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# Math Essay

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The following listing of course content is intended to aid students efforts at planning college time and also intended to avoid disagreements in interpretation of requirements. Since there may be class cancellations or other reasons to modify the schedule, I reserve the right to change any of the material contained below, thus superseding what is written here. It is the students responsibility to attempt to attend all classes; and to check with me when that is not possible.

Session 1: Course logistics & expectancies, Math Departments Course Outline, info sheet on student data.

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Review of Algebra: inequality symbols, open/closed intervals, slope of a line, three forms of the equation of a line, substitution. Initiate familiarization with TI 82 calculator; on/off, entering functions, domain and range, graphing.

Assignment: P14-17 # 7 – 27 (a selection of these). Also #65- 68, 70,77, 78 with TI 82, or by hand.

Session 2: Section 1.2: Review of Algebra: Laws of Exponents. TI 82; use of exponentiation button ( ^ ), Intersection.

P22, P25, P27 – Graphing Calculator Exploration.

Some Graphing Calculator terminology is available in the text on Pages xi, and following.

Assignment: P30 – 31 #4, 6, 18, 83, 85, 86. May also add #62 , 63.

Session 3: Section 1.3: Review of Algebra: Functions. Recognize Linear and Quadratic functions. Graph both. Solve quadratic by any of three ways; factoring, quadratic formula, or using TI 82.

P42 Graphing Calculator ExplorationAssignment: P47 50 # 1- 10, 31 – 40, 46. Also, in #50, what happens, what does it mean?Session 4: Section 1.4: Review of Algebra: Polynomial Functions and special cases; n = 1,2,3.

Rational Functions, piece-wise linear functions, the Absolute Value function, composite functions. (exponential functions will be studied in Chapter 4). Review also the graphing of these functions, including intercepts on both axes.

Assignment: P69 – 72 # 5 – 31, 35, 36, 67 – 75.

Calculus Limits & Continuity as Introductory TopicsSession 5: Section 2.1 Limits and Continuity.

Determine Limit (value the function or dependent variable, perhaps y) is approaching, as the independent variable(x ,h, or t) approaches a given value.

Determine continuity for a given function, at a given value of the independent variable (x); using the three tests for continuity.

Assignment: from P94 – 97 #13 – 38, 51 – 73.

For more practice, see the chapter review problems on P186 (and following). # 13 20 are appropriate for this section.

Session 6: Review Limits and Continuity, as required. Section 2.2: The Derivative. Use concepts of limit and slope of a secant line to define derivative as slope of the tangent line,Use concepts of limit, average rate of change, and slope to define derivative as instantaneous rate of change.

Introduce the idea of difference quotient, and then its limit as two points on a graph approach each other; thus giving another interpretation to the derivative. Note the different math symbols used to designate the derivative of an expression;for f(x), the derivative is f (x) or f prime of xfor y, the derivative is y or y prime. Note also the useful Leibnitz notation introduced.

Assignment: P111 – 112 # 1 – 4, 7 – 14.

Session 7: Section 2.3: Differentiation using the Power, Constant Multiple, Sum & Difference Rules.

Marginals as derivatives in Business and Economics.

Session 8: Problem solving session on Section 2.3.

Session 9: Section 2.4: Differentiation by the Product and Quotient RulesAssignment: P145 – 147 # 1 9, 19 24, 33, 34, 55 59. Also, # 49, 50 eview problems on P186 (and following) # 35, 36, 43, 44, 46.

Independently, be able to compute Second & Third derivatives (from Section 2.5).

Sessions 10,11: Section 2.6: Differentiation using the Generalized Power Rule, and the Chain Rule.

Note the Quadratic Regression Examples using the TI82. Assignment: P174 – 177 #11 26, 29, 30, 33, 34, 47, 48. Also # 53, 57 using NDERIV.):Leibnitz form of the Chain Rule.

Some problems from other texts will be discussed and assigned.

Assignment: complete work on Section 2.6.

For more practice in preparation for the quiz, and for the Final Exam on this Chapter:In the Chapter Review: P189 # 63 – 74, 94 – 96. Also, #62, using the TI82 to find cubic regression. Session 13: Section 3.1: Graphing Using the Derivatives and the Graphing Calculator.

Use the First Derivative Test to find the Critical Values of the independent variable- x. Use the Graphing calculator to find the corresponding value of the dependent variable y so that the resulting pair (x,y) can be plotted as a maximum (highest) or minimum ( lowest) point of a graph, in a given interval or as some other important point concerning the graph of a function.

Assignment: P203 – 205 # 15 22, 29, 30, 43, 44, 63.

Session 14: Section 3.1 (cont), if needed. More graphing of polynomial and rational Functions.

Also, Limits at Infinity. This topic is not in the text.

Session 15: Section 3.2: Determining Concavity. Also, the Second Derivative as a tool for finding the Inflection Point(s). Note examples of Inflection Points in real life situations.

Optional for Students: Text EXAMPLE 4 which is the alternative Second Derivative Test for finding maxima and minima.

Assignment: P220 – 222 # 7 – 10, 28 30, 53 – 56Session 16: Section 3.3: Some of the Optimization topics;maximize profit or revenue, minimize cost.

Exponential and Logarithmic Functions; and their DerivativesSession 17: Section 4.1: Exponential Functions.

Assignment: Vocabulary; exponential function, compound interest formula, present value formula, depreciation.

Session 18, 19: Section 4.1: Finding compound (or total) amount of money (or bacteria, or anything that is growing exponentially) at the end of a period of time- or the amount left, after a period of exponential decay or loss. Formulas A = Pe^rt and A = P(1 + (r/k))^nk.

Graphing Calculator Exploration. Note: a comfort level must be reached with the TI82, in this chapter- the work of this chapter cannot be done by hand. Assignment: P293 – 296 # 1 6, 9, 10, 13 16, 19 25, 27, 31, 33, 35.

Session 20: Section 4.2: Logarithms. The idea that logarithms are exponents and therefore obey the Laws of Exponents .

Find logarithms (logs) of given numbers to base 10 and base e. Convert exponential expressions to logarithmic expressions, and vice versa.

Graph exponential and log functions.

Use base 10 and base e logs to solve equations where the unknown variable is an exponent.

Learn the calculator INTERSECT method of solution also.

Solve exponential growth and decay application problems for the unknown time exponent.

Exponential and log functions are inverses.

Assignment; P314 – 316 # 1 30, 40 – 44.

Session 21,22: Section 4.3: Derivatives of Exponential Functions;e^x , e^ f (x), andLogarithmic Functions;ln x,ln f(x). Use previous and new derivative rules to find instantaneous rate of change.

Solve problems of learning rates, growth rates, maximizing consumer expenditure.

Assignments: P329 – 332 # 140, 49, 50, 53 55, 60 64, 68 70. Also, formulas for finding the derivatives of functions involving any base; b^ f(x) , log to any base f(x). (P333-334).

There will be a chapter quiz on Chapter 4. It will be 30 – 45 minutes long. There will be a lecture following that quiz.

Antidifferentiation and The IntegralSession 23: Section 5.1: What is antidifferentiation? Indefinite integration as the reverse of differentiation.

From given rate expressions, compute the quantitative functions. Assignment: P365 – 366 # 1 14, 21 22, 25 28, 31 32, 39 40, 43 – 44.

Session: 24: Section 5.2: Integration forms for log and exponential functions.

Assignment: P376 378 # 1 8, 11 14, 19 26, 29 30, 33 34, 37 – 38.

Note: Portions of the last three classes will be devoted to review for the Final Exam.

Session: 25, 26: Section 5.3: Riemann Sum, Area under the curve, Definite Integrals.

Do in class: Find area under the curve by using integration; and by the use of the TI82.

Quinnipiacs course evaluation forms may be completed during these classes.

Assignment: P397 – 400 # 13 – 19, 27, 28, 61 66, 79 80.Note: Section 5.6, Integration by Substitution, may be assigned to honors students.

Session 27: normally a review class with the content dictated by students requests.

The final exam in MA118 is scheduled by the college; but designed and corrected by your professor. For evening classes, the exam has, in the past, been held at 6 PM on a Monday or Wednesday. It is mandatory for all students; and is designed to be completed in less than the two hours allotted. Bibliography:

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