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Course: CALC 1,2,3, Spring 2008
School: Lehigh
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31, January 2005 Announcements Assigned reading for the week: 7.1, 7.2 and 7.3 My office hours on Wednesday February 2nd, 23pm, are cancelled. Today 7.1: Integration by Parts 1 Formula for Integration by Parts f (x)g (x) = dx f (x)g(x) - f (x)g(x) dx or, setting u = f (x) and v = g(x) we often write this as u dv = uv - v du (which is easier to remember). For Definite Integrals: b a f (x)g (x) dx = f...

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31, January 2005 Announcements Assigned reading for the week: 7.1, 7.2 and 7.3 My office hours on Wednesday February 2nd, 23pm, are cancelled. Today 7.1: Integration by Parts 1 Formula for Integration by Parts f (x)g (x) = dx f (x)g(x) - f (x)g(x) dx or, setting u = f (x) and v = g(x) we often write this as u dv = uv - v du (which is easier to remember). For Definite Integrals: b a f (x)g (x) dx = f (x)g(x) b a - b a f (x)g(x) dx
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Lehigh - CALC - 1,2,3
Lehigh - CALC - 1,2,3
11.9 Representations of Functions as Power Series Differention and Integration of Power Series Theorem 2 If the power series cn (x - a)n has radius of convergence R &gt; 0, then the function f defined by f (x) = c0 + c1 (x - a) + c2 (x - a)2 + = n=0
Lehigh - CALC - 1,2,3
11.6 Absolute convergence and the ratio and root tests 1.Theorem3(p.732) If a series an is absolutely convergent, then it is convergent. Remark: By using this result, we can generalize the use of Integral Test and Comparison Test by determining the c
Lehigh - CALC - 1,2,3
March 7, 2005Announcements This Week: More differential equations and Review Homework #8 (Week 9 Problems) (Covers 9.1, 9.3 and 9.4; see web for assignment) Due Tuesday, March 8 - will not be collected. Office hours this week at MSC Chen: Monday
Lehigh - CALC - 1,2,3
February 25, 2005Announcements Modification to Week 8 homework: Problems 1, 5, 7, 11, 12 and 15 in 8.3 are NOT part of the assigned homework. Tuesday March 1st, last quiz of the quarter. The midterm will be return to you in Section on Tuesday, Ma
Lehigh - CALC - 1,2,3
February 18, 2005Announcements Midterm # 2 is next week! Thursday, February 24th (Covers 6.4 - 7.8) Start doing practice Midterms. Modification to Week 8 homework: Problems 1, 5, 7, 11, 12 and 15 in 8.3 are NOT part of the assigned homework.Tod
Lehigh - CALC - 1,2,3
February 16, 2005Announcements Midterm # 2 is next week! Thursday, February 24th (Covers 6.4 - 7.8) Start doing practice Midterms. Modification to Week 8 homework: Problems 1, 5, 7, 11, 12 and 15 in 8.3 are NOT part of the assigned homework.Tod
Lehigh - CALC - 1,2,3
February 9, 2005Today 7.5 Strategy for Integration1Table of indefinite integrals n+1 n dx = x x +Cn+1(n = -1)1 dx = ln |x| + C x ex dx = ex + C sin x dx = - cos x + C cos x dx = sin x + C sec2 x dx = tan x + C 1 cos x dx = - +C
Lehigh - ASIA/SSP - 198
.new media &amp; societyCopyright 2002 SAGE Publications London, Thousand Oaks, CA and New Delhi Vol4(2):141162 [14614448(200206)4:2;141162;023410]THEMED SECTION: THE INTERNET IN CHINATowards a digital economy with Chinese characteristics?..XI
Lehigh - CALC - 1,2,3
7.7 Approximate IntegrationIf we wish to evaluate a definite integral involving a function whose antiderivative we cannot find, then we must resort to an approximation technique. We describe three such techniques in this section.A. Midpoint RuleB
Lehigh - CALC - 1,2,3
Lehigh - ASIA/SSP - 198
Rural Poverty and Education in ChinaEmily Hannum and Jennifer AdamsDraft: 7/25/2006Abstract As China's economy has marketized, having an education has become increasingly important for guaranteeing economic security, and those who lack access to
Lehigh - ASIA/SSP - 198
Lehigh - CALC - 1,2,3
Lehigh - ASIA/SSP - 198
EDUCATION IN THE REFORM ERA Emily Hannum*, Jere Behrman*, Meiyan Wang*, and Jihong Liu* Draft: 12/30/2005 * Population Studies Center, University of Pennsylvania. * Insti
Lehigh - ASIA/SSP - 198
Social Issues in Contemporary ChinaSocial Welfare Service Provision: Health CareHealth Care System: Pre-Reform After Mao Tse-tung and the Chinese Communist Party took control of China in 1949, they created a health care system that was typical of
Tulane - FINC - 725
FINC 727: Corporate transactions and business valuationProfessor Robert HansenAssignment 5. HLTsBLAZER TELECOM's perpetual earnings before interest and taxes is \$400, the corporate tax rate is 40%. To help finance the project BLAZER will use a
Lehigh - CALC - 1,2,3
8.1 Arc LengthDefinition:If the function given by y f (x) represents a smooth curve on the interval [a, b], then the arc length of f between a and b is given bybLa1f ' ( x) dxa2b1dy dx2dxSimilarly, for a smooth curve given by
Lehigh - ASIA/SSP - 198
Social Issues in Contemporary ChinaIntroductionMain Topics of ClassNew Social IssuesInequality and poverty Rapid demographic changes Provision of public health services Provision of education services Becoming an &quot;information societ
Lehigh - CALC - 1,2,3
Lehigh - CALC - 1,2,3
Lehigh - CALC - 1,2,3
6.1 Areas Between CurvesSuppose we want to find the area of the region S as shown in Figure 1. yf S gbxFigure 1anAlimn i 1 b af ( xi )g ( xi )xf ( x)g ( x) dxyxff ( xi ) g ( xi )g axiFigure 2bxWhen the grap
Lehigh - ASIA/SSP - 198
Social Issues in Contemporary ChinaDemographic Changes and ChallengesChronological Order of Major Political Campaigns1949: founding of New China 1947-52: Land Reform 1952: Collectivization in rural and urban 1951: Three-Against (San Fan): against
Tulane - FINC - 725
PROFESSIONAL ASSET MANAGEMENTBasic CategoriesPrivate Management: Clients each have a separate account {popular with institutions}Investor 1\$\$ Account 1 Account 2Asset managerInvestor 2\$Basic CategoriesInvestment Companies: Sell shares
Lehigh - ASIA/SSP - 198
Social Issues in Contemporary ChinaEducationImportance of EducationNow a person's access to education matters a lot for her/his lifetime economic security: better job, higher pay Returns to education in urban China have been rising since the ons
Lehigh - CALC - 1,2,3
Lehigh - CALC - 1,2,3
Lehigh - CALC - 1,2,3
March 2, 2005Announcements: The last homework will not be collected. K. Ross has changed her office hours for the rest of the quarter to Monday 4:30pm-5:30pm MSC, and Wednesday 4:30pm-5:30pm MSC.Today 9.3 Separable equations and mixing problems
Lehigh - CALC - 1,2,3
February 7, 2005Announcements Reading for the week:7.4, 7.5 and 7.7. Homework #5 (Week 5 Problems) (Covers 7.1, 7.2 and 7.3; see web for assignment) Collected Tomorrow: Tuesday, February 8. Today 7.4 Integration of Rational Functions by Partial F
Lehigh - CALC - 1,2,3
February 2, 2005Announcements T. Toro's office hours have been cancelled today. Today 7.2 Trigonometric Integrals1Trigonometric identities sin2 x + cos2 x = 1 sin2 x = 1 (1 - cos 2x) 22 x = 1 (1 + cos 2x) cos2 sin x cos x =1 sin 2x
Lehigh - CALC - 1,2,3
January 28, 2005 Announcements Exams will be returned in Section on Tuesday Detailed solutions are posted on the web under highlights. I will report on the overall class performance (statistics) and how to interpret your grade in Lecture on Monday
Lehigh - CALC - 1,2,3
January 24, 2005Reading from the book: Review sections 4.10, 5.1-5.5, 6.1-6.3. Sections 6.4 and 6.5. Announcements No quiz on Tuesday, January 25. One sheet (8 1 11) of handwritten notes (one sided) 2 allowed during the midterm. Sections cover
Lehigh - CALC - 1,2,3
January 14, 2005 Today 5.5 The substitution rule.The substitution rule If u = g(x) is a differentiable function whose range is an interval I and f is continuous on I, then f (g(x)g (x) dx = f (u) du.The substitution rule for definite integrals I
Lehigh - CALC - 1,2,3
January 19th, 2005 Announcements Assigned reading for the week: 6.1, 6.2 and 6.3 First Midterm: Thursday, January 27, 2005 Sample midterms can be found at http:/weber.math.washington.edu/~m125Today 6.1: Areas between 2 curves. 6.2: Volumes (sl
Lehigh - CALC - 1,2,3
January 21, 2005 Announcements First Midterm: Thursday, January 27, 2005 Sample midterms can be found at http:/weber.math.washington.edu/~m125Today 6.2: Volumes (slicing method) 6.3: Volumes (shell method)1Definition (Slicing method): Let S
Lehigh - CALC - 1,2,3
Integrals of Rational FunctionsGuidelines for Partial Fraction Decomposition off (x) g(x)1. If the degree of f ( x ) is not lower than the degree of g ( x ) , use long division to obtain the proper form. 2. Express g ( x ) as a product of linear
Lehigh - CALC - 1,2,3
CALCULUS 2: STRATEGY FOR EVALUATING INTEGRALS1. A few general tactics In trying to evaluate an integral with the collection of methods we have seen in Chapters 5 and 7, some general ideas are worth keeping in mind: Find antiderivatives first: It is
Lehigh - CALC - 1,2,3
Derivatives IDx c0 cDx u ( x ) cu ( x )Dx cu ( x ), where c is a real constant.Dx u(x) v(x) Dx u(x) v(x)Dx u(x ) v (x )Dx u(x) u(x)Dx v(x)Dx v(x)u (x ) v (x ) u( x ) v ( x ) v ( x ) u ( x )v (x )u (x ) u(x )v (x ) v (x )2v(x)Dx u
Lehigh - CALC - 1,2,3
&quot;TAYLOR NOTES&quot;Math 126: Taylor Polynomials and Infinite Series (An Epilogue to Single Variable Calculus) K. P. Bube University of Washington, Department of Mathematics, Seattle, WA 98195 March 2005IntroductionIn this &quot;Epilogue to Single Variable
Lehigh - CALC - 1,2,3
Basic Course Information: Math 125A&amp; BInstructor: Tatiana Toro, office: Padelford C-332, email: toro@math.washington.edu, phone: 543-1173. Office Hours: Monday 1-2, Wednesday 2-3 at the Math Study Center. Visit the class website (and explore each of
Lehigh - CALC - 1,2,3
January 5, 2005 Announcements You need to have the &quot;Math 125 course pak&quot;. (\$8.50 from the UW Copy Center in Communications (CMU) B042.) Always bring this to your Tu &amp; Th sections. All the problems from the book Calculus, Early Transcendentals by Ja
Lehigh - CALC - 1,2,3
January 7, 2005 Today 5.2 The Definite Integral: definition and properties.1When solving the area problem we encountered, Riemann sums, which are expressions of the formn i=1f (x)x = if (x )x + f (x )x + + f (x )x. n 1 2 We also studied
Lehigh - CALC - 1,2,3
January 10, 2005 Announcements Assigned reading for this week: 5.3, 5.4 and 5.5 Homework #1 (Week 1 Problems) will be collected tomorrow, Tuesday, January 11 (Covers 4.10, 5.1 and 5.2; see web for assignment)Today:5.3 The Fundamental Theorem of
Lehigh - CALC - 1,2,3
January 12, 2005 Today 5.4: Indefinite Integrals 5.4: Net Change Theorem and applications1Definition. Let f be a continuous function on an interval. The indefinite integral of f is the most general antiderivative of f and it is denoted by f (
Lehigh - CALC - 1,2,3
Positive-Term SeriesTheorems on Convergence or Divergence of a Positive-Term Series 1. Ifa n is a positive-term series and if there exists a number M such thatSn a1 a2 anM for every n, then the series converges and has a sum Sdiverges. 2. Inte
Lehigh - CALC - 1,2,3
SequencesTheorems on Sequences: I. Modeling Theorem Let {an } be a sequence, let f (n) an , and suppose that f ( x) exists for every real number x 1 . (i) lim f ( x) L , then lim f (n) L .x n(ii) lim f ( x)x(or) , then lim f (n)n(or).
Lehigh - CALC - 1,2,3
Formulae for Calculus 151 p. 1Differentiation Definition: f (a + h) - f (a) f (a) = lim h0 h General formulas: Product: (uv) = u v + uv Quotient: (u/v) = [u v - uv ]/v 2 Chain rule: [f (u)] = f (u) u Constant multiple: (cu) = cu Special functions:
Lehigh - CALC - 1,2,3
February 23, 2005 Announcements:1. Office hours today: A. Chen - 2:30-4:30 MSC K. Ross - 4:30-6:30 MSC T. Toro - 1:30-3:30 MSC 2. Bring your scientific calculator to the midterm tomorrow, you will need it. Recall graphing calculators are NOT all
Lehigh - CALC - 1,2,3
Lehigh - CALC - 1,2,3
January 26, 2005Announcements Math 125 A&amp;B Joint Marathon Review Session! Today (Wednesday) 5:30 7:30 PM in GUG 317 . (Thanks to Bill, Kiana and Allen.) Sections covered by the midterm: 4.10, 5.1-5.5, 6.1-6.3. One sheet (8 1 11) of handwritten
Lehigh - ASIA/SSP - 198
Childhood in Urban China: Only HopeOne-Child Policy and ModernizationFong argues that the one-child policy and the cultural model of modernization has created extreme motivation and pressure on China's youth. How do the one-child policy and ec
Lehigh - CALC - 1,2,3
Lehigh - CALC - 1,2,3
Trigonometric SubstitutionsFor Expression in the IntegrandUse Trigonometric SubstitutionTo Obtaina 1 sin 2 a cosa2x2xa sin ,22a2x2xa tan ,2 02ora 1 tan 2a secx2a2xa sec ,2 3 2a sec 21a tansinx a
Tulane - FINC - 725
Risk and Risk AversionBKM Chapter 6 part 1What is risk? How do we measure risk? The trade-off between risk and return Risk-return assumptions of portfolio theory Utility functions and indifference curves Risk Q) What is risk? A) Two definitions
Lehigh - ECO - 001
Chapter 10Answers to End of Chapter Problems and Applications 2. Quantity of Workers 0 1 2 3 4 5 6 7 Total Output Marginal Product of Labor 0 400 900 1500 1900 2200 2400 2300 - 400 500 600 400 300 100 100 Average Product of Labor - 400 450 500 475
Lehigh - ECO - 001
Chapter 1 Answers to End-of-Chapter Problems and Applications 2. Yes, even Bill Gates faces scarcity because his wants exceed his resources. Gates has established a foundation with billions of dollars to spend on worthy causes like eradicating malari
Lehigh - ASIA/SSP - 198
Review of Income and Wealth Series 53, Number 1, March 2007URBAN POVERTY IN CHINA AND ITS CONTRIBUTING FACTORS, 19862000 by Xin Meng* and Robert GregoryAustralian National Universityand Guanhua WanUnited Nations UniversityWorld Institute for De
Lehigh - CALC - 1,2,3
Indefinite Integrals III1 1 ux1 1 ux22u x dxArcsin u xCu x dxArc tan u xC1 ux ux2u x dx 1Arcsec u xCsinh u xu x dxcosh u xCcosh u xu x dxsinh u xCsech2 u xu x dxtanh u xCcsch2 u xu x dxcoth u x
Lehigh - CALC - 1,2,3
Integrals of Rational FunctionsGuidelines for Partial Fraction Decomposition off (x) g(x)1. If the degree of f ( x ) is not lower than the degree of g ( x ) , use long division to obtain the proper form. 2. Express g ( x ) as a product of linear
Lehigh - CALC - 1,2,3
Derivatives IIIDx Arcsin u( x ) 1 Dx Arccos u( x ) 1Dx Arctan u( x )1 ux 1 ux2 2u ( x)u ( x)1 1 ux1 1 u x2u ( x)D x Arccot u( x )2u ( x)Dx Arcsec u( x ) ux Dx Arccsc u( x ) ux1 ux 1 ux2 2u ( x) 1 u ( x) 1D x sinh u( x )
Lehigh - CALC - 1,2,3
Indefinite Integrals Ik dxkxC k u( x ) dxku( x ) dxwhere k is a real constant .[u( x ) v ( x )]dxnu( x )dxv ( x )dx1[u( x)]u ( x)dx[u( x)]n n 1C, if nC C1sin u( x ) u ( x )dx cos u( x ) u ( x )dxcos u( x ) sin u( x )