MAT 140 SYLLABUS - ANALYTIC GEOMETRY ANDCALCULUS IANDREW SCHWARTZ, PH.D.Catalog Description: 140-04 Analytic Geometry and Calculus I (Fall 2010)Analytic geometry, functions, limits, derivatives and integrals of algebraic, trigono-metric, and exponential functions with applications. Prerequisites: MA 133 with agrade of C or higher and MA 134 with a grade of ’C’ or higher, or MA 135 with agrade of ’C’ or higher. (5)Text: Stewart, James (2008) Single Variable Calculus: Early Transcendentals(Sixth Edition), Belmont, CA: Brooks/Cole-Thomson Learning.Office Location and Hours: Johnson Hall 307 – WR 2:25pm-3:55pm andwhenever I’m around (I want you to always feel free to stop by and see if I’m in.If I’m not, see if the Mathematics Learning Center can help with your question. Ifnone of these times or situations work for you, you can make an appointment thatis an appropriate time for the both of us.)Contact Information: office phone: (573) 651-5065 e-mail: [email protected] homepage: http://cstl-csm.semo.edu/aschwartzClassroom Location and Hours: JH 101 – MTWRF 1:30pm-2:20pmClass Webpage: http://cstl-csm.semo.edu/aschwartz/ma140fa10Course Objectives: This course, MA145, and MA240 form the three courseAnalytic Geometry and Calculus sequence. The purpose of this sequence overall isto give students a working knowledge of the above, particularly the limit, the deriv-ative, the integral, basic sequences, and basic series and their analysis. The theorybehind the derivative and definite integral will be discussed and students may beexpected to compute (for example) simple derivatives using only the definition.Overall, however, the course emphasizes techniques rather than theory. Trigono-metric, polynomial, rational, radical, exponential, and logarithmic functions arecovered.Upon completion of this course in particular, you should be able to (among others):• Find one or two-sided limits of a function f (x) as x approaches a realnumber, a, evaluate limits at infinity and infinite limits.• Interpret continuity and limits in a graphical context.• Interpret the derivative both as the slope of a tangent line and as instan-taneous rate of change; find average and instantaneous rates of change.• Find derivatives of algebraic, logarithmic, exponential, and trigonometricfunctions. Demonstrate knowledge of the sum, difference, product, quo-tient, and chain rules for derivatives.• Find an equation of the tangent line to the graph of a function at a givenpoint.• Find higher order derivatives for a given function.• Apply derivatives to solve ’real life’ problems.Date: Fall 2010.12 ANDREW SCHWARTZ, PH.D.• Recognize and interpret the relationships among f, f0, and f00, in a graph-ical context. Be able to sketch the graph of the function.• Find integrals of polynomial, rational, logarithmic, exponential, and trigono-metric functions.• Evaluate definite integrals. Be able to apply definite integrals especially ina business context.Tentative Schedule:(1) Intro, Syllabus(2) 1.1 Functions and Models: Four Ways to Represent a Function # 2, 6, 8,16, 20, 24, 30, 36, 38, 66(3) 1.2 Functions and Models: Mathematical Models: A Catalog of EssentialFunctions # 2, 4, 8, 12, 16(4) 1.3 Functions and Models: New Functions from Old Functions # 2, 4, 10,16, 22, 30, 32, 36, 40, 50(5) 1.4 Functions and Models: Graphing Calculators and Computers # 2, 4, 6,8, 10, 12, 16, 18, 20, 32(6) 1.5 Functions and Models: Exponential Functions # 2, 4, 6, 8, 10, 14, 16,18, 22, 26(7) 1.6 Functions and Models: Inverse Functions and Logarithms # 8, 12, 16,18, 20, 22, 36, 52, 54, 66(8) REVIEW over Chapter 1(9) TEST over Chapter 1(10) 2.1 Limits and Derivatives: The Tangent and Velocity Problems # 2, 4, 6,8, 9(11) 2.2 Limits and Derivatives: The Limit of a Function # 2, 4, 6, 8, 14, 18,22, 26, 28, 32(12) 2.3 Limits and Derivatives: Calculating Limits Using the Limit Laws # 4,8, 14, 18, 24, 26, 30, 36, 46, 48(13) 2.4 Limits and Derivatives: The Precise Definition of a Limit # 2, 16, 22,24, 26, 32(14) 2.5 Limits and Derivatives: Continuity # 4, 6, 10, 16, 20, 24, 32, 36, 38, 48(bank)(15) 2.6 Limits and Derivatives: Limits at Infinity; Horizontal Asymptotes # 4,6, 8, 14, 18, 20, 30, 34, 40, 42(16) 2.7 Limits and Derivatives: Derivatives and Rates of Change # 4, 6, 10,28, 30 (bank)(17) 2.8 Limits and Derivatives: The Derivative as a Function # 2, 4, 22, 24, 26(18) 2.1-2.8 - to be determined by class(19) 2.1-2.8 - to be determined by class(20) 2.1-2.8 - to be determined by class(21) REVIEW over Chapter 2 (bank)(22) TEST over Chapter 2(23) 3.1 Differentiation Rules: Derivatives of Polynomials and Exponential Func-tions # 8, 12, 16, 22, 24, 30, 34, 46, 48, 52(24) 3.2 Differentiation Rules: The Product and Quotient Rules # 4, 6, 8, 10,12, 14, 24, 28, 30, 44(25) 3.3 Differentiation Rules: Derivatives of Trigonometric Functions # 2, 6,8, 10, 14, 16, 24, 26, 40, 46MAT 140 SYLLABUS - ANALYTIC GEOMETRY AND CALCULUS I 3(26) 3.4 Differentiation Rules: The Chain Rule # 6, 8, 12, 16, 26, 34, 36, 42,48, 62(27) 3.5 Differentiation Rules: Implicit Differentiation # 2, 6, 8, 10, 12, 14, 18,26, 30, 34 (bank)(28) 3.6 Differentiation Rules: Derivatives of Logarithmic Functions # 4, 6, 10,12, 20, 24, 28, 38, 42, 46(29) 3.7 Differentiation Rules: Rates of Change in the Natural and Social Sci-ences # 6, 10, 16, 20, 30 (bank)(30) 3.8 Differentiation Rules: Exponential Growth and Decay # 2, 4, 6, 8, 10(bank)(31) 3.9 Differentiation Rules: Related Rates # 14, 16, 18, 20, 28(32) 3.10 Differentiation Rules: Linear Approximations and Differentials # 2, 4,12, 14, 16, 18, 20, 22, 24, 28(33) 3.11 Differentiation Rules: Hyperbolic Functions # 2, 4, 8, 12, 18, 20, 30,34, 38, 46 (bank)(34) 3.1-3.11 - to be determined by class(35) 3.1-3.11 - to be determined by class(36) 3.1-3.11 - to be determined by class(37) 3.1-3.11 - to be determined by class(38) 3.1-3.11 - to be determined by class(39) 3.1-3.11 - to be determined by class(40) REVIEW over Chapter 3 (bank)(41) TEST over Chapter 3(42) 4.1 Applications of Differentiation: Maximum and Minimum Values # 4,6, 8, 18, 24, 32, 36, 42, 50, 54(43) 4.2 Applications of Differentiation: The Mean Value Theorem: # 2, 4, 6,12, 14(44) 4.3 Applications of Differentiation: How Derivatives Affect the Shape of aGraph # 8, 10, 12, 14, 18, 24, 38, 40, 44, 46 (bank)(45) 4.4 Applications of Differentiation: Indeterminate Forms and L’Hospital’sRule # 6, 10, 12, 18, 20, 22, 28, 34, 40, 60(46) 4.5 Applications of