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

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] Comments Optional Work HW #1 8-24 A.1 Review of Real Numbers A.3 Multiplying and Factoring  1.1 pp 3-6 Moodle 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 #28-27 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 8-28/30* 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 again! [19] HW #4 8-31/9-4* 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 Moodle Practice Quiz on Functions On-line Mapping Figure Activities-  (this may be slow downloading) HW #5 9-6/7* 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 9-7/10/11* 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 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 #6.59-11/13/14** 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 9-13/14* 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 #89-17/18* 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) try Moodle Practice quiz on writing responses. HW #99-18/20* 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) Practice Quiz on Slopes of Tangent Lines using 4 steps. HW #9.5 9/24 Quizzes 3 and 4 [on-line] 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 9/24 3.4(Again)  The Derivative:  Simple Rules 3.4: 61, 65, 67, 71, 79; 29, 37, 41, 42, 53, 55, 63, 64 HW #11 9/25 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 9/27-28 4.1: Quotient Rule 4.1: 35, 37, 38, 43; 53, 59, 62 4.2.2 The Quotient Rule (Disc 1, 13:10) HW #1310/1 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 10/1-2* 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 10/4-5* 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) Midterm Exam #1 Self-Scheduled  10-10: Covers Material from HW # 1-15 and related sections. see Sample Exam on Moodle. HW #16 10/8 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 10/8-9* 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 #1810/12-15* 2 .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 #1910/15-16* 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 10/16-18-19* 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 10/19-22 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 10/23-25-26* 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 10/26-29* 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 #2310/29-30-11/1* 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 11/2-11/5* 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 11/5-6* 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 11/6-8* 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 11/9 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) 7.2.2 Using the Tangent Line Approximation Formula (Disc 2, 24:22) On-line Problems on Linear Estimation   L1-6; A1-5; App1-3 Exam #2 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 Moodle. 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 11/15 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 9.1.2 Antiderivatives of Powers of x (Disc 2, 17:56)9.1.1 Antidifferentiation (Disc 2, 13:59) HW #29 11/16 6.1 Applications p 359-361 6.1: 15,17, 27, 35, 41-44,51 HW #30 11/27,29* IV.E 6.3. The Definite Integral As a Sum. p 373-376, 380 6.2 Substitution pp364-367 6.3: 1-5 odd, 15, 19, 21 6.2: 1-6; 21,23 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 11/27,29* 8.1 Functions of Several Variables. p467-471 6.4 The Definite Integral: Area p384-386 6.5 pp392-395    The Fundamental Theorem 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 11/29,30* 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 12/3-4* 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 ##34 12/3,4-6* 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) 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) The second type of ... [8] 17.1.3 Infinite Limits of Integration, Convergence, and Divergence (Disc 4, 11:50) 5.5 Elasticity and other economic applications of the derivative 7.4 Future and present value. ASSIGNMENT INVENTORY  From SPRING, 2007 Reading INVENTORY Problems INVENTORY CD Viewing INVENTORY Optional INVENTORY The 20 minute review. Common Mistakes [16] 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 7.6 7.6: 1,3,13 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 8-20 Course Introduction Numbers, Variables Algebra Review Begin Functions. More functions review The coordinate plane.  Functions, graphs. Week 2 8-27 Functions, graphs and models. Points and Lines Lines and models. More Functions Models: Linear Functions. Slopes and  rates Summary of Weeks 1&2 Due Friday 3 pm. 9-3 NO Class.... LABOR DAY More linear models. Quadratic functions. Estimation. More Quadratics. Extremes and the tangent problem. Week 4 (Graphing, Technology) 9-10Average rates, and slopes of secant and tangent lines. Instantaneous Rates. The Derivative More Motivation: Marginal cost, rates and slopes. The Derivative and algebra. More on finding the derivative.Finding the derivative as function. Week 5 Summary of Weeks 3&4. Due Friday 3 pm. 9-17 Begin: The Derivative Calculus Definition of the derivative. Graphical Derivative as function graphs Justification of the power rule for  n>0. Der. of  1/x Justify the sum and constant multiple rules. Discuss Sum rule interpretations. Constant Multiple Rule Interpretations Notation. Marginal Applications. Applications: Marginal vs. Average Cost Week 6 9-24  Start Product rule. Justify product rule. Start Quotient Rule. More on the Quotient rule. Week 7 Summary of Week 5&6  Due Friday 3 pm. 10-1 The Chain Rule Implicit functions. More Chain Rule  Implicit Differentiation More Implicit Functions and related rates. More Implicit Functions and related rates. More Implicit Functions and related rates.  Examples: f  does not have a derivative at a. Week 8 Midterm Exam #1 Self-Scheduled  10-10 10-8 Begin Exponential functions Interest and value. More exponentials. e and compunding interest continuously. Review for Exam #1 More exponentials. e and compunding interest continuously. Derivatives of exponentials, esp'ly exp'(x)=exp(x) Week 9 Summary of Weeks 7 and 8  Due 4pm  Friday 10-15Finish derivatives of exp's, etc.  Logarithmic functions. Start Logarithmic functions. Derivatives of Logarithms and Exponentials More on models with exp and log equations. More on log properties. Logarithmic differentiation Logarithmic scales. Slide Rules!? More on log properties. Logarithmic differentiation   Make-up Exam #1 at 4:00 pm. BSS 308 Week 10 10-22  Finish logs/exps. limits and continuity, Continuity  IVT More on continuity and limits. More on Continuity. IVT.. Week 11 Summary of Weeks  9 & 10 Due Friday 10-29 Begin Optimization  and  First Derivative Analysis First Derivative Analysis More Optimization and Graphing. Optimization: revenue example Optimization  and IVT . More Optimization and Graphing. The fence problem Optimization: revenue example Begin Second Derivatives- acceleration Concavity and Curves Week 12 11-5 More on Concavity Horizontal Asymptotes. Vertical Asymptotes  Linear Estimation and "Differentials." Estimating cost changes from marginal costs. Differential Notation(started) Costs, marginal costs, and estimation. 11-10 Relative error. Begin Differential equations and integration IV.A week 13 Self Scheduled   Exam #2 Wednesday 11-14 Lab ? 11-12 No Class Veteran's Day Holiday Review for Exam #2? More DE's. Acceleration and integration Introduction to the definite Integral. IV.E Euler's Method. The Definite Integral Week 14 Fall Break- No Classes 11-19 to 11-23 Fall Break Week 15 This week! Summary of Weeks 12-15 Due Friday 11-26 Intro to functions of  2 or more.  Functions of many variables. Tables for 2 variables. Riemann Sums  and Estimating Change The definite integral and The FTofC. Substitution in an indefinite integral! Area . Finding area by estimates and using anti-derivatives. Fundamental Theorem I More Notation, Area and applications:  Interpreting definite integrals. Average Value.Partial derivatives. 1st order. linear estimation. Review Substitution then substitution in definite integrals Week 16 12- 3 Linear Estimations and Partial Derivatives. Area between curves. More on Area and integration. Consumer& Producer Surplus; Social Gain. Extremes (Critical points) Least Squares example  Elasticity 2nd order partial derivatives Improper Integrals I and II Future and present value. Visualizing Functions of 2 variables: level curves, graphs of z=f(x,y) Week 17 Final Examination Review Session  Sunday 1-3pm BSS 308 Dec 10 1240-1440  FH 111 Dec. 13 1240-1430 FH 111 Dec. 14 1500-1700  Sci B 133
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

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