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Mathematics Xb™

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Mathematics Xb

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Schedule for Weeks 1-2

Week	Date	Topic	Homework Due	Reading	Goals / Notes
1	2/6/06	Course introduction & Implicit differentiation (17.1)	None	§17.1, particularly p. 536 (example 17.1 part b)	Understand goals and structure of course, Be able to follow logarithmic differentiation
	2/7/06	No workshop this week
	2/8/06	Logarithmic Differentiation (17.2)	PS1: §17.1 #1, 2, 3	§17.2	Be able to use logarithmic differentiation to find a derivative of a function, Be able to recognize when to use logarithmic differentiation
	2/9/06	No problem session this week
	2/10/06	Implicit Differentiation (17.3)	PS2: §17.2 #1, 2, 3, 4, 7	§17.3, particularly examples 17.1 and 17.4	Understand what is meant by an implicitly defined function, Be able find derivatives of functions given implicitly, Use implicit differentiation to find the slope of the tangent line to a curve at a point, Understand when to use implicit differentiation
2	2/13/06	Related Rates (17.4)	PS3: §17.3 #1, 3, 5, 6, 11, 12(b,e,g)	§17.4	Be able to use implicit differentiation to solve problems ("related rates" problems)
	2/14/06	Workshop #1
	2/15/06	Geometric Sums (18.1)	PS4: §17.4 #2, 3, 4 [5, 9, 14 are recommended but you do not have to turn in]	§18.1	Be able to recognize a finite geometric sum and identify its common ratio, Be able to express a geometric sum in closed form, Be able to compute a numeric geometric sum
	2/16/06	Gateway exam: Differentiation and Advanced Algebra Gateway exams will be given in the problem sessions. The gateway exams will be held during the problem sessions.
	2/17/06	Geometric Series and Summation Notation (18.2)	PS5: §18.1 #2, 3, 19, 25, [6, 7, 15, 16, 30, 33 are recommended but you do not have to turn in]	§18.2, 18.4	Be able to understand the terminology associated with infinite geometric series, Be able to determine if a given geometric series converges or diverges, Be able to find the sum of a given convergent geometric series, Be able to express a geometric sum or series using summation notation

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Schedule Weeks 3-4

Week	Date	Topic	Homework Due	Reading	Goals / Notes
3	2/20/06	No class: President's Day
	2/21/06	No workshop this week
	2/22/06	Applications of Geometric Series	PS6: §18.1 #30; §18.2 #12, 13, 14; §18.4 #4, 10, 12, 13	§18.5	To use geometric sums and series to solve problems in a variety of contexts, to gain experience in communicating mathematical ideas
	2/23/06	Problem Sessions: Mandatory review sessions for anyone who did not pass the first gateway.
	2/24/06	Sine and Cosine (19.1)	PS7: §18.5 #4, 11, 16, 19	§19.1, particularly p. 594 and 599	Understand how to define the sine and cosine functions as a function of arc length on the unit circle, Be able to approximate the sine and cosine, Understand and be able to use some trigonometric identities
4	2/27/06	Graphs of Sine and Cosine (19.2)	PS8: §19.1 #1, 2, 3, 4, 5, 6 [ Calibrated Unit Circle]	§19.2, particularly p. 603-4	Be familiar with the graphs of the sine and cosine, Be able to identify the period, balance value, and amplitude of a sinusoidal graph, Be able to write an equation whose graph matches the given sinusoidal graph
	2/28/06	Workshop #2
	3/1/06	Tangent Function, Angles, and Arc Length (19.3 & 19.4)	PS9: §19.2 #5, 9, 10 [6 and 14 are recommended but you don't have to turn in]	§19.3 and 19.4	Understand the definition of tangent as the slope of a certain line, Understand the graph of the tangent, including the relationship to the graphs of the sine and cosine, Be able to use radian measure of angles, Be comfortable with the relationship between radian measure and arc length, Be able to find trigonometric functions of angles by taking advantage of circle symmetry
	3/2/06	Problem Sessions
	3/3/06	Right triangle trigonometry (20.1 & 20.2)	PS10: §19.3 #3, 4, 10; §19.4 #2, 3, 4, 6, 11	§20.1	Be able to use a right triangle to find trigonometric functions, Be able to solve real-world problems using right triangles and trig functions, Be familiar with 45-45-90 and 30-60-90 triangles

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Schedule Weeks 5-6

Week	Date	Topic	Homework Due	Reading	Goals / Notes
5
	3/6/06	Inverse trig functions (20.3)	PS11: §20.1 #1, 3, 6; §20.2 #3, 5, 8	§20.3, particularly p. 645-6	Understand inverse trig functions, Be able to simplify expressions involving inverse trig functions using triangles
	3/7/06	Workshop #3: Inverse Trigonometric Functions
	3/8/06	Solving trig equations (20.4)	PS12: §20.3 #1, 4, 7	§20.4	Be able to solve trigonometric equations on restricted and unrestricted domains
	3/9/06	Gateway II: Trigonometric Functions. The gateway exam will be given during the problem sessions.
	3/10/06	Laws of sines, cosines, and trig identities (20.5 & 20.6)	PS13: §20.4 #1, 3 (be sure to explain why you can't just cancel cos x in part b), 8, 21	§20.5	Be able to apply the laws of sines and cosines, Be able to use the addition formulas and other identities to simplify trig expressions [ Trig Identities Handout]
6	3/13/06	Derivatives of trig functions (21.1 & 21.2)	PS14: §20.4 #4, 7; §20.5 #1, 5, 7; §20.6 #2, 7, 8	§21.1 and 21.2, particularly p. 688 and Example 21.1 on p. 692	Be able to follow the derivation of the derivative of the sine function, Be able to find derivatives of trigonometric functions
	3/14/06	Workshop #4
	3/15/06	Applications of trig derivatives: Related Rates (21.3)	PS15: §21.1 #4; §21.2 #1, 2	§21.3, example 21.3	Be able to solve related rates problems using trigonometric derivatives
	3/16/06	Review Session from 5-6:30pm in Science Center Hall A.
	3/17/06	Optimization and Curve sketching of trig functions (21.3)	PS16: §21.3 #7, 8, 15	§21.3, example 21.2	Be able to optimize functions involving trigonometric expressions, Be able to sketch functions involving trig expressions

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Schedule Weeks 7-9

Week	Date	Topic	Homework Due	Reading	Goals / Notes
7
	3/20/06	Derivatives of inverse trig functions (21.4)	PS17: 21.3 #1, 2, 3, 10, 18, 23 [5, 6, 12, 14 are recommended but you do not have to turn them in]	§21.4	Understand how to use implicit differentiation to find the derivatives of inverse trig functions, Be able to find derivatives of expressions involving inverse trig functions
	3/21/06	Workshop #5: Exam Review
	3/22/06	L' Hospital's Rule	PS18: §21.4 #1, 2, 3, 4, 5	Appendix F	Be able to recognize limits of "indeterminate form" 0/0, ∞/∞, 0⋅∞, 1^∞, ∞^0, and 0^0, Be able to evaluate limits of the above forms using L' Hospital's Rule
	3/23/06	Midterm I from 7-9pm in Science Center Hall D. Note that your CA may be holding a problem session at an alternate day/time. Check with your CA for details.
	3/24/06	Net change (22.1)	No homework	§22.1	Be able to find net change in a function given a constant rate of change for the function, Be able to approximate the net change in a function given a rate of change which is not constant, Be able to visualize net change as the area under a particular curve
8	3/28/06	Spring break
9
	4/3/06	Definite integral (22.2)	PS19: §22.1 #4; p. 1118 # 3, 4, 6, 11, 13	§22.2, particularly p. 725-272, You may want to review §18.4	Be able to approximate the area under a curve using left- and right-hand sums, Understand the definition of the definite integral as the limit of a sum, Understand the signed area under a curve, Be able to calculate simple definite integrals, Be able to interpret the derivative as the signed area under a curve or as the net change in amount
	4/4/06	Workshop #6
	4/5/06	Signed Area (22.3)	PS20: §22.2 #1, 4	§22.3	Be able to evaluate certain integrals by examining the signed area underneath the curve.
	4/6/06	Problem sessions: Trigonometry review. These are mandatory review sessions for anyone who did not pass the second gateway exams. They are optional for those who did pass the second gateway.
	4/7/06	Properties of the Definite Integral (22.4)	PS21: §22.2 #5, 6 §22.3 #1, 3, 5 (Note that the 22.3 problems are all to be done by thinking in terms of signed area. Show your work. No credit will be given for answers found using other formulas and methods).	§22.4	Be able to simplify integrals using the properties stated on p. 738
	4/7/06	Project Topic and Groups Assigned: This semester, you will be required to learn an advanced calculus topic and to prepare a lesson on the topic. The topics will be assigned, then the group will learn the topic together and meet with the instructor to assess their understanding. Later in the semester, the group will turn in a short paper on the topic, an outline of what they plan to do for the lesson. The lesson will be presented during reading period. More details will be given in class.

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Schedule Weeks 10-11

Week	Date	Topic	Homework Due	Reading	Goals / Notes
10	4/10/06	Area function (23.1)	PS22: §22.4 #1, 2, 3, 5, 6, 8 (Note #1 and #2 should be done using the properties and signed area.)	§23.1, particularly the "Big Picture" on p. 743 and Example 23.1	Understand the area function and how it can also be interpreted as a net change function, Be able to find the area function for certain simple functions
	4/11/06	Workshop #7
	4/12/06	Properties of the area function (23.2) Let your TF know which project topic your group has selected by today	PS23: §23.1 #2, 3, 4;	§23.2, particularly Example 23.2	Be able to determine characteristics of the area function (such as increasing/decreasing, concave up/down, extrema) given a graph of the original function, Explore the relationship between the area function and the original function.
	4/13/06	Problem Session: A quiz covering the same types of questions as were on the first part of the midterm exam will be given during problem session. This quiz will be counted as part of your quiz/homework grade.
	4/14/06	Fundamental Theorem of Calculus I (23.3)	PS24: §23.2 #1, 2, 3	§23.3, particularly the statement of the fundamental theorem on p. 758	Understand the statement and the proof of the Fundamental Theorem of Calculus, part I
11
	4/17/06	Fundamental Theorem of Calculus II (24.1)	PS25: §23.3 #1, 2, 3, 4	§24.1	Understand the Fundamental Theorem of Calculus, part II and be able to use it to calculate definite integrals, find area under curves, and determine net change given rate of change
	4/18/06	Workshop #8
	4/19/06	Average value (24.2) and Antidifferentiation (25.1)	PS26: §24.1 #2, 5	§24.2, particularly p. 777; §25.1, particularly the definition on p. 783	Be able to calculate the average value of a function
	4/20/06	Review Session from 5-6:30 pm in Science Center Hall A.
	4/21/06	"Guess and Check" and Substitution I (25.2) Draft of project summary papers due to your TF today by 4pm.	PS27: §24.1 #6, 8, 11; §24.2 #1, 3	§25.2, particularly example 25.2	Be able to use "guess and check" to find antiderivatives of certain functions, Understand the connection between the chain rule and the method of substitution, Be able to use substitution to find certain antiderivatives and definite integrals

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Schedule Weeks 12-13

Week	Date	Topic	Homework Due	Reading	Goals / Notes
12	4/24/06	Substitution II (25.3)	PS28: §25.1 #1, 5; §25.2 #1, 2, 3;	§25.3	Be able to use the method of substitutions to find more complex antiderivatives
	4/25/06	Workshop #9: Exam Review
	4/26/06	Slicing I (27.1)	PS29: §25.1 #19; §25.3 #2	§27.1, examples 27.1 and 27.2	Be able to find total "mass" when density varies and to solve similar problems that involve slicing
	4/27/06	Exam II from 7-9pm in Science Center Hall D. Your CA may be holding their problem session at a different time and place than normal.
	4/28/06	Slicing II (27.1)	Nothing due
13	5/1/06	Introduction to differential equations (15.2)	§27.1 #1, 2, 6, 8, 10, 20	§15.2, particularly p. 298	Understand the basic terminology of differential equations, Be able to determine whether a given function is a solution of a given differential equation, Be able to solve the differential equation y'=ky
	5/2/06	Workshop#10
	5/3/06	Differential equations (31.1)	§15.2 #1, 2, 3, 6, 9	§31.1, particularly example 31.2	Be able to write a differential equation which models a particular situation (including "mixing problems")
	5/4/06	Problem Session
	5/5/06	Solutions to Differential Equations (31.2)	§31.1 #1, 2, 3	§31.2, p. 992	Be able to use a slope field to visualize a differential equation, Be able to determine whether a given function is a solution of a given differential equation, Be able to solve differential equations of the form dy/dt=f(t) [Click here for dfield]

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