Martin Flashman's Courses
Math 106 Calculus for Business and Economics
Spring, '05
Current Assignment and Schedule
Self Schedule for Final Examinations
CHECKLIST FOR REVIEWING FOR THE FINAL
 Due Date Reading for 3rd Edition Problems CD Viewing [# minutes] Optional 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] 1.1 Functions and tables.  A.5  pp A.22-24   Solving equations A.5 1-7 odd, 13-19 odd Functions [19] 1.2 Graphs   Sensible Calculus 0.B.2 Functions Do the reading first! 1.1: 1-5, 7,9, 12, 15, 16, 22, 23, 25, 33 1.2: 1,2,4,5 [Draw a mapping-transformation figure for each function in this problem] [Read SC 0.B.2  to find out more about the mapping-transformation figure.] Functions [19] 1.3 Linear functions  Summary: 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 Graphing Lines [28] Try The Blackboard Practice Quiz on Functions On-line Mapping Figure Activities-  (this may be slow downloading) 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 1.4 Linear Models. 2.1 Quadratic functions  A.5 ppA23-A25 1.4:  12, 19, 21,22,25 On-line Mapping Figure Activities-  (Again... ;) 2.1Quadratic functions 2.1: 1-9 odd, 25, 27, 33 Parabolas [22] 3.1 Average Rate of Change 3.1: 1-10, 13-16, 21, 39, 40 The Two Questions of Calculus [10] 3.2 Pages 154-158 The Derivative: A Numerical and Graphical  Viewpoint 3.2: 1, 2, 5, 9,12 Rates of Change, Secants and Tangents [19] 3.2 derivative estimates  3.3 The Derivative: An Algebraic Viewpoint Graphing, Technology problems from lab 3.2: 13, 16, 17, 19, 20; 23, 24  Use  "4-step process" from class 3.3: 1, 2, 5 [Ignore the problem instruction!] (For Thursday!) Finding Instantaneous Velocity [20] 3.2 (graphical) 3.3 The Derivative: An Algebraic Viewpoint 3.2: 33, 47, 49, 57, 58, 71, 83 3.3: 6,13 ,15,17, 23, 25 [Use  "4-step process"] The Derivative [12] 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 3.4 The Derivative:  Simple Rules 3.4:1-11 odd; 14-17; 19-21 Short Cut for Finding Derivatives [14] *The Derivative of the Reciprocal Function [18] Weeks 3 and 4 3.4 (Again)  3.4 The Derivative:  Simple Rules 3.4: 61, 65, 67, 71, 79 Uses of The Power Rule [20] *The Derivative of  the Square Root [16] 3.5 Marginal analysis  Chapter 3 Summary as relevant. 3.5: 1,5,6,9,11,13 3.4: 29, 37, 41, 42, 53, 55, 63, 64 3.2: 65 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] 4.1: Quotient Rule 4.1: 35, 37, 38, 43; 53, 59, 62 The Quotient Rule [13] 4.2 The Chain Rule 4.1: 63, 64, 71, 73 4.2 : 13- 17, 55 Introduction to The Chain Rule [18] 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] 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] More on Instantaneous Rate [19] 4.4: 53 Using Implicit Differentiation [23] A.2: Exponents A.2: 15,19, 23, 39, 41, 71 The Baseball Problem [19] Differentiability [3]  Morale Moment Math Anxiety [6] HW# 21 5.4 Related Rates 2.2: Exponential Functions 5.4 17,  21, 25 2.2 : 3,4,9,11, 7, 13, 17 Exponential Functions [10] HW #22 2.2 pp94-104(middle) 2.2: 45, 47, 51, 63, 73, 59, 61 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 EXAMINATION  # 1 will cover material from Assignments HW 1 to  21 and related sections of the text. HW #23 exp'(x) = exp(x) Notes. 4.3: 7,8,45,51,53,85 Derivatives of Exp'l Functions [23] Sensible Calculus I.F.2 HW #24 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 Logarithmic Functions [19] Derivative of log functions [14] HW #25 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 HW #26 2.3  Example 3 4.4 log differentiation Ex. 3 2.3: 9, 11, 15 4.4: 31 , 32 Slide Rules! UNDERSTAND HOW + WHY a slide works, a full explanation HW #27 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] HW #28 The Intermediate Value Theorem 3.8 pp225- 230 middle: limits and continuity (alg)  On-line: cont and diff. 5.1:  Maxima and Minima 3.7: 20,27, 28 3.8: 39, 41, 46, 53 5.1: 1-7 odd, 8-10, 12, 13, 15, 21, 23, 24, 25 The connection between Slope and Optimization [28] Critical Points [18] Three  Big Theorems [Begin-3.5min] The Fence Problem[25] continuity and differentiablity on-line materials( A and B) HW #29 5.1:  Maxima and Minima 5.2. Applications of Maxima and Minima 5.1: 35,  39, 41, 44 5.2: 5, 11, 13 Intro to Curve Sketching [9] The First Derivative Test [3] The Box Problem [20] HW #30 5.2. Applications of Maxima and Minima 5.2:15, 21 Regions where a function is increasing...[20] Higher order derivatives and linear approximations.[first 5 minutes only!] 4-8 Summary of Weeks  10 & 11 HW # 31 4-7 5.3 2nd deriv.pp317-320 5.3: 1-5,7,9,11,14 Acceleration & the Derivative [6] HW #32 4-8 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] HW #33 4-11 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 Asymptotes and criti' pts [17] HW #34 4-12 3.6,3.8  Review! 5.5 Elasticity and other economic applications of the derivative On-Line: Linear Estimation 5.5: 1, 3, 14 3.8: 15,17,21,23,33,35,37 5.3: 39, 43, 45 3.6: 25, 27,29 Graphing ...asymptotes [10] Functions with Asy.. and holes[ 4] On-line Problems on Linear Estimation   L1-6; A1-5; App1-3 HW #35 4-14 6.1 The Indefinite Integral  p 353-358 On-line tutorial for 6.1. 6.1: 1-13odd Antidifferentiation[14] SC.III.AThe Differential HW #36 4-15 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] HW #37 4-18 3.7, 5.3 Review p321-323 3.7: 15,17, 28-30 5.3: 47, 51, 63, 71 6.1: 53-55, 57 EXAMINATION  # 2 will cover material from Assignments HW 21 to 37 and related sections of the text. For Sample Exam II see Blackboard 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) HW #38 4-19 6.3. The Definite Integral As a Sum. p 373-376, 380 6.3: 1-5 odd, 15, 19, 21 Approximating Areas of Plane regions [10] SC IV.E HW #39 4-21 and 4-22* 6.4 The Definite Integral: Area p384-386 6.4: 1-5 odd, 21 Areas, Riemann Sums, and Definite Integrals [14] The Fundamental theorem[17] SC IV.E HW # 40 4-25 6.5 pp392-395    The Fundamental Theorem 6.5 : 17-20; 67,68 Illustrating the FT[14] Evaluating Definite Integrals [13] HW #41 4-26 6.2 Substitution pp364-367 6.5 pp 395  - 396 8.1 Functions of Several Variables. p467-471 6.2: 1-6; 21,23 6.5: 27-30, 61,63 Undoing the chain rule.[9]   Integrating polynomials by Substitution [15] HW #42 4-28 6.4  pp 384- 388 6.2 pp 368-371 Substitution 6.5 example 5 8.1 Functions of Several Variables. p467-471 6.2: 27-33,59, 60 6.5: 45,47,59,63,64 8.1: 1-9 odd, 19, 20, 21, 29, 39, 43 Area between two curves [9] Integrating composite exponential and rational functions by substitution [13] HW #43 4-29 7.2 pp416-420 (area between curves) 8.3 pp 490 - 492 7.2:1,3,5,11, 15 8.3:  1- 7 odd, 13, 41, 45 Limits of integration-Area [15] HW #44 5-2 7.2 p420-426 (Surplus and social gain) 7.3  pp 430-431 7.2: 25, 37, 49 7.3: 1- 5odd, 29, 35a Finding the Average Value of a Function [8] HW #45 5-3 7.5 p 442-445 + 8.2 8.4 p498-501 Critical points 7.5: 1-7 The first type of improper integral[10]  Infinite Limits of integration ... [12] Solution to 7.2:42 (See the student solutions manual). HW #46 5-5 8.2 8.4 p498-501 Critical points 8.3 Second order partials 8.2: 1-9 odd; 11-18; 19-25 odd;41, 49 8.4: 1-9 odd, 33, 37 8.3: 19-25 odd; 29,33,38,51, 53 The 20 minute review. Reading INVENTORY Problems INVENTORY CD Viewing INVENTORY Optional INVENTORY 7.5 8.4 pp 504-505 7.5: 11, 13, 17 8.4 :13, 15,17,19 The second type of ... [8] The 20 minute review. 7.6 7.6: 1,3,13 7.4 Future and present value. Common Mistakes [16] The 20 minute review. 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

 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 compound 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 1-17 NO Class.... MLK DAY 1-18 Course Introduction 1-20 Numbers, Variables, Algebra Review Begin Functions. More Algebra review. Week 2 1-24  More functions review The coordinate plane.  Functions, graphs. 1-25 Functions, graphs and models. Points and Lines. Especially Lines and models. 1-27 More Functions and Models: Linear Functions. Slopes, rates and estimation. Summary of Weeks 1&2 Due Friday or Monday 4 pm. 1-31 More linear models. Quadratic functions. 2-1 More Quadratics. 2-3 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 2-7(Graphing, Technology)  More on finding the derivative. 2-8 More: Finding the derivative as function. 2-10 Begin: The Derivative Calculus I Graphical Derivative as function graphs More on the definition of the derivative: Limits and notation. Week 5 Summary of Weeks 3&4. Due Friday 4 pm. 2-14Justification of the power rule. 2-15  Sum and Constant Multiple Rules Introduced. 2-17 More Notation for the derivative. Marginal Applications.Marginal vs. Average Cost Justify the sum rule. Discuss rule interpretations. Product rule. Week 6 2-21 Justify product rule. Quotient Rule. 2-22 More on the quotient rule Chain Rule 2-24 More Chain Rule.Implicit functions. Begin related rates. Implicit Functions and related rates.More on Implicit Differentiation Week 7 Summary of Week 5&6  Due..Monday, 2-28. 2- 28  More Implicit Differentiation and Related Rates. 3-1 Begin Exponential functions Interest and value 3-3 More on exponentials. More on exponential functions and graphs. Week 8 Midterm Exam #1 Self-Scheduled 3-9 3-7 Derivatives of exponentials, esp'ly d(b^x)/dx = k b^x 3-8 exp'(x)=exp(x). Review for Exam #1 3-10 Start Logarithmic functions. Derivatives of Logarithms and Exponentials Examples: f  does not have a derivative at a. Finish derivatives of log's, etc. Logarithmic functions. Week 9 3-14 Spring Break No Class 3-15 Spring Break 3-17 Spring Break Spring Break Week 10 Summary of Weeks 7 and 8  Due 4pm , Thursday,3-24. 3-21 More on models with exp and log equations. 3-22 More on Properties of Logs. Change of basis. Solving exponential equations with logs. 3-24. Logarithmic differentiation Logarithmic scales   limits and continuity, Continuity IVT. Week 11 Slide Rules? 3-28More on continuity and limits. Begin Optimization  and  First Derivative Analysis 3-29 More Optimization and Graphing. The fence problem. Optimization  and IVT 3-31:No Class. CC Day. First Derivative Analysis Optimization: revenue example Week 12 Summary of Weeks  10 & 11 Due Friday 5pm 4-8 4-4 More on first derivative 4-5 Second Derivatives- acceleration Concavity and Curves 4-7 More on Concavity Horizontal Asymptotes. Vertical Asymptotes. Relative change. Elasticity. Week 13 4-11 Linear Estimation and "Differentials." Begin Differential equations and integration IV.A. Acceleration and integration. Estimating cost changes from marginal costs. 4-12 More DE's. Costs, marginal costs, and estimation. 4-14 Euler's Method. Differential Notation(started)The Definite Integral week 14 Lab ? Summary of Weeks 12&13 Self Scheduled   Exam #2 4-20 4-18 Introduction to the definite Integral. 4-Review for Midterm 4-21 Interpreting definite integrals. Geometric Area. Riemann Sums  and Estimating Area . The definite integral and The FTofC.  IV.E Finding area by estimates and using anti-derivatives. Week 15 4-25 19 Start Substitution! More Area and applications: Intro to functions of  2 or more. 4-26 Substitution in definite integrals Functions of many variables. Tables for 2 variables. Partial derivatives. Area between curves. Consumer& Producer Surplus;  Social Gain Average Value. Week 16 Summary of Weeks 14 & 15 Due Tuesday 4 pm. 5-2  Improper integrals I  Extremes (Critical points) 5-3 2nd order partial derivatives  Visualizing Functions of 2 variables: level curves, graphs of z=f(x,y)and linear estimation. Improper Integrals I and II Least Squares example 5-5 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? Fundamental Theorem I???? Week 17 Final Examination Review Session  Sunday 3-5pm Lib 56 Self Schedule for Final Examinations