Martin Flashman's Courses
Math 106 Calculus for Business and Economics
Spring, '04
Current Assignment and Schedule
CHECKLIST FOR REVIEWING FOR THE FINAL

 Due Date Reading for 3rd Edition Problems CD Viewing [# minutes] Optional 1-22 HW #1 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] 1-23 HW #2 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] 1-26 HW # [NONE] 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 Blackboard Practice Quiz on Functions 1-27 HW #3 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) 1-29 HW #4 1.4 Linear Models 1.3: 37- 49 odd, 55, 57, 59  1.4: 1-9 odd 1.4: 49 1-30 HW #5 1.4 Linear Models. 1.4:  12, 19, 21,22,25 Average Rates of Change [11] On-line Mapping Figure Activities-  (this may be slow downloading) 2-2 HW #6 2.1 Quadratic functions  A.5 ppA23-A25 2.1: 1-9 odd, 25, 27, 33 Parabolas [22] 2-3 HW #7 3.1 Average Rate of Change 3.1: 1-10, 13-16, 21, 39, 40 Rates of Change, Secants and Tangents [19] 2-5 HW #8 3.2 The Derivative: A Numerical and Graphical  Viewpoint 3.2: 1, 2, 5, 9,12 2-6 HW #9 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] 2-9 HW #10 3.2 derivative estimates  3.3 The Derivative: An Algebraic Viewpoint 3.2: 33, 39, 41, 42, 47, 49, 57, 58, 71, 83 The Derivative [12] 2-10 HW #11 3.2 Derivative function graphs, interpretation 3.3 The Derivative: An Algebraic Viewpoint 3.2 59-64, 97,98, 109, 110 3.3: 6,13 ,15,17, 23, 25, 39 Slope of a Tangent Line [12] Equation of a Tangent Line [18] 3.2: 73,74, 86 2-12 HW #12 3.4 The Derivative:  Simple Rules 3.4:1-11 odd; 14-17; 19-21 Blackboard Practice Quiz on Slopes of Tangent Lines using 4 steps. Instantaneous Rate [15] 3.2: 65 2-13 HW #13 3.4 (Again)  Chapter 3 Summary as relevant. 3.4: 29, 37, 41, 42, 53, 55, 63, 64 Short Cut for Finding Derivatives [14] 2-16 HW #14 3.4 (Again) 3.5 Marginal analysis  Chapter 3 Summary as relevant. 3.4: 61, 65, 67, 71, 79 3.5: 1,5,6,9,11,13 Uses of The Power Rule [20] *The Derivative of  the Square Root [16] *The Derivative of the Reciprocal Function [18] 2-17 HW #15 3.5 (Again) 4.1  Product Rule only! pp 241-244 3.5: 19, 21,28 4.1: 13, 15, 16, 21, 22 The Product Rule [21] 2-19 HW #16 4.1: Quotient Rule 4.1: 35, 37, 38, 43; 53, 59, 62 The Quotient Rule [13] Summary of Weeks 3&4. Due Friday 2-20 2-20 HW #17 4.1 4.1: 63, 64, 71, 73 More on Instantaneous Rate [19] Differentiability [3] 2-23 #18 4.2 The Chain Rule 4.2 : 13- 17, 55 Introduction to The Chain Rule [18] 2-24 #19 4.2 The Chain Rule 4.2: 25, 26, 33, 35; 47, 51, 53, 61, 62, 65 Using the Chain Rule [13] 2-26 #20 4.4 Implicit Differentiation (Skip Examples 2 and 3!) 4.4 :11, 12, 15, 35, 36, 47 Finding the derivative implicitly [12] Intro to Implicit Differentiation [15] 2-27 #21 5.4 Related Rates Especially  Ex. 1-3 A.2: Exponents 5.4: 9, 11, 13 A.2: 15,19, 23, 39, 41, 71 The Ladder Problem [14] 4.4: 53 Using Implicit Differentiation [23] 3-1 #22 2.2: Exponential Functions 5.4 17,  21, 25 2.2 : 3,4,9,11 2.2:  7, 13, 17, 59, 61 Exponential Functions [10] The third Summary is due by 4:00 pm. Morale Moment Math Anxiety [6] The Baseball Problem [19] Midterm Exam #1 covers  HW #1-#21. 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 3-2 #23 2.2: Exponential Functions 2.2: 45, 47, 51, 63, 73 3-4 #24 2.3: Logarithmic functions 2.3: 1-4, 19 Logarithmic Functions [19] 3-5 #25 2.3: Logarithmic functions 2.3: 5, 7, 20, 21, 25,31, 45a, 48 a 3-9 #26 2.3 Log's Properties on line. 4.3: Derivatives for Log's & Exponential Functions 4.3:7,8,45,51,53,85 Derivatives of Exp'l Functions [23] 3-11 #27 4.3: Derivatives for Log's & Exponential Functions 4.3:1,2,15,17,19, 23; 27, 29, 33, 73 Derivative of log functions [14] Sensible Calculus I.F.2 exp'(x) = exp(x) Notes. 3-12 #28 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 3-22,23 #29 3.6: limits (numerical/graphical)  P209-216 omit EX.3. 3.7: limits and continuity 3.8 limits and continuity (alg) pp225- 228 On-line: cont and diff. The Intermediate Value Theorem 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] 3-23,25 #30 3.8 pp225- 230 middle: limits and continuity (alg) 5.1:  Maxima and Minima 3.7: 20,27, 28 3.8: 39, 41, 46, 53 5.1: 1-7 odd, 8-10,12 The connection between Slope and Optimization [28] continuity and differentiablity on-line materials( A and B) 3-25 #31 5.1:  Maxima and Minima 5.1: 13,15,21,23,24,25 Critical Points [18] 3-26 #32 5.2. Applications of Maxima and Minima 5.1: 35,  39, 41, 44 5.2: 5, 11, 13 Intro to Curve Sketching [9] The Fence Problem[25] 3-29 #33 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!] Regions where a function is increasing...[20] The First Derivative Test [3] Acceleration & the Derivative [6] The Box Problem [20] 3-30 #34 5.3 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] 4-1 #35 5.2 and 5.3 again! 5.2: 33, 35, 41, 45 5.3: 35- 37,41, 63, 67 Graphs of Poly's [10] The 2nd Deriv. test [4] Horizontal asymptotes  [18] 4-2 #36 3.6: p212-216 3.8: p229 5.3: p321-324 3.6: 1-11 odd 3.8: 15,17,21,23 5.3: 39, 43, 45 Vertical asymptotes [9]   Graphing ...asymptotes [10] Functions with Asy.. and holes[ 4] Functions with Asy..and criti' pts [17] 4-6 #37 3.6,3.8  Review! On-Line: Linear Estimation 3.6: 25, 27,29 3.8: 33,35,37 On-line Problems on Linear Estimation   L1-6; A1-5; App1-3 Using tangent line approximations [25] Cusp points &... [14] SC.III.AThe Differential 4-8 #38 Differential equations and integration SC IV.A  6.1 The Indefinite Integral  p 353-358 On-line tutorial. 6.1: 1-19 odd, 27, 35 Antidifferentiation[14] 4-9 #39 6.1 Applications p 359-361 6.1: 41-44,51 Antiderivatives of powers of x [18] Antiderivatives and Motion [20] 4-9 #40 5.5 Elasticity and other economic applications of the derivative 5.5: 1, 3 4-12 #41 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 4-12 End of material covered in Exam #2 Midterm Exam #2 covers Assignments 22 - 41 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) 4-13 #42 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 4-15 #43 6.4 The Definite Integral: Area p384-386 6.4: 1-5 odd, 21, 23 Areas, Riemann Sums, and Definite Integrals [14] 4-16 #44 6.5 pp392-395    The Fundamental Theorem 6.5 : 17-20; 67,68 The Fundamental theorem[17]   Illustrating the FT[14] 4-19 #45 6.5 pp 395  - 396 6.2 Substitution pp364-367 6.2: 1-6; 21,23 6.5: 27-30, 61, 63 Undoing the chain rule.[9]   Integrating polynomials by Substitution [15] 4-20(22) #46 6.2 pp 368-371 Substitution 6.5 example 5 7.2 pp416-420 (area between curves) 6.2: 27-33,59, 60 6.5: 45,47,59,63,64 7.2:1,3,5,11, 15 Evaluating Definite Integrals [13] Area between two curves [9] 4-22 #47 7.2 p420-426 (Surplus and social gain) 7.2: 25, 37, 49 Limits of integration-Area [15] Integrating composite exponential and rational functions by substitution [13] 4-23 #48 7.3  pp 430-431 7.3: 1-5 odd, 29, 35a Finding the Average Value of a Function [8] 4-26 #49 8.1 Functions of Several Variables. p467-471 8.3 pp 490 - 492 8.1: 1-9 odd, 19, 20, 21, 29, 39, 43 8.3:  1- 7 odd, 13, 41, 45 4-27 #50 8.2 8.2: 1-9 odd; 11-18; 19-25 odd;41, 49 4-29 #51 8.3 Second order partials 8.4 p498-501 Critical points 8.3: 19-25 odd; 29,33,38,51, 53 8.4: 1-9 odd, 33, 37 4-30 #52 7.6 7.6: 1,3,13 5-3 #53 7.5 p 442-445 7.5: 1-7 The first type of improper integral[10] Infinite Limits of integration ... [12] 5-4 #54 7.5 8.4 pp 504-505 7.5: 11, 13, 17 8.4 :13, 15,17,19 The second type of ... [8] 5-6 #55 7.4 Future and present value. Common Mistakes [16] The 20 minute review. Optional Last assignment Future and present value. Probability and  DARTS The 20 minute review. 7.4:1, 9, 21, 27 Reading INVENTORY Problems INVENTORY CD Viewing INVENTORY Optional INVENTORY 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 The 20 minute review. Final Examination:

 Monday Tuesday Thursday Friday Week 1 1-19 No Class- MLK Day 1-20 Course Introduction 1-22 Numbers, Variables, Algebra Review 1-23 The coordinate plane.  Points and Lines.  Begin Functions. More Algebra review. Week 2 1-26 Functions, graphs. Especially Lines and models. 1-27 Functions, graphs and models. 1-29 More Functions and Models: Linear Functions. 1-30 Quadratic functions.  Slopes, rates and estimation. More linear models. Quadratics. Week 3  Summary of Weeks 1&2 Due Friday, 2-6. 2-2 Quadratics. Begin Average rates, and slopes of secant and tangent lines. 2- 3 Average rates, and slopes of secant and tangent lines. Instantaneous Rates & The Derivative. 2-5  More Motivation: Marginal cost, rates and slopes. the Derivative and algebra. 2-6 Graphing, Technology, Meet in SH 119. More on the Derivative. and Week 4 2-9 More on finding the derivative. Begin the Derivative Calculus 2-10  The Derivative Calculus I 2-12 Justification of the power rule. 2-13 Marginal Applications. Justify the sum rule. Week 5 Summary of Weeks 3&4. Due Friday 2-20 2-16 Discuss Sum rule interpretations. Start Product rule. 2-17 Justify Constant Multiple Rule. Start Quotient Rule. Justify product rule. 2-19 More on the Quotient rule. Applications: Marginal vs. Average Cost Breath 2-20 Discuss Constant Multiple Rule. Examples: f  does not have a derivative at a. The Chain Rule Week 6 2-23 More Chain Rule Implicit functions. Implicit Differentiation 2-24 Implicit Functions and Related rates. 2-26 More Implicit Functions and related rates. 2-27 Exponential functions Interest and value Week 7 Summary of Week 5&6  Due 3-1. Midterm Exam #1 Self-Scheduled Wednesday  3-3  8:00-11:30am; 5:00 - 8:30pm Lib 56 3-1 More on exponentials. Start Logarithmic functions. 3-2 Review for Exam #1 3-4 Logarithmic functions. 3-5 Models using exponentials Week 8 3-8 Derivatives of Logarithms and Exponentials 3-9 Finish derivatives of log's, etc. 3-11 Logarithmic differentiation   Slide Rules! 3-12 limits and continuity, Continuity Spring break week 3-15 No Class 3-16 No Class 3-18 No Class 3-19 No Class Week 9 Summary of Weeks 7 and 8  Due 3-22 IVT Optimization  and  First Derivative Analysis 3-23 More Optimization and Graphing. 3-25 The fence problem. First Derivative Analysis More optimization  and IVT 3-26 Optimization: revenue&profit Begin Second Derivatives- acceleration Concavity and Curves Week 10 3-29 More on Concavity 3-30 Horizontal Asymptotes. 4-1 Vertical Asymptotes 4-2  Linear Estimation and "Differentials." Relative error. Week 11 Summary of Weeks  9 & 10 Due 4-5. 4-5 Differentials Begin Differential equations and integration IV.A 4-6 More on DE's and integration. 4-8 Elasticity. 4-9 Acceleration and integration. Estimating cost changes from marginal costs.  More DE's. Week 12 Self Scheduled   Exam #2 Wed. 4-14 4-12 Costs, marginal costs, and estimation. Introduction to the definite Integral.. 4-13 Riemann Sums  and Estimating Area .Finding area by estimates and using anti-derivatives  The definite integral and The FTofC. Finding Area exactly!  IV.E? 4-15 More Area and applications:  FT of calculus I . 4-16 Substitution! week 13 Summary of Weeks 11&12 Due 4-22 4-19 Substitution in definite integrals Interpreting definite integrals. Geometric Area. 4-20 More on area and substitution. Consumer& Producer Surplus; Social Gain. 4-22 Average Value. Intro to functions of  2 or more. Partial derivatives. 1st order. 4-23 Meet in SH 119 Visualizing Functions of 2 variables: level curves, graphs of z=f(x,y) Week 14 4-26 More on partial derivatives and linear estimation. Visualizing functions of 2 variables. 4-27 2nd order partial derivatives  Extremes (Critical points) 4-29 DE's -Separation of variables: Growth models and exponential functions. 4-30 Improper integrals I Week 15 Summary of Weeks 13 & 14 Due 5-4 5-3 Improper integrals II 5- 4 Least Squares example 5-6 Future and present value. Applications of linear regression to other models using logarithms Probability and  DARTS? 5-7 ???? Week 16 Final Examination Review Session  Sunday 4-6 pm Lib 56 5-10 5-11 Wed.5-12 Th. 5-13

 I.  Differential Calculus:            A. *Definition of the Derivative                 Limits / Notation                 Use to find the derivative                 Interpretation ( slope/ velocity )            B. The Calculus of Derivatives                * Sums, constants, x n, polynomials                 *Product, Quotient, and  Chain rules                  *logarithmic and exponential functions                 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                 The differential and 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.