# Math 2420: Differential Equations

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Summer 2018

Synonym: 55690, Section: 001, Northridge 2244
Monday / Wednesday 10:30 am- 1:05 pm

Differential Equations, MATH 2420, Learning Outcomes

STUDENT LEARNING OUTCOMES - A student who has taken this course should be able to:

1. Identify and classify homogeneous and nonhomogeneous equations/systems, autonomous equations/systems, and linear and nonlinear equations/systems.
2. Solve first order differential equations using standard methods, such as separation of variables, integrating factors, exact equations, and substitution methods; use these methods to solve analyze real-world problems in fields such as economics, engineering, and the sciences.
3. Solve second and higher order equations using reduction of order, undetermined coefficients, and variation of parameters; use these methods to solve analyze real-world problems in fields such as economics, engineering, and the sciences.
4. Solve systems of equations and use eigenvalues and eigenvectors to analyze the behavior and phase portrait of the system; use these methods to solve analyze real-world problems in fields such as economics, engineering, and the sciences.
5. Use LaPlace transforms to solve initial value problems.
6. Solve boundary value problems and relate the solution to the Fourier series; use these methods to solve analyze real-world problems in fields such as economics, engineering, and the sciences.

The objectives of Differential Equations are for the students to understand the following topics and to be able to apply these concepts to solve application problems.

Differential Equations covers the following topics.

1.     First order differential equations, slope fields, numerical solution methods and the basic analytical solution methods: separation of variables, solving exact equations, solving linear equations, and substitution methods.

2.     Higher order linear differential equations, both homogeneous and nonhomogeneous with methods of reduction of order, undetermined coefficients, and variation of parameters.

3.     Systems of linear differential equations, phase portraits, numerical solution methods and analytical solution methods: using eigenvalues and eigenvectors and using systematic elimination.

4.     Use of the LaPlace transform and series methods for solving differential equations. Other topics will be explored as time permits

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You are expected to conduct yourself professionally with respect and courtesy to all. Anyone who thoughtlessly or intentionally jeopardizes the health or safety of another individual will be immediately dismissed from the day’s activity, may be withdrawn from the class, and/or barred from attending future activities.

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Course Outline and Approximate Calendar:
Please note:  schedule changes may occur during the semester.
Any changes will be announced in class.

 Week Dates Sections Topics 1 5/28/18 Holiday - no class 5/30/18 1.1 - 1.4 Mathematical models, integrals as solutions, slope fields, and separation of variables 2 6/4/18 1.5 - 1.6 Linear first order equations and substitution methods 6/6/18 1.6, 2.1 More substitution methods, exact equations, and population models 3 6/11/18 2.2 - 2.3 Equilibrium solutions and acceleration/velocity models 6/13/18 2.4 - 2.6 Numerical approximation methods Test 1 – Dates to be announced in class 4 6/18/18 5.1 - 5.2 Intro to systems of equations, review of matrices, the eigenvalue solution method 6/20/18 5.2 - 5.3 More on eigenvalue solutions - complex eigenvalues, phase portraits 5 6/25/18 5.3, 5.5 More on phase portraits, repeated eigenvalues 6/27/18 5.7 Non-homogeneous systems 6 7/2/18 6.1-6.3 Nonlinear systems and ecological models 7/4/18 Holiday - no class Test 2 – Dates to be announced in class 7 7/9/18 3.1-3.3 Higher order linear equations, solving homogeneous equations with constant coefficients 7/11/18 3.5 Non-homogeneous equations with undetermined coefficients, the Exponential Input Theorem 8 7/16/18 3.4, 3.7, 3.8 Mechanical applications and electrical circuits, reduction of order and basic boundary value problems with eigenvalues 7/18/18 7.1 – 7.2 Laplace transforms and initial value problems 9 7/23/18 7.3 - 7.4 Translations, derivatives, integrals, and products of transforms 7/25/18 7.5 - 7.6 Periodic and piecewise continuous functions and transforms, impulse and delta functions Test 3 – Dates to be announced in class 10 7/30/18 8.1 - 8.2 Series and series solutions near ordinary points 8/1/18 9.1 – 9.2 Fourier series and convergence 11 8/6/18 9.3 Even and odd extensions and Fourier Sine and Cosine series 8/8/18 9.5 Separation of variables and the heat equations 12 8/13/18 Final Exam

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It was last updated on May 24, 2018 .