # 1-39 odd 6.9 Logrithms s integrls 1 Consider dx x 1 e x vs. ln x Definition of e revisited Integrls whose limits re functions Assignment: p. 434 # 1,4,7,9,13,18,20,21,31, Are etween two curves Verticl nd horizontl strips Assignment: p. 448 # 1-5, 7-23 odd, 41, Volumes y slicing Solids of revolution Disks nd wshers strip is perpendiculr to xis of rottion dv = πy 2 dx dv = π(r 2 r 2 ) dx etc. Assignment: p. 456 # 1-4, 5-17 odd, odd, odd 7.3 Volumes y cylindricl shells Strip is prllel to xis of rottion. dv = 2πxy dx, etc. Assignment: p. 464 # 1-4, 5-15 odd, 20, 21, 23, Length of plne curve Polygonl pth 1 ( y') 2 dx Note use of either dx or dy Prmetric curves Assignment: p. 469 # 1,2, 3-13 odd, Are of surfce of revolution Note formul for lterl re of frustum of cone A = 2 2 y 1 ( y') dx Assignment: p. 474 # 1-7 odd, 21, 22

7 7.6 Averge vlue of function Definition using the definite integrl Applictions Assignment: p. 479 # 1,2, 3-19 odd, 23, 25, Work: W = F d For vrile force, W = f ( x) dx Hooke s Lw; lifting lyers of fluid Work-energy theorem: Work = chnge in kinetic energy Assignment: p. 488 # 1-5, 6, 10, 11, 13, 17, 19, 21, Fluid Pressure nd Force Pressure, mss density, weight density Pscl s Principle Fluid force on sumerged surfce: F = See exmples in text Assignment: p. 495 # 1-15 ρ h(x) w(x) dx The following chpter is prt of the mitious syllus. It my or my not e covered this yer. It is not prt of the ONU requirements. 8.1 An overview of integrtion methods Use of formuls Assignment: p. 512 # 1-31 odd 8.2 Integrtion y prts Bsic formul: f(x) g (x) dx = f(x)g(x) - g(x) f (x) dx or: u dv = u v - v du See severl exmples in text, pp Reduction formuls Assignment: p. 520 # 1-45 odd, 48, 49, 50, Trigonometric integrls Products of sines nd cosines Powers of tngent nd secnt Products of tngents nd secnts Note Merctor Projection Assignment: p. 529 # 1-49 odd 8.4 Trigonometric sustitutions The generl method s pplied to rdicl integrnds Completing the squre Assignment: p. 535 # 1-27 odd, odd 8.5 Integrtion y prtil frctions Finding prtil frction decomposition

8 Liner fctor rule Qudrtic fctor rule See exmples in text Assignment: p. 543 # 1-8, 9-31 odd Using CAS nd tles of integrls Perfect mtches vs. mtches tht require dditionl techniques See exmples through exmple 6 Assignment: p. 553 # 1-31 odd, odd 8.7 Numericl integrtion nd Simpson s Rule Riemnn sum pproximtion Trpezoid pproximtion Simpson s Rule using prolic curves Error estimtes Assignment: p. 566 # 1, 5, 7, 11, 19, 21, 25, Improper integrls Infinite discontinuities nd infinite integrls Convergence vs. divergence Use of limits to evlute improper integrls See exmples in text. Assignment: p. 576 # 1,2, 3-33 odd