Martin Flashman's Courses
Math 106 Calculus for Business and Economics
Fall, '04
CHECKLIST FOR REVIEWING FOR THE FINAL
Current Assignment and Schedule
 Due Date Reading for 3rd Edition Problems CD Viewing [# minutes] Optional HW #1   8-26 A.1 Review of Real Numbers A.3 Multiplying and Factoring  1.1 pp 3-6 BLACKBOARD background assessment quiz.   A.1: 1-21 odd  A.3: 1-13 odd; 31-39 odd Introduction [in class]  How to Do Math [in class] HW #2      8-27 1.1 Functions and tables.  A.5  pp A.22-24   Solving equations 1.1: 1-5, 7,9, 12, 15, 16, 22, 23, 25, 33   A.5 1-7 odd, 13-19 odd Functions [19] HW # [NONE] 8-30 1.2 Graphs   Sensible Calculus 0.B.2 Functions 1.2: 1,2,4,5 [Draw a mapping-transformation figure for each function in this assignment] [NO BLACKBOARD REPORT!]  [Read SC 0.B.2  to find out more about the mapping-transformation figure.] Graphing Lines [28] Try The Blackboard Practice Quiz on Functions HW #3 8-31 1.3 Linear functions  Functions and Linear Models 1.2: 13, 17, 31  Draw a mapping figure for each function. 1.3 : 1-9 odd, 11,12,29,41,33 The Two Questions of Calculus [10] On-line Mapping Figure Activities-  (this may be slow downloading) HW #4 9-2 1.4 Linear Models 1.3: 37- 49 odd, 55, 57, 59  1.4: 1-9 odd Average Rates of Change [11] 1.4: 49 HW #5 9-3 1.4 Linear Models. 1.4:  12, 19, 21,22,25 On-line Mapping Figure Activities-  (Again... ;) HW #6 9- 9 2.1 Quadratic functions  A.5 ppA23-A25 2.1: 1-9 odd, 25, 27, 33 Parabolas [22] HW #7 9-10 3.1 Average Rate of Change 3.1: 1-10, 13-16, 21, 39, 40 Rates of Change, Secants and Tangents [19] HW #8 9-13 3.2 Pages 154-158 The Derivative: A Numerical and Graphical  Viewpoint 3.2: 1, 2, 5, 9,12 HW #9 9-14 3.2 (graphical)  3.3 The Derivative: An Algebraic Viewpoint 3.2: 13, 16, 17, 19, 20; 23, 24  3.3: 1, 2, 5 [Use  "4-step process" from class for all] Finding Instantaneous Velocity [20] HW #10 9-16 3.2 derivative estimates  3.3 The Derivative: An Algebraic Viewpoint 3.2: 33, 47, 49, 57, 58, 71, 83 3.3: 6,13 ,15,17, 23, 25 The Derivative [12] HW #11 9-17 3.2 Derivative function graphs, interpretation 3.3 The Derivative: An Algebraic Viewpoint 3.2 :39, 41, 42, 59-64, 97,98, 109, 110 Blackboard Practice Quiz on Slopes of Tangent Lines using 4 steps. Slope of a Tangent Line [12] Equation of a Tangent Line [18] 3.2: 73,74, 86 HW #12 9-20 3.4 The Derivative:  Simple Rules 3.4:1-11 odd; 14-17; 19-21 Short Cut for Finding Derivatives [14] HW #13 9-21 3.4 (Again)  Chapter 3 Summary as relevant. 3.4: 29, 37, 41, 42, 53, 55, 63, 64 3.4: 61, 65, 67, 71, 79 Uses of The Power Rule [20] *The Derivative of  the Square Root [16] *The Derivative of the Reciprocal Function [18] 3.2: 65 HW #14 9-23 3.5 Marginal analysis  Chapter 3 Summary as relevant. 3.5: 1,5,6,9,11,13 HW #15 9-24 Summary of Weeks 3&4. Due Friday 9-24 4.1 Product Rule only! pp 241-244 3.5: 19, 21,28 4.1: 13, 15, 16, 21, 22 The Product Rule [21] Instantaneous Rate [15] HW #16 9-27 4.1: Quotient Rule 4.1: 35, 37, 38, 43; 53, 59, 62 The Quotient Rule [13] HW #17 9-28 4.2 The Chain Rule 4.1: 63, 64, 71, 73 4.2 : 13- 17, 55 Introduction to The Chain Rule [18] Differentiability [3] HW #18 9-30 4.2 The Chain Rule 4.4 Implicit Differentiation (Skip Examples 2 and 3!) 4.2: 25, 26, 33, 35 4.4 :11, 12, 15, 35, 36, 47 Using the Chain Rule [13] Finding the derivative implicitly [12] Intro to Implicit Differentiation [15] More on Instantaneous Rate [19] HW #19 10-1 5.4 Related Rates Especially  Ex. 1-3 4.2: 47, 51, 53, 61, 62, 65 5.4: 9, 11, 13 (watch Ed for #11) The Ladder Problem [14] 4.4: 53 Using Implicit Differentiation [23] HW #20 10-4 The third Summary is due by 4:00 pm. A.2: Exponents 5.4 Related Rates A.2: 15,19, 23, 39, 41, 71 5.4 17,  21, 25 The Baseball Problem [19] Sample Exam #1 Chapter 3 review: 2,3,4,5,9  Chapter 4 review: 1(a-d), 2(a,b), 4(a,b) Chapter 5 review: 7 Morale Moment Math Anxiety [6] #21 10-5 Midterm Exam #1 covers  HW #1-#20. 2.2: Exponential Functions 2.2 : 3,4,9,11, 7, 13, 17 Exponential Functions [10] #22 10-8 2.2 pp94-104(middle) 2.2: 45, 47, 51, 63, 73, 59, 61 Logarithmic Functions [19] (Preparation for Friday class) #23 10-11 exp'(x) = exp(x) Notes. 4.3: 7,8,45,51,53,85 Derivatives of Exp'l Functions [23] Sensible Calculus I.F.2 #24 (note changed due to error-10-12) 10-13! 2.3: pp. 110-113 [Logarithmic functions] 4.3: Example 1,3; pp 265-267. Derivatives for Log's & Exponential Functions 2.3: 1-4, 19 4.3:1,2,15,17,19 Derivative of log functions [14] #25 10-14 2.3:pp112-116 Logarithmic functions Log's Properties (on line). 4.3  Examples 1-5. 2.3: 5, 7, 20, 21, 25,31, 45a, 48 a 4.3: 23, 27, 29, 33, 73 #26 10-15 2.3  Example 3 2.3: 9, 11, 15 #27 10-18 4.4 log differentiation Ex. 3 4.4: 31 , 32 Slide Rules! UNDERSTAND HOW + WHY a slide works, a full explanation #28 10-19(20) The Fourth Summary is due by 4:00 pm. 10-19! 3.6: limits (numerical/graphical)  P209-216 omit EX.3. 3.7: limits and continuity 3.8 limits and continuity (alg) pp225- 228 3.6: 19, 21(a,b), 23(a-e), 25(a-e), 26(a-e) 3.7: 13,14, 15 One Sided Limits [6] Continuity and discontinuity [4] Three  Big Theorems [Begin-3.5min] #29 10-21 3.8 pp225- 230 middle: limits and continuity (alg) 3.7: 20,27, 28 3.8: 39, 41, 46, 53 continuity and differentiablity on-line materials( A and B) #30 10-22 and 25! On-line: cont and diff. 5.1:  Maxima and Minima 5.1: 1-7 odd, 8-10, 12, 13, 15, 21, 23, 24, 25 The connection between Slope and Optimization [28] Critical Points [18] The Fence Problem[25] #31 10-26 5.1:  Maxima and Minima The Intermediate Value Theorem 5.1: 35,  39, 41, 44 Intro to Curve Sketching [9] #32 10-28 5.2. Applications of Maxima and Minima 5.2: 5, 11, 13 Regions where a function is increasing...[20] The First Derivative Test [3] The Box Problem [20] #33 10-29 5.2. Applications of Maxima and Minima 5.3 2nd deriv.pp317-320 5.2:15, 21 5.3: 1-5,7,9,11,14 Higher order derivatives and linear approximations.[first 5 minutes only!] Acceleration & the Derivative [6] #34 11-1 5.5 Elasticity and other economic applications of the derivative 5.5: 1, 3, 14 #35 11-2 5.2 and 5.3 again! 5.2: 25,  27, 29 5.3 : 17-20, 23; 25, 29,31 Using the second derivative [17]   Concavity and Inflection Points[13] The Can Problem[21] #36 11-4 3.6: p212-216 3.8: p229 5.3: p321-324 5.2: 33, 35, 41, 45 5.3: 35- 37,41, 63, 67 3.6: 1-11 odd Graphs of Poly's [10] The 2nd Deriv. test [4] Vertical asymptotes [9]  Horizontal asymptotes  [18] Functions with Asy..and criti' pts [17] #37 11-5 3.6,3.8  Review! 6.1 The Indefinite Integral  p 353-358 On-line tutorial for 6.1. On-Line: Linear Estimation 3.8: 15,17,21,23,33,35,37 5.3: 39, 43, 45 3.6: 25, 27,29 6.1: 1-13odd Graphing ...asymptotes [10] Functions with Asy.. and holes[ 4] Antidifferentiation[14] On-line Problems on Linear Estimation   L1-6; A1-5; App1-3 #38 11-7 Differential equations and integration SC IV.A 6.1 Applications p 359-361 6.1: 15,17, 27, 35, 41-44,51 Using tangent line approximations [25] Antiderivatives of powers of x [18] Cusp points &... [14] Antiderivatives and Motion [20] SC.III.AThe Differential End of material covered in Exam #2 Midterm Exam #2 covers Assignments 21 - 38 Review for Exam #2: (will not be collected): p 136: 2,3,4 p288: 1(a,e,g,i),2(c,d),3a,8a p350: 1(a,d,f),2,4a,5(a-c) p362: 39 p407: 1(a,b) Sample Exam II see Blackboard #39 11-8 3.7, 5.3 Review p321-323 3.7: 15,17, 28-30 5.3: 47, 51, 63, 71 6.1: 53-55, 57 SC IV.E #40 11-12 6.3. The Definite Integral As a Sum. p 373-376 6.3: 1-5 odd, 15, 19, 21 Approximating Areas of Plane regions [10] SC IV.E #41 11-15 6.4 The Definite Integral: Area p384-386 6.4: 1-5 odd, 21, 23 Areas, Riemann Sums, and Definite Integrals [14] The Fundamental theorem[17] #42 11-16 6.5 pp392-395    The Fundamental Theorem 6.5 : 17-20; 67,68 Illustrating the FT[14] Evaluating Definite Integrals [13] #43 11-18 6.2 Substitution pp364-367 6.4  pp 384- 388 6.2: 1-6; 21,23 6.5: 63 Undoing the chain rule.[9]   Integrating polynomials by Substitution [15] #44 11-19/29 6.5 pp 395  - 396 6.2 pp 368-371 Substitution 6.5 example 5 7.2 pp416-420 (area between curves) 6.5: 27-30, 61 6.2: 27-33,59, 60 6.5: 45,47,59,63,64 7.2:1,3,5,11, 15 Area between two curves [9] Integrating composite exponential and rational functions by substitution [13] #45 11-29 7.2 p420-426 (Surplus and social gain) 7.2: 25, 37, 49 Limits of integration-Area [15] #46 11-30 7.3  pp 430-431 8.1 Functions of Several Variables. p467-471 8.3 pp 490 - 492 7.3: 1- 5odd, 29, 35a 8.1: 1-9 odd, 19, 20, 21, 29, 39, 43 8.3:  1- 7 odd, 13, 41, 45 Finding the Average Value of a Function [8] #47 12-2/3 8.2 8.2: 1-9 odd; 11-18; 19-25 odd;41, 49 Solution to 7.2:42 (See the student solutions manual). #48 12-6/7 8.4 p498-501 Critical points 7.5 p 442-445 + 8.4: 1-9 odd, 33, 37 7.5: 1-7 The first type of improper integral[10] Infinite Limits of integration ... [12] The second type of ... [8] #49 12-7 8.3 Second order partials 8.3: 19-25 odd; 29,33,38,51, 53 The 20 minute review. #50 7.5 8.4 pp 504-505 7.5: 11, 13, 17 8.4 :13, 15,17,19 The 20 minute review. Reading INVENTORY Problems INVENTORY CD Viewing INVENTORY Optional INVENTORY 7.6 7.6: 1,3,13 #54 #55 7.4 Future and present value. Common Mistakes [16] The 20 minute review. Optional Last assignment Future and present value. Probability and  DARTS 7.4:1, 9, 21, 27 3.6: 31 3.8: 11-25 odd; 39-42 6.5  396-398 6.4:22 6.5: 9,11,41-45 odd, 42, 65,81 7.3:25 7.6:25, 27 Domain restricted functions ...[11] Three  Big Theorems [11]   5.2: 56 Gravity and vertical motion [19]  Solving vertical motion [12] Distance and Velocity [22] 8.2: 45 2.3 2.3:1,3,4,5,7,11,13,31 Final Examination:

 I.  Differential Calculus:            A. *Definition of the Derivative                 Limits / Notation                 Use to find the derivative                 Interpretation ( slope/ velocity/ Marginal  cost-revenue-profit )            B. The Calculus of Derivatives                * Sums, constants, x n, polynomials                 *Product, Quotient, and  Chain rules                  *logarithmic and exponential functions                               *basic information about these functions and their use in applications                               such as compund interest                Implicit differentiation                 Higher order derivatives            C. Applications of derivatives                  *Tangent lines                  *Velocity, acceleration, marginal rates (related rates)                   *Max/min problems                  *Graphing: * increasing/ decreasing                             concavity / inflection                            *Extrema  (local/ global)                   Asymptotes                 Linear approximation D. Theory                 *Continuity  (definition and implications)                 *Extreme Value Theorem                  *Intermediate Value Theorem       E. Several Variable Functions                   Partial derivatives. (first and second order)                   Max/Min's and critical points. II. Differential Equations and Integral Calculus:            A. Indefinite Integrals (Antiderivatives)                 *Definitions and basic theorem about constants.                 *Simple properties [ sums, constants, polynomials]                 *Substitution         *Simple differential equations with applications              B. The Definite Integral                  Definition/ Estimates/ Simple Properties / Substitution                 *Interpretations  (area / change in position/ Net cost-revenues-profit)                 *THE FUNDAMENTAL THEOREM OF CALCULUS -                                                  evaluation form                 Infinite integrals             C. Applications                 *Recognizing sums as the definite integral          *Areas (between curves).                 Average value of a function.                 Consumer Savings.

 Monday Tuesday Thursday Friday Week 1 8-22 Course Introduction Numbers, Variables, Algebra Review Begin Functions. More Algebra review. More functions review The coordinate plane.  Functions, graphs. Week 2 8-29 Functions, graphs and models. Points and Lines. Especially Lines and models. More Functions and Models: Linear Functions. Slopes, rates and estimation. More linear models. Quadratic functions. Summary of Weeks 1&2 Due Friday 3 pm. 9-6 NO Class.... LABOR DAY More Quadratics. Extremes and the tangent problem. Average rates, and slopes of secant and tangent lines. Instantaneous Rates. The Derivative More Motivation: Marginal cost, rates and slopes. The Derivative and algebra. Week 4 (Graphing, Technology) 9-13 More on finding the derivative. More: Finding the derivative as function. Begin: The Derivative Calculus I Graphical Derivative as function graphs Justification of the power rule. Week 5 Summary of Weeks 3&4. Due Friday 3 pm. 9-20 Justify the sum rule. Discuss Sum rule interpretations. Marginal Applications.Constant Multiple Rule Interpretations. Applications: Marginal vs. Average Cost Start Product rule. Justify product rule. Start Quotient Rule. Week 6 9-27 More on the Quotient rule. The Chain Rule More Chain RuleImplicit functions. Implicit Differentiation More Implicit Functions and related rates. More Implicit Functions and related rates. Week 7 Summary of Week 5&6  Due. Midterm Exam #1 Self-Scheduled Wednesday 10-68:00- 12:30 NHE Room 102 5:00 - 8:30pm Lib 56 10-4 Examples: f  does not have a derivative at a. Begin Exponential functions Interest and value Review for Exam #1 More on exponentials. Derivatives of exponentials, esp'ly exp'(x)=exp(x). Week 8 Makeup For Exam #1 Wed. 10-13.  8 or 9 a.m. Lib 56 See BB Announcements. 10-11 Start Logarithmic functions. Derivatives of Logarithms and Exponentials Finish derivatives of log's, etc. Logarithmic functions. More on models with exp and log equations. Logarithmic differentiation Logarithmic scales.   Slide Rules! Week 9 Summary of Weeks 7 and 8  Due 4pm  Tuesday 10-19 10-18 limits and continuity, Continuity More on continuity and limits. IVT Begin Optimization  and  First Derivative Analysis The fence problem. More Optimization and Graphing. Week 10 10-25 Optimization  and IVT First Derivative Analysis More on first derivative Optimization: revenue example Begin Second Derivatives- acceleration Concavity and Curves Elasticity. (Guest Lecture) Week 11 Summary of Weeks  9 & 10 Due Friday Nov. 5 11-1More on Concavity Horizontal Asymptotes. Vertical Asymptotes Linear Estimation and "Differentials." Begin Differential equations and integration IV.A. Acceleration and integration. Estimating cost changes from marginal costs.  More DE's. Relative error. Differentials Week 12 Self Scheduled   Exam #2 Wednesday 11-10 11-8 Costs, marginal costs, and estimation. Introduction to the definite Integral. Euler's Method. Differential Notation(started) The Definite Integral Riemann Sums  and Estimating Area . Finding area by estimates and using anti-derivatives. week 13 Lab ? Summary of Weeks 11&12 11-15 The definite integral and The FTofC.  IV.E Start Substitution! More Area and applications:  Interpreting definite integrals. Geometric Area. Substitution in definite integrals More Area Intro to functions of  2 or more. Partial derivatives. 1st order. Consumer& Producer Surplus; Social Gain. Week 14 Fall Break- No Classes 11-22 Fall Break Week 15 11-29 Fundamental Theorem I Average Value. Functions of many variables. Tables for 2 variables. Partial derivatives. Visualizing Functions of 2 variables: level curves, graphs of z=f(x,y)and linear estimation. Improper integrals I Week 16 Summary of Weeks 13 & 15 Due Tuesday 4 pm. 12- 6 2nd order partial derivatives  Extremes (Critical points) Improper integrals I Improper Integrals I and II Least Squares example Future and present value. Applications of linear regression to other models using logarithms DE's -Separation of variables: Growth models and exponential functions. Probability and  DARTS? ???? Week 17 Final Examination Review Session  Sunday **pm Lib 56 Self Schedule for Final Examinations