Martin Flashman's Courses
Math 106 Calculus for Business and Economics
Spring, '07
Current Assignment and Schedule
Checklist of topics for Final Exam

Tentative Assignments Assignments are official when a due date is assigned.
*Early or Just in time:
When two due dates are given,
the first date is for preparation and/or starting problems,
the second date is for completion of problem work
.
On-line Sensible Calculus is indicated by SC.

*Early or Just in time:
When two due dates are given,
the first date is for preparation and/or starting problems,
the second date is for completion of problem work

 Due Date Reading for 3rd Edition Problems CD Viewing [# minutes] Optional HW #1 1-19/22/23* 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 1-22/23/25* 1.1 Functions and tables.  A.5  pp A.22-24   Solving equations A.5 1-7 odd, 13-19 odd Functions [19] HW #3 1-25/29/30* 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] HW #4 1-30/2-1* 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) HW #5 2-5/6* 1.4 Linear Models 2.1 Quadratic functions 1.3: 37- 49 odd, 55, 57, 59 1.4: 1-9 odd 2.1: 1-9 odd, 25, 27, 33 Average Rates of Change [11] Parabolas [22] 1.4: 49 HW #6 2-6/8/9* 1.4 Linear Models. A.5 ppA23-A25 3.1 Average Rate of Change 1.4:  12, 19, 21,22,25 3.1: 1-10, 13-16, 21, 39, 40 [Changed 2-6] 3.1.1 Rates of Change, Secants, and Tangents (Disc 1, 18:53) On-line Mapping Figure Activities-  (Again... ;) The Two Questions of Calculus [10] HW #6.5 2-9/12* 3.2 Pages 154-158 The Derivative: A Numerical and Graphical  Viewpoint 3.2: 1, 2, 5, 9,12 3.1.1 Rates of Change, Secants, and Tangents (Disc 1, 18:53) HW #7 2-13/15* 3.2 derivative estimates  3.3 The Derivative: An Algebraic Viewpoint 3.2: 13, 16, 17, 19, 20; 23, 24  Use  "4-step process" from class 3.3: 1, 2, 5 [Ignore the problem instruction!] 3.1.2 Finding Instantaneous Velocity (Disc 1, 19:57) HW #8 2/15*16 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"] 3.1.3 The Derivative (Disc 1, 11:14) Blackboard Practice Quiz on Slopes of Tangent Lines using 4 steps. HW #9 2/16*19 3.3 The Derivative: An Algebraic Viewpoint 3.4 The Derivative:  Simple Rules 3.4:1-11 odd; 14-17; 19-21 3.3.1 The Derivative of the Reciprocal Function (Disc 1, 17:56)3.3.2 The Derivative of the Square Root Function (Disc 1, 15:19) 4.1.1 A Shortcut for Finding Derivatives (Disc 1, 14:03) 4.1.2 A Quick Proof of the Power Rule (Disc 1, 9:48)4.1.3 Uses of the Power Rule (Disc 1, 19:43) HW #9.5 2/20 3.2 Derivative function graphs, interpretation 3.2 :39, 41, 42, 59-64, 97,98, 109, 110 .2.1 The Slope of a Tangent Line (Disc 1, 11:16) 3.2.3 The Equation of a Tangent Line (Disc 1, 17:53) 3.2: 73,74, 86 HW#10 2/20 3.4 (Again)  3.4 The Derivative:  Simple Rules 3.4: 61, 65, 67, 71, 79; 29, 37, 41, 42, 53, 55, 63, 64 HW #11 2/22*23 3.5 Marginal analysis  Chapter 3 Summary as relevant. 4.1 Product Rule only! pp 241-244 3.5: 1,5,6,9,11,13 3.5: 19, 21,28 4.1: 13, 15, 16, 21, 22 4.2.1 The Product Rule (Disc 1, 20:43) 3.2.2 Instantaneous Rate (Disc 1, 14:38) 3.2: 65 HW #12 2/23*26 4.1: Quotient Rule 4.1: 35, 37, 38, 43; 53, 59, 62 4.2.2 The Quotient Rule (Disc 1, 13:10) HW #13 2/26*27 4.2 The Chain Rule 4.1: 63, 64, 71, 73 4.2 : 13- 17, 55 4.3.1 An Introduction to the Chain Rule (Disc 1, 17:51) HW #14 2/27*3/1 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 4.3.2 Using the Chain Rule (Disc 1, 12:53)6.1.2 Finding the Derivative Implicitly (Disc 2, 12:14) 6.1.1 An Introduction to Implicit Differentiation (Disc 2, 14:43) HW#15 3/2 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) 7.3.2 The Ladder Problem (Disc 2, 14:18) More on Instantaneous Rate [19] 4.4: 536.2.1 Using Implicit Differentiation (Disc 2, 22:24) HW #16 3/6 A.2: Exponents A.2: 15,19, 23, 39, 41, 71 7.3.3 The Baseball Problem (Disc 2, 18:21) 3.1.4 Differentiability (Disc 1, 2:35) 7.3.5 Math Anxiety (Disc 2, 5:30) HW #17 3/6-8*9 5.4 Related Rates 2.2: Exponential Functions 5.4 17,  21, 25 2.2 : 3,4,9,11, 7, 13, 17 5.2.1 Graphing Exponential Functions (Disc 1, 10:08) HW #18 3/19*20 2 5.2.2 Derivatives of Exponential Functions (Disc 1, 23:17).2 pp94-104(middle) exp'(x) = exp(x) Notes. 2.2: 45, 47, 51, 63, 73, 59, 61 4.3: 7,8,45,51,53,85 5.2.2 Derivatives of Exponential Functions (Disc 1, 23:17) HW #19 3/22 2.3: pp. 110-116 [Logarithmic functions] Log's Properties (on line). 2.3: 1-4, 19 5.3.1 Evaluating Logarithmic Functions (Disc 2, 18:37) Sensible Calculus I.F.2 HW #19.5 3/23*26 4.3: Examples 1-5; pp 265-267. Derivatives for Log's & Exponential Functions 4.3:1,2,15,17,19 2.3: 5, 7, 20, 21, 25,31, 45a, 48 a 4.3: 23, 27, 29, 33, 73 5.3.2 The Derivative of the Natural Log Function (Disc 2, 13:24) HW #20 3/29 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 #21 4/2 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 2.1.5 One-Sided Limits (Disc 1, 5:18) 2.1.6 Continuity and Discontinuity (Disc 1, 3:39) HW #22 4/3*5? 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 7.4.1 The Connection Between Slope and Optimization (Disc 2, 27:18) 8.2.1 Critical Points (Disc 2, 17:43) 8.1.2 Three Big Theorems (Disc 2, [Begin-3.5min]) continuity and differentiablity on-line materials( A and B) HW #23 4/5*6*9 5.1:  Maxima and Minima 5.2. Applications of Maxima and Minima 5.1: 1-7 odd, 8-10, 12, 13, 15, 21, 23, 24, 25 5.1: 35,  39, 41, 44 5.2: 5, 11, 13 7.4.2 The Fence Problem (Disc 2, 25:03)  8.1.1 An Introduction to Curve Sketching (Disc 2, 8:44) HW #24 4/12 5.2. Applications of Maxima and Minima5.1:  Maxima and Minima 5.3 2nd deriv.pp317-320 5.2:15, 21 5.2: 25,  27, 29 5.3: 1-5,7,9,11,14 7.4.3 The Box Problem (Disc 2, 20:38)  7.1.1 Acceleration and the Derivative (Disc 2, 5:44) 8.2.3 The First Derivative Test (Disc 2, 2:46)  8.2.2 Regions Where a Function Increases or Decreases (Disc 2, 20:17) 7.4.4 The Can Problem (Disc 2, 20:47) HW #25 4/13*16 5.2 and 5.3 again! 5.3 : 17-20, 23; 25, 29,31 5.2: 33, 35, 41, 45 8.3.1 Concavity and Inflection Points (Disc 2, 13:12)  8.3.2 Using the Second Derivative to Examine Concavity (Disc 2, 17:01) 7.2.1 Higher-Order Derivatives and Linear Approximation (Disc 2, 20:57)[first 5 minutes only!] HW#26 4/16 3.6: p212-216 3.8: p229 5.3: p321-324 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 #27 4/16 3.6,3.8  Again! 3.8: 15,17,21,23,33,35,37 3.6: 25, 27,29 5.3: 39, 43, 45 8.5.3 Graphing Functions with Asymptotes (Disc 2, 10:15) 8.5.4 Functions with Asymptotes and Holes (Disc 2, 3:2 Exam #2 4/18 EXAMINATION  # 2 will cover material from Assignments 15-27 and related sections of the text. Note this includes related rates again. For Sample Exams II see Blackboard Review for Exam #2: (will not be collected): p 136[138]: 2,3,4 p288[294]: 1(a,e,g,i),2(c,d),3a,8a p350[361]: 1(a,d,f),2,4a,5(a-c) HW #28 4/19*20 6.1 The Indefinite Integral  p 353-358 Differential equations and integration SC IV.A On-line tutorial for 6.1. On-Line: Linear Estimation 6.1: 1-13odd 7.2.2 Using the Tangent Line Approximation Formula (Disc 2, 24:22) 9.1.2 Antiderivatives of Powers of x (Disc 2, 17:56)9.1.1 Antidifferentiation (Disc 2, 13:59) On-line Problems on Linear Estimation   L1-6; A1-5; App1-3 HW #29 4/20 6.1 Applications p 359-361 6.1: 15,17, 27, 35, 41-44,51 HW #30 4/23*24 IV.E 6.2 Substitution pp364-367 6.3. The Definite Integral As a Sum. p 373-376, 380 6.2: 1-6; 21,23 6.3: 1-5 odd, 15, 19, 21 9.4.1 Approximating Areas of Plane Regions (Disc 3, 9:39)10.1.1 Antiderivatives and Motion (Disc 3, 19:51) SC.III.AThe Differential HW #31 4/26*27 6.4 The Definite Integral: Area p384-386 6.5 pp392-395    The Fundamental Theorem 8.1 Functions of Several Variables. p467-471 6.4: 1-5 odd, 21 6.5 : 17-20; 67,68  8.1: 1-9 odd, 19, 20, 21, 29, 39, 43 9.2.1 Undoing the Chain Rule (Disc 3, 8:30) 9.4.2 Areas, Riemann Sums, and Definite Integrals (Disc 3, 13:40) 9.4.3 The Fundamental Theorem of Calculus, Part II (Disc 3, 16:28) 9.4.4 Illustrating the Fundamental Theorem of Calculus (Disc 3, 13:55) 9.4.5 Evaluating Definite Integrals (Disc 3, 12:53) SC IV.E 9.2.2 Integrating Polynomials by Substitution (Disc 3, 15:24) HW #32 4/27 6.5 pp 395  - 396 6.5: 27-30, 61,63 9.3.2 Integrating Composite Exponential and Rational Functions by Substitution (Disc 3, 13:30) HW # 33 4/27*30 6.4  pp 384- 388 6.2 pp 368-371 Substitution 6.5 example 5 8.3 pp 490 - 492 6.2: 27-33,59, 60 6.5: 45,47,59,63,64 8.3:  1- 7 odd, 13, 41, 45 10.2.1 The Area between Two Curves (Disc 3, 9:04) HW ##34XXXXX 7.2 pp 416-420 (area between curves) 7.2 p420-426 (Surplus and social gain) 7.3  pp 430-431 7.2:1,3,5,11, 15 7.2: 25, 37, 49 7.3: 1- 5odd, 29, 35a 10.2.2 Limits of Integration and Area (Disc 3, 15:16) 18.1.1 Finding the Average Value of a Function (Disc 4, 8:18) The 20 minute review. Common Mistakes [16] Reading INVENTORY Problems INVENTORY CD Viewing INVENTORY Optional INVENTORY 5.5 Elasticity and other economic applications of the derivative 7.5 p 442-445 + 8.2 8.4 p498-501 Critical points 7.5: 1-7 17.1.1 The First Type of Improper Integral (Disc 4, 9:42) 17.1.3 Infinite Limits of Integration, Convergence, and Divergence (Disc 4, 11:50) 5.5: 1, 3, 14 3.7, 5.3 Review p321-323 3.7: 15,17, 28-30 5.3: 47, 51, 63, 71 6.1: 53-55, 57 Cusp points &... [14] Graphing, Technology problems from lab SC IV.E Solution to 7.2:42 (See the student solutions manual). 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. 7.5 8.4 pp 504-505 7.5: 11, 13, 17 8.4 :13, 15,17,19 The second type of ... [8] 7.6 7.6: 1,3,13 7.4 Future and present value. 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

 Monday Tuesday Thursday Friday Week 1 1-15  MLK Day. No Class Course Introduction Numbers, Variables, Algebra Review Week 2 1-22 Begin Functions. Functions, graphs and models. The coordinate plane.  Functions, graphs. Points and Lines. More Functions Class Cancelled! Summary of Weeks 1&2 Due Friday  or Monday (new)  3pm 1-29  More Functions More Functions and Models: Linear Functions. Slopes, rates. More linear models. Cost and demand. Week 4 (Graphing, Technology) 2-5 Quadratic function and estimations. Extremes and the tangent problem. Average rates, and slopes of secant and tangent lines. Instantaneous Rates.The Derivative Begin: More Motivation: Marginal cost, rates and slopes. The Derivative and algebra. Week 5 Summary of Weeks 3&4. Due Friday 3 pm. 2-12 More on finding the derivative. Finding the derivative as function. Graphical Derivative as function graphs. Marginal Applications. Applications: Marginal vs. Average Cost More examples using 4 step The Derivative Calculus Start Power Rue Discuss Sum rule interpretations Constant Multiple Rule Interpretations. Week 6 2-19 Justification of the power rule. Sum rule interpretations Justify the sum rule. Constant Multiple Rule Interpretations. Start Product rule. Justify product rule. Start Quotient Rule More on the Quotient rule. The Chain Rule Week 7 Summary of Week 5&6  Due Friday 3 pm. 2- 26 More Chain Rule Implicit Functions. Implicit Functions and related rates. More related rates. Examples: f  does not have a derivative at a. Week 8 Midterm Exam #1 Wed 3-7:Self-Scheduled 3-5 Begin Exponential functions More on exponentials. Review for Exam #1 Interest and value Models using exponential functions. Derivatives of exponentials, esp'ly exp'(x)=exp(x). Week 9 3-12 Spring Break Week 10 Summary of Weeks 7 and 8  Due 4pm  Friday 3-19 Derivatives of  Exponentials More on models with exp and log equations. Start Logarithmic functions. Week 11 3-26 Derivatives of Logarithms and Exponentials Logarithmic differentiation Logarithmic scales.  Begin limits and continuity. Slide Rules!? 3-30 CC Day No classes Week 12 Summary of Weeks   10 & 11 Due Friday 4-2.More on continuity and limits. IVT Begin Optimization  and  First Derivative Analysis The fence problem Optimization  and IVT  First Derivative Analysis More Optimization and Graphing. First Derivative Analysis week 13 4-9  Begin Second Derivatives- Concavity and Curves More on Concavity acceleration Optimization: revenue example Horizontal Asymptotes Vertical Asymptotes Week 14 Self Scheduled   Exam #2 4-18 Lab ? 4-16 Linear Estimation and "Differentials." Begin Differential equations and integration IV.A Differential Notation(started) More DE's. Introduction to the indefintie integral. Acceleration and integration Estimating cost changes from marginal costs. Costs, marginal costs, and estimation. Relative error.Introduction to the definite Integral? Week 15 Summary of Weeks 12-15 Due Friday 4-23 Euler's Method. IV.E Start Substitution! The Definite Integral  Riemann Sums  and Estimating Area . Finding area by estimates and using anti-derivative  The definite integral and The FTofC. More Area and applications:  Interpreting definite integrals. Fundamental Theorem I Intro to functions of  2 or more.  Functions of many variables. Tables for 2 variables. More Area and applications:  Interpreting definite integrals. Fundamental Theorem I Partial derivatives. 1st order. Geometric Area. Week 16 4-30 Substitution in definite integrals Visualizing Functions of 2 variables: level curves, graphs of z=f(x,y) Extremes (Critical points) Least Squares example Future and present value.  Improper Integrals I and II  Elasticity???? Week 17 Final Examination Review Session  Sunday 2:00pm-3:50pm  Lib 56 Self Schedule for Final Examinations Tues. May 8 10:20-12:10  FH 125Wed. May 9 10:20-12:10 SH 128Wed. May 9 12:30-14:20 SH 116Fri. May 11 10:20-12:10 FH 125* (as per Exam Schedule)
Checklist of topics for Final Exam
 I.  Differential Calculus:            A. *Definition of the Derivative                 Limits / Notation                 Use to find the derivative                 Interpretation ( slope/ velocity/marginal *** )            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 order        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