Santa Monica College
Mathematics Department Addendum
Math 11–Multivariable Calculus
Prerequisite Comparison Sheet – exit skills of Math 8 and entry skills for Math 11.
Exit Skills for Math 8
Upon successful completion of Math 8, the student will be able to:
A.
Differentiate and integrate hyperbolic, logarithmic, exponential and inverse
trigonometric functions.
B.
E.
Evaluate integrals using techniques including integration by parts, partial fractions,
trigonometric integrals, and trigonometric and other substitutions.
Solve integral application problems including surface area of surfaces of revolution
and center of mass.
Identify and evaluate indeterminate forms and improper integrals using techniques
including L’Hôpital’s Rule.
Graph polar curves and curves described by parametric equations.
F.
Determine whether an infinite sequence converges or diverges.
G.
Determine whether an infinite series converges absolutely, converges conditionally
or diverges using techniques including the direct comparison, limit comparison,
root, ratio, integral, p-series, nth-term and alternating series tests.
Determine the radius and interval of convergence of a power series.
C.
D.
H.
I.
J.
Compute the sum of a convergent geometric series and a convergent telescoping
series.
Determine the Taylor series of a given function at a given point.
:
Entry Skills for Math 11.
Prior to enrolling in Math 11. students should be able to
1.
.2.
Apply concepts of limits, continuity and differentiability in two dimensions. M7
(A,B,C)
Differentiate and integrate exponential and logarithmic functions. M8 (A)
3.
Differentiate and integrate transcendental functions and inverses. M8 (A)
4.
Perform integration by parts. M8 (B)
5.
Perform integration using trigonometric substitution. M8 (B)
6.
Perform integration with powers of trigonometric functions. M8 (B)
7.
Resolve indeterminate forms using L’Hopital’s Rule. M8 (D)
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Entry Skills for Math 11.
8.
Set up Taylor series representations of transcendental functions. M8 (J)
9.
Use polar coordinates for plane curves. M8 (E)
10. Use of parametric equations for plane curves. M8 (E)
11. Find center of mass/ centroid. M8 (C)
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Santa Monica College
Student Learning Outcomes
Date: December 2009
Course Name and Number:
Math 11 Multivariable Calculus
Student Learning Outcome(s):
 Individual faculty members will develop and reports on assessments for SLOs.
1.
Given vector-valued or real-valued functions involving two or more independent variables,
students will identify and use appropriate techniques to analyze the fundamental properties of
those functions. Included would be partial and directional derivatives, gradients, differentials,
and integrals over lines, surfaces and solid regions.
2.
Students will be able to setup and solve physical applications problems related to all aspects
of motion along a curve. Included would be the arclength parametrization of a curve and the
use of tangent, velocity, normal and binormal vectors, curvature, and the tangential and
normal components of acceleration and their relationship to the osculating plane containing
the circle of best fit at a point on the curve.
3.
Students will be able to apply Green's Theorem, Stokes' Theorem, and Gauss' Divergence
Theorem with the concepts of divergence and curl and flux. Students will solve problems
related to vector fields including magnetic fields, flow fields, and conservative vector fields.
Demonstrate how this course supports/maps to at least one program and one 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 about more advanced mathematical functions, students will analyze
and solve abstract and practical problems.
2.
Institutional Outcome(s):
As a result of studying instructor feedback given during lecture, or written on
homework and exams, students will evaluate information critically and present
solutions in a clear and logical manner.
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Textbook: Earl Swokowski, Calculus, The Classic Edition, Brooks/Cole Publishing Co., 1991.
A Sample Schedule for Math 11 Multivariable Calculus
This schedule assumes a standard meeting schedule of 1 hour 5 minutes with 4 class meetings per
week.
Session
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
Text Section/Activity
Introduction, 14.1 - Vectors in Two Dimensions
14.1 Vectors in Two Dimensions
14.2 Vectors in Three Dimensions
14.3 The Dot Product
14.4 The Vector Product
14.5 Lines and Planes
14.5 Lines and Planes
14.6 Surfaces 1st day
14.6 Surfaces 2nd day
15.1 Vector-Valued Functions and Space Curves
Exam 1
15.2 Limits, Derivatives, and Integrals
15.3 Motion
15.4 Curvature
15.4 Curvature
15.5 Tangential and Normal Components of Acceleration
16.1 Functions of Several Variables
16.1 Functions of Several Variables
16.2 Limits and Continuity
16.2 Limits and Continuity
16.3 Partial Derivatives
16.4 Increments and Differentials
Exam 2
16.4 Increments and Differentials
16.5 Chain Rules
16.6 Directional Derivatives
16.6 Directional Derivatives
16.7 Tangent Planes and Normal Lines
16.8 Extrema of Functions of Several Variables
16.8 Extrema of Functions of Several Variables
16.9 Lagrange Multipliers
16.9 Lagrange Multipliers
Exam 3
17.1 Double Integrals
17.1-17.2 Double Integrals and Area and Volume
17.2 Area and Volume
17.3 Double Integrals in Polar Coordinates
17.4 Surface Area
17.5 Triple Integrals
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Session
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
Text Section/Activity
17.5 Triple Integrals
17.6 Moments and Center of Mass
17.7 Cylindrical Coordinates
17.8 Spherical Coordinates
Exam 4
18.1 Vector Fields
18.2 Line Integrals
18.2 Line Integrals
18.3 Independence of Path
18.3 Independence of Path
18.4 Green's Theorem
18.5 Surface Integrals
18.5 Surface Integrals
18.6 The Divergence Theorem
18.7 Stokes' Theorem
18.7 Stokes' Theorem
Exam 5
Review
Review