# Math 2420: Differential Equations

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Fall 2018

SySynonym: 62618, Section: 002, Northridge 2245
Monday / Wednesday 7:35 pm - 9:20 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.

• 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.
• Higher order linear differential equations, both homogeneous and nonhomogeneous with methods of reduction of order, undetermined coefficients, and variation of parameters.
• Systems of linear differential equations, phase portraits, numerical solution methods and analytical solution methods: using eigenvalues and eigenvectors and using systematic elimination.
• Use of the LaPlace transform and series methods for solving differential equations. Other topics will be explored as time permits

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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 8/27/18 1.1 - 1.2 Mathematical models, integrals as solutions 8/29/18 1.3 - 1.4 Slope fields, and separation of variables 2 9/3/18 Holiday - no class 9/5/18 1.5 - 1.6 Linear first order equations and substitution methods 3 9/10/18 1.6, 2.1 More substitution methods, exact equations, and population models 9/12/18 2.2 - 2.3 Equilibrium solutions and acceleration/velocity models 4 9/17/18 2.4 - 2.5 Numerical approximation methods 9/19/18 2.6 More numerical methods and review for Test 1 Test 1 – Dates to be announced in class 5 9/24/18 5.1 Intro to systems of equations, review of matrices, 9/26/18 5.2 The eigenvalue solution method 6 10/1/18 5.2 More on eigenvalue solutions 10/3/18 5.3 Phase portraits 7 10/8/18 5.5 Repeated eigenvalues 10/10/18 5.7 Non-homogeneous systems 8 10/15/18 6.1-6.2 Nonlinear systems 10/17/18 6.3 Ecological models and review for Test 2 Test 2 – Dates to be announced in class 9 10/22/18 3.1-3.3 Higher order linear equations, solving homogeneous equations with constant coefficients 10/24/18 3.5 Non-homogeneous equations with undetermined coefficients 10 10/29/18 3.4, 3.7 Mechanical applications and electrical circuits 10/31/18 3.7, 3.8 More electrical circuits, reduction of order and basic boundary value problems with eigenvalues 11 11/5/18 7.1 – 7.2 Laplace transforms and initial value problems 11/7/18 7.3 - 7.4 Translations, derivatives, integrals, and products of transforms 12 11/12/18 7.5 Periodic and piecewise continuous functions and transforms 11/14/18 7.6 Impulse and delta functions and review for Test 3 Test 3 – Dates to be announced in class 13 11/19/18 8.1 - 8.2 Series and series solutions near ordinary points 11/21/18 8.3 Cauchy-Euler equations and series solutions near regular singular points 14 11/26/18 9.1 – 9.2 Fourier series and convergence 11/28/18 9.3 Even and odd extensions and Fourier Sine and Cosine series 15 12/3/18 9.4 Applications of Fourier series 12/5/18 9.5 Separation of variables and the heat equations 16 12/10/18 Final Exam, Part 1 12/12/18 Final Exam, Part 2

This webpage was created by Marcus McGuff.
It was last updated on August 26, 2018 .