MATH 206-209 Syllabi Phase in 2011-1012 (Sept. 16,2011)

Text: James Stewart, Calculus: Early Transcendentals 7th ed. Brooks-Cole, 2012ISBN: 978-0-538-49790-9

MATH 206: (Effective Fall 2(11) (27 sections)Ch. 1 Quick review of Sections 1,2, and 3

Sections 3-6Ch.2 Sections 1-8Ch.:3 Sections 1-6, 9, 10 (Optional: Sect. 11)Ch.4 Sections 1-5, 7, 9 (See 4.6 omitted - assumes a graphing calculator)

MATH 207: (Effective Winter 2012) (19 sections)Ch.4 Quick review of Section 4.9Ch.5 Sections 1-5cn.s Sections 1-3. 5Ch.7 Sections 1-4, 8 (7.5 is a nice summary of strategies)

(Optional: Section 7.6)Ch.8 Section 1Ch, 10 Sections 1-4

MATH 208: (Effective Spring 2(12) (19 sections)Ch. 11 Sections 1-6,8-10 (11.7 is a nice summary of strategies)Ch, 12 Sections 1-6Ch. 13 Sections 1-4

MATH 209: (Effective Summer 2012)Ch. 14 Sections 1-8eh. 15 Sections 1-9Ch. 16 Sections 1-4, 6

(22 sections)

Note: These sections are selected so as to make the topics in each course the sameas they were in the previous syllabus keyed to the previous text: Stewart, EssentialCalculus: Early Transcendentals, 6th ed. The new text is not an "Essentials" version(not yet available for the 7th edition). You have a more extended presentation of thetopics, more examples, and more exercises available. Thus a bit of caution is inorder. You will not likely have time to treat all examples and details in class. Someplanning and judicious choices are likely needed for time management.

MATH 206-209 (Sept. 16,2011)Correspondences between Stewart, Essential Calcuius 6th ed. and Calculus 7th ed.(Both Early Transcendentals )(Sections in parentheses are optional or omitted.]

MATH 206Essential Calculus 6th ed i Calculus 7th ed.1.1 Functions and representations 11.1 Representing a function I

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1.2Essential functions i 1.2 Models - Essential functions Ii 1.3 New functions from old-"'~'~'

1.3 The limit of a function 2.2 Limit of.a functions2.4 Precise definition of limit

----1.4 Calculating limits 2.3 Calculating limits using laws1.5 Continuity I 2.5 Continuity1.6 Limits involving infinity 2.6 Limits at infinity - asymptotes ,2.1 Derivative and rate of change 2.7 Derivative and rate of change2.2 Derivative as a function 2.8 Derivative as a function2.3 Differentiation formulas 3.1 Derivatives of polys and exp I3.3 Derivatives of trig functions_ .._-_ .. --r-"2.4 Product and q~Q.t.!~.r.!!.!:.l!les _____tB...!?rQ9uct afl~.9uotient rules2.5 Chain rule 3.4 Chain rule2.6 Implicit differentiation 3.5 Implicit differentiation2.7 Related rates 3.9 Related rates2.8 Linear approximation - differentials 3.10 Linear approximation - differentials---_._. --3.1 Exponential functions 1.5 Exponential functions3.2 Inverse functions and logarithms 1.6 Inverse functions and logarithms3.3 Derivatives of log and exp 3.1 Derivatives of polys and exp

; 3.6 Derivative of log(3.4) ExponentiaIgrowth and d~cay (3.8) Exponential growth and decay3.5 Inverse trig functions 1 in 3.5 Implicit differentiation(3.6) Hyperbolic functions ! (3.11) Hyperbolic functions3.7 L'Hopital's rule T 4.4 L'Hopital's rule.4.1 Maxima and Minima I 4.1 Maxima and Minim~ __ . i

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4.2 Mean Value Theorem 4.2 Mean Value Theorem =l4.3 Derivatives and shapes of graphs 4.3 Derivatives and shapes of gra~hs __ I4.4 Curve sketching 4.5 Summary of curve sketching ~

(4.6 Graphing with calculus & calculator)4.5 Optimization problems 4.7 Optimiz~!12~p.!:.'?.!:>lems. I

(4.6) Newton's method (4.8) Newton's method;

I4.7 Antiderivatives 4.9 Antiderivatives i

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4.7 Antiderivatives 4.9 Antidertvatives __ 15.1 Areas and distances 5.1 Areas and distances !5.2 The definite inte.EL..r;:::.;al~ --+-.:5:..-. 2--.::.T-.:h:..:.e.....:d.....:e~fi.....:n;:::.;it....:..e....:..in....:..t;:...:;e£!.g-.:ra_l -l

5.3 Evaluating definite integrals 5.4 Indefinite integrals and net change ISA-The Fundamental Theorem 5.3 The Fundamental The;rem---··-l

6.5 Average value I

~:~ i~t.~~t:~~~:~nbYparts-.=-=---I7.2 Trigonometric integrals7.3 Trigonometric substitution

____________ .. (7.S Strategy for integration) !7.4 Partial fractions !

5.S Substitution6.1 Integration by parts6.2 Trig integrals and substitutions

6.3 Partial fractions(6.4 Tables and computer systems) (7.6 Tables and computer systems) i

_~.6 Improper integrals7.1 Areas between curves ---7.2 Volumes

7.8 Improper integrals I6.1 Areas between curves I----+--6.2 Volumes I

7.3 Volumes by cylindrical shells 6.3 Volumes by cylindrical shells7.4 Arc length 8.1 Arc length9.1 Parametric curves 10.1 Parametric curves9.2 Calculus with parametric curves 10.2 Calculus with parametric curves9.3 Polar coordinates9.4 Areas and lengths in polar coords.

I I, 10.4 Areas and lengths in polar coords,

10.3 Polar coordinates I

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MATH208Essential Calculus 6th ed i Calculus 7th ed.8.1 Sequences ._________ +~1.1 Se3uences I

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8.2 Series 11.2 SeriesI8.3 Integral and comparison tests 11.3 Integral test and estimates

11.4 Comparis_ontests __. I-

8.4 Other convergence tests 11.5Alternating series11.6 Absolute convergence

ratio and root tests(11.7 Strategy for testing ~erjes)

8.5 Power series 11.8 Power series8.6 Represent functions by power series 11.9 Represent functions by power

series8.7 Taylor and Maclaurin series 11.10 Taylor and Maclaurin series(8.8 App Taylor Polynomials) (11.11 App Taylor Polynomials)10.1 3QJe~~~_QKl:l.Ji:ll~~oordinates -.--- ..

12.1 3D rectangular coor~inates10.2 Vectors 12.2 Vectors--10.3 Dot Product 12.3 Dot Product10.4 Cross Product 12.4 Cross Product10.5 Equations of lines and planes 12.5 Equations of lines and planes10.6 Cylinders and quadric surfaces 12.6 Cylinders and quadric surfaces I

10.7 Vector functions & space curves 13.1 Vector functions & space curves i

13.2 Calculus of vector functions10.8 Arc length and curvature 13.3 Arc length and curvature10.9 Motion: velocity and acceleration I 13.4 Motion: velocity and acceleration i

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