Course and Title
MATH 2320: Ordinary Differential Equations
Discipline/Program
Mathematics
Program/Discipline
Goals: If Applicable
Prefix
MATH - Mathematics
Course Level
Sophomore
Course Title
Ordinary Differential Equations
Course Rubric and
Number (e.g. HIST 1301)
Semester with Course
Reference Number
(CRN)
Course Location/Times
MATH 2320
Course Semester Credit
Hours (SCH) (lecture,
lab) If applicable
3 credit (3 lecture).
Course Contact Hours –
specify total numbers
48
Audience
This is a sophomore level mathematics course, which requires a background consisting of
Calculus I and II.
Course Continuing
Education Units (CEU): If
applicable
Course Length (number
of weeks)
Type of Instruction:
Instructor contact
information (phone
number and email
address)
Office location and
hours
Course Description:
ACGM or WECM
Solutions of ordinary differential equations and applications.
Course Description: HCC
Catalog Description
MATH 2320 Ordinary Differential Equations. Topics include initial value problems for first order
and linear second order equations, Picard iterations, series solutions, and boundary value
problems. Laplace transforms and numerical methods.
Course Prerequisite(s)
MATH 2414.
Course Goal
This course provides the background in sciences for further study in mathematics and its
applications.
1. Classify and solve first- and second-order differential equations, and use these methods to
solve applied problems.
2. Solve higher-order linear differential equations and systems of differential equations, and use
these methods to solve applied problems.
3. Find Laplace transforms and inverse transforms, and apply these to solve differential
equations.
4. Use numerical methods to approximate the solution of a differential equation.
Course Student Learning
Outcomes (SLO): 4 to 7
SLO Assessment(s)
Learning
Objectives(Numbering
system should be linked
to SLO – e.g., 1.1, 1.2,
1.3, etc.)
SCANS or Core
Curriculum
Competencies: If
Applicable
1.1 Verify that a function is a solution for a given differential equation.1.2 Derive a differential
equation from a given physical situation.1.3 Determine by inspection at least two solutions of a
given initial-value problem.1.4 Solve a given differential equation by separation of variables or
by using an appropriate substitution.1.5 Solve given exact differential equations subject in
indicated initial conditions.1.6 Solve the given Ricatti equation.1.7 Use Picard’s method to find
y1, y2, y3 for a given differential equation.1.8 Find the orthogonal trajectories of a given family
of curves.2.1 Determine whether a set of functions are linearly dependent or independent on (∞,∞).2.2 Determine whether an nth-order differential equation is homogeneous, or
nonhomogeneous.2.3 Apply the superposition principle for homogeneous and
nonhomogeneous equations.2.4 Given a differential equation and one solution, find the second
solution.2.5 Solve a given differential equation by undetermined coefficients.2.6 Find a linearly
independent function that is annihilated by a given differential operator.2.7 Solve given
differential equations by variation of parameters or by involving Cauchy-Euler equation.2.8 Solve
the given system of differential equations by either systemic elimination or determinants.2.9
Use the Laplace transform to solve a given system of differential equations.2.10 Rewrite a given
system in normal form.2.11 Solve a given system of equations by either Gaussian elimination or
Gauss-Jordan elimination.2.12 Solve a given system of linear first-order equations using
matrices.2.13 Solve a given system of homogeneous linear systems.2.14 Use the method of
undetermined coefficients to solve a given system on (-∞,∞).2.15 Use variation of parameters
to solve a given system of equations.2.16 Use matrix exponentials.3.1 Find the Laplace
Transform of a given function.3.2 Find the inverse Laplace Transform of a given function.3.3
Given a Laplace Transform of an integral, evaluate the transform without evaluating the
integral.3.4 Use the Laplace transform to solve the given differential equation subject to the
given boundaries.
1.1 Verify that a function is a solution for a given differential equation.
1.2 Derive a differential equation from a given physical situation.
1.3 Determine by inspection at least two solutions of a given initial-value problem.
1.4 Solve a given differential equation by separation of variables or by using an appropriate
substitution.
1.5 Solve given exact differential equations subject in indicated initial conditions.
1.6 Solve the given Ricatti equation.
1.7 Use Picard’s method to find y1, y2, y3 for a given differential equation.
1.8 Find the orthogonal trajectories of a given family of curves.
2.1 Determine whether a set of functions are linearly dependent or independent on (-∞,∞).
2.10 Rewrite a given system in normal form.
2.11 Solve a given system of equations by either Gaussian elimination or Gauss-Jordan
elimination.
2.12 Solve a given system of linear first-order equations using matrices.
2.13 Solve a given system of homogeneous linear systems.
2.14 Use the method of undetermined coefficients to solve a given system on (-∞,∞).
2.15 Use variation of parameters to solve a given system of equations.
2.16 Use matrix exponentials.
2.2 Determine whether an nth-order differential equation is homogeneous, or
nonhomogeneous.
2.3 Apply the superposition principle for homogeneous and nonhomogeneous equations.
2.4 Given a differential equation and one solution, find the second solution.
2.5 Solve a given differential equation by undetermined coefficients.
2.6 Find a linearly independent function that is annihilated by a given differential operator.
2.7 Solve given differential equations by variation of parameters or by involving Cauchy-Euler
equation.
2.8 Solve the given system of differential equations by either systemic elimination or
determinants.
2.9 Use the Laplace transform to solve a given system of differential equations.
3.1 Find the Laplace Transform of a given function.
3.2 Find the inverse Laplace Transform of a given function.
3.3 Given a Laplace Transform of an integral, evaluate the transform without evaluating the
integral.
3.4 Use the Laplace transform to solve the given differential equation subject to the given
boundaries.
4.1 Find the interval of convergence of a given power series.
4.2 For a given differential equation, find two linearly independent power series solutions about
a point.
4.3 Use the method of Frobenius to obtain two linearly independent series solutions about the
point x0=0.
4.4 Sketch the direction field for a given differential equation.
4.5 Given an initial-value problem, use Euler formula to obtain a four-decimal approximation.
4.6 Given an initial-value problem, use Runge-Kutta methods to obtain a four decimal
approximation.
4.7 Use the finite difference method to approximate a solution for a second-order differential
equation.
Course Calendar
Course Outline: Instructors may find it preferable to cover the course topics in the order listed
below. However, the instructor may choose to organize topics in any order, but all material must
be covered.
UNIT I - Introduction to Differential Equations Sections: 1.1, 1.2, 1.3
(4 hours)
This unit begins with some definitions and introduces certain terminology. Included are InitialValue problems and some mathematical modeling.
UNIT II - First-order Differential Equations Sections: 2.1, 2.2, 2.3, 2.4, 2.5, 2.6
(6 hours)
This unit includes the solution of first-order differential equations using the following
techniques/methods: separation of variables, exact equations, linear equations, solutions by
substitution, and a numerical solution.
UNIT III - Modeling with First-Order Differential Equations Sections: 3.1, 3.2, 3.3
(4 hours)
This unit solves some of the problems that commonly arise in modeling applications.
UNIT IV - Differential Equations of Higher Order Sections: 4.1, 4.2, 4.3, 4.4, 4.5,
(8 hours)
4.6, 4.7, 4.8, 4.9
This unit begins with some preliminary theorems including reduction of order. Also included are
the techniques to solve homogeneous linear equations (with constant coefficients). CauchyEuler equations and some nonlinear equations. The chapter includes the study of Undetermined
Coefficients (Superposition approach). Undetermined Coefficients (Annihilator approach ) and
Variation of parameters.
UNIT V - Modeling with Higher Order Differential Equations Sections: 5.1, 5.2, 5.3
(3 hours)
This unit begins with Linear Equations and initial-value problems. Also, included are Linear
Equations - Boundary-Value problems and nonlinear equations.
UNIT VI -Series Solutions of Linear Equations Sections: 6.1, 6.2, 6.3,
(4 hours)
This unit begins with a review of Power Series and then proceeds to Power Series solutions. Also
included are solutions about ordinary and singular points. The two special functions - Bessel’s
equation and Legendre’s equation.
UNIT VII -Laplace Transform
Sections: 7.1, 7.2, 7.3,
(7 hours)
7.4, 7.5, 7.6,This unit begins with the definition of the Laplace transform with
some introductory examples. Included are the theorems of first and second translation,
derivatives of a transform. Also, transforms of derivatives, integrals and periodic functions and
the Dirac Delta Function. The chapter concludes with systems of Linear Equations.
UNIT VIII -Systems of First-Order Linear Differential Equations Sections: 8.1, 8.2, 8.3,
(7 hours)
8.4(Optional)
This unit begins with the preliminary theory to solve Homogeneous Linear Systems with
Constant Coefficients (including distinct real eignenvalues, repeated eigenvalues and complex
eigenvalues). Also, included are variation of parameters and matrix exponential.
UNIT IX -Numerical Methods for Ordinary Differential Equations Sections: 9.1, 9.2, 9.3
(5 hours)
9.4(Optional)
Included in this chapter are Direction Fields, Euler-Methods, Runge-Kutta Method and Multstep
methods.
Instructional Methods
Requisites
Student Assignments
Student Assessment(s)
Instructional Materials
A First Course in Differential Equations with Modeling Applications, Zill, Dennis, Brooks Cole
Publishing Company, 7th ed., 2001.ISBN 0534379990
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1. Each instructor must cover all course topics by the end of the semester. The final exam is
comprehensive and questions on it can deal with any of the course objectives.
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the first week of class.
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final examination must be taken by all students.
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5. The final exam must count for at least 25 to 40 percent of the final grade.
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90-100 "A"; 80-89 "B"; 70-79 "C"; 60-69 "D"; Below 60 "F"