Santa Monica College
Mathematics Department Addendum
Math 15 – Differential equations
Prerequisite Comparison Sheet – exit skills of Math 8 and entry skills for Math 15
Exit Skills for Math 8
Upon successful completion of Math 8, the student will be able to:
A.
Differentiate and integrate exponential, logarithmic, hyperbolic functions..
B.
Use various techniques of integrations and applications
C.
Analyze infinite series (congruence and divergence).
D.
Use Power and Taylor series to express an infinite series
E.
F.
Recognize indeterminant forms and improper integral (using polar coordinates or
parametric equations).
Use analytical geometry (rotation of axes) to differentiate and integrate
G.
Evaluate limits using L'Hopital's Rule.
H.
Find center of mass (centroid) and surface area.
:
Entry Skills for Math 15
Prior to enrolling in Math 15 students should be able to
1.
.2.
Differentiate and integrate hyperbolic, logarithmic, exponential and inverse
trigonometric functions.
Evaluate integrals using techniques including integration by parts, partial
fractions, trigonometric integrals, and trigonometric and other substitutions.
3.
Identify and evaluate indeterminate forms and improper integrals using
techniques including L’Hopital’s Rule.
4.
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
5.
Determine the radius and interval of convergence of a power series.
6.
Determine the Taylor series of a given function at a given point.
Santa Monica College
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Santa Monica College
Student Learning Outcomes
Date: Fall 2009
Course Name and Number:
Math 15 Differential Equations
Student Learning Outcome(s):
 Individual faculty members will develop and reports on assessments for SLOs.
1.
Given a first/second order or nonhomogeneous linear differential equation, students will
determine and apply appropriate strategies to solve the differential equation.
2.
Given applied differential equation problems such as physical motion, orthogonal trajectories,
mixtures, springs or electrical circuits, students will determine and apply appropriate strategies
to set up and solve the problems.
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 concepts, 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.
Santa Monica College
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Textbook: Zill, Dennis G., A First Course in Differential Equations, The Classic 5th Ed., Brooks/Cole,
2001
A Sample Schedule for Math 15
This schedule assumes a standard meeting schedule of 1 hr 20 min with 2 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
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Text Section/Activity
1.1 Basic Definitions
2.1 Preliminary Theory
2.2 First Order Separable Equations
2.3 First Order Homogeneous Equations
2.4 First Order Exact Equations
2.5 First Order Linear Equations
2.6, 2.7 First Order Bernoulli, Ricatti, and Clairaut Equations; Substitutions
Exam 1
4.1 Linear DEs of Higher Order
4.1 Linear DEs of Higher Order (cont.)
4.1, 4.2 Nonhomogeneous Linear DEs of Higher Order, Reduction of Order
4.3 Homogeneous Linear Equations with Constant Coefficients
4.5, 4.6 Differential Operators, Annihilator Approach
4.7 Variation of Parameters
Review
Exam 2
5.1 Simple Harmonic Motion (Spring Motion)
6.1 Cauchy-Euler Equations
6.2 Power Series Review and Power Series Solutions
6.3 Series Solutions about Ordinary Points
6.4 Series Solutions near Singular Points: Method of Frobenius
7.1 Laplace Transform Introduction
7.2 Inverse Laplace Transform
Exam 3
7.3, 7.4
Translation Theorems, Derivative of Transform, Transforms of
Derivatives
7.5 Solving Initial-Value Problems by Laplace Transforms
8.1, 8.2 Solving Systems of DEs using Operators and Laplace Transforms
3.2/8.3 Applications: Mixing Problems
Review