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
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