Santa Monica College Mathematics Department Addendum Math 8 Calculus 2

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Santa Monica College

Mathematics Department Addendum

Math
8



Calculus 2

Prerequisite Comparison Sheet


exit skills of Math
7

and entry skills for Math
8



Exit Skills for Math 7

Upon successful completion of Math 7, the student will be able to:

A.

Eva
luate limits using basic limit theorems and the epsilon
-
delta definition.

B.

State and apply the definition of continuity to determine a function’s points of
continuity and discontinuity.


C.

Differentiate elementary functions using basic derivative theo
rems and the
definition of the derivative.


D.

Integrate elementary functions using basic integral theorems and the definition of
the definite integral.


E.

Approximate definite integrals using numerical integration (trapezoidal and
Simpson’s rules).


F
.

Solve derivative application problems including optimization, related rates,
linearization, curve sketching and rectilinear motion.


G.

Solve integral application problems including area, volume, arc length and work.

H.

State and apply the Mean Value T
heorems, Extreme Value Theorem, Intermediate
Value Theorem, Fundamental Theorem of Calculus, and Newton’s Method.




Entry Skills for Math 8

Prior to enrolling in Math 8 students should be able to

1.

Evaluate limits using basic limit theorems and the ep
silon
-
delta definition.

2.

State and apply the definition of continuity to determine a function’s points of
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5.

Approximate definite integrals using numerical integration (trapezoidal and
Simpson’s rules).


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6.

Solve derivative application problems including
optimization, related rates,
linearization, curve sketching and rectilinear motion.


7.

Solve integral application problems including area, volume, arc length and work.

8.

State and apply the Mean Value Theorems, Extreme Value Theorem, Intermediate
Value

Theorem, Fundamental Theorem of Calculus, and Newton’s Method.




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Santa Monica College

Student Learning Outcomes




Date:

December, 2009


Course Name and Number:

Math 8, Calculus 2


Student Learning Outcome(s):




Individual faculty members will devel
op and reports on assessments for SLOs.




1.

Students will set up and solve applications problems involving limits, areas, volumes, arc
length, indeterminate forms, center of mass, and improper integrals using differentiation and
integration
techniques with transcendental functions.


2.

Students will determine the divergence or type of convergence of various infinite series, find
the domain (interval of convergence) of power series and derive and apply Taylor Series.


3.

Students will graph and analyze curves using parametric equations and/or polar coordinates
and solve applications involving functions in either polar or parametric form.



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Demonstrate how this course supports/maps to at least one program and on
e institutional
learning outcome
. Please include all that apply
:


1.

Program Outcome(s):


The student will demonstrate an appreciation and understanding of mathematics in order to
develop creative and logical solutions to various abstract and

practical problems.


As a result of learning
calculus
, students will
be able to demonstrate the ability to
analyze
and solve
higher
-
level
abstract and practical problems.





2.

Institutional Outcome(s):



Through their experiences at SMC, students will obtain the knowledge and academic skills
necessary to access, evaluate, and interpret ideas, images, and information critically in order
to communicate effect
ively, reach conclusions, and solve problems.


As a result of knowledge gained through lectures, homework and exams, students will be
able to evaluate calculus
-
level problems critically and present solutions in a clear and logical
manner
.





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Textbook
:

Swokowski, Earl,
Calculus, The Classic Edition
, Brooks/Cole Publishing, 1991



A Sample Schedule for Math
8


This schedule assumes a standard meeting schedule of
1 hr 5 min
with
4

class meetings per week.



Session

Text Section/Activity

1

Review of li
mits

2

Review of continuity

3

Review of derivatives

4

Review of integrals/Quiz/Exam

5

6.5 Surface Area (omit arclength)

6

6.7 Moments and Center of Mass

7

7.1 Inverse Functions

8

7.2 The Natural Logarithm

9

7.3 The Exponential Function

10

7.4 Integrals

11

7.5 Logarithms and exponentials with base b

12

7.6 Growth and Decay

13

8.1 Inverse Trig Functions

14

8.2 Derivatives and Integrals of Inverse Trig. Functions

15

8.3 Hyperbolic Functions

16

Review

17

Exam 1 on Chapters 6, 7 an
d 8

18

9.1 Integration by Parts

19

9.2 Trigonometric Integrals

20

9.3 Trigonometric Substitution

21

9.4 Rational Functions

22

9.5 Quadratic Expressions

23

9.6 Miscellaneous Substitutions

24

Review

25

Exam 2 on Chapter 9

26

10.1 Indetermina
te Forms

27

10.2 Other Indeterminant Forms

28

10.3 Integrals with Infinite Limits

29

10.4 Discontinuous Integrands

30

Review

31

Exam 3 on Chapter 10

32

11.1 Sequences

33

11.1 Sequences

34

11.2 Infinite Series

35

11.2 Infinite Series

36

11.
3 Positive Term Series

37

11.3 Positive Term Series

38

11.4 Ratio and Root Tests

39

11.5 Alternating Series and Absolute Convergence

40

11.5 Alternating Series and Absolute Convergence

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Session

Text Section/Activity

41

11.6 Power Series

42

11.7 Power Series Representations of Functions

43

11.8 MacLaurin and Taylor Series

44

11.9 Applications of Series

45

11.10 Binomial Series

46

Review

47

Exam 5 on Chapter 11

48

13.1 Plane Curves (parametric form)

49

13.2 Tangent Lines and Arc L
ength

50

13.3 Polar Coordinates

51

13.3 Polar Coordinates

52

13.4 Integrals in Polar Coordinates

53

13.5 Polar Equations of Conic Sections

54

13.5 Polar Equations of Conic Sections

55

Review

56

Exam 5 on Chapter 13

57

Review for Final

58

Revi
ew for Final