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| * | Group - Dept | Status | Approved | Date Reviewed | Reviewer | Comments |
|---|---|---|---|---|---|---|
| 1 | Curriculum Routing - MAT Mathematics | Completed | Approved | 01/31/2020 | Julie Napier | |
| 2 | Curriculum and Assessment - MAT Mathematics | Completed | Approved | 01/31/2020 | Carey Minnis | |
| 3 | Curriculum Committee - MAT Mathematics | Completed | Approved | 02/12/2020 | Carey Minnis | |
| 4 | Curriculum and Assessment (Second Review) - MAT Mathematics | Completed | Approved | 02/12/2020 | Carey Minnis | |
| 5 | Catalog and Articulation - MAT Mathematics | Completed | Approved | 02/12/2020 | Julie Napier |
| Originator: | Clifford, Laurel Status: Approved Department: MAT Mathematics |
| Date Created: | 01/30/2020 Submitted: 01/30/2020 Completed: 02/12/2020 To ACETS: |
| Course Number: | 260 |
| Course Information: | Course Modification to an existing course |
| Effective Academic Year: | 2020 |
| Course Full Title: | Introduction to Differential Equations |
| Program Modification Required?: | No |
| If yes, list the degree or certificate: | |
| Course Impact?: | No |
| If yes, list the degree or certificate: | |
| Purpose of Submission: | Change to an Established Course |
| Reason for Evaluation: | Objectives, Outcomes, and/or Competencies changes |
| Mode of Instruction: | traditional plural |
| If other, please explain: | |
| Catalog Course Description: | Introduces differential equations and their theoretical and practical solution techniques with an emphasis upon applications and problem solving using MATLAB. Includes solutions of first order differential equations, numerical techniques, linear equations of higher order, systems of linear differential equations, and Laplace transforms. |
| Prerequisite(s): | Successful completion (C or better) of MAT 241 |
| Corequisite(s): | |
| Previous Credit (Total): | 4 |
| Previous Lecture Hours: | 4 |
| Previous Lab Hours: | |
| Previous Clinical Hours: | |
| New Credit Hours (Total): | |
| New Lecture Hours: | |
| New Lab Hours: | |
| New Clinical Hours: | |
| New Internship Hours: | |
| Explanation of proposed modifications to course: | |
| Contact person/email: | Laurel Clifford, lclifford@mohave.edu; Matt Wienke, mwienke@mohave.edu |
| Is this course identified as a Writing Across the Curriculum (WAC) course?: | No |
| SUN Course?: | Yes |
| If yes, please provide the established SUN number: | MAT 2262 |
| Is this an AGEC course: | Yes |
| Articulated?: | Yes |
| Transfer?: | ASU NAU UA |
| Course Learning Outcomes: | 1. Solve first-order linear, separable, and exact equations. 2. Compute general solutions of higher-order linear Ordinary Differential Equations (ODEs) via undetermined coefficients, variation of parameters, power series, and Green's functions 3. Solve oscillatory systems (mechanical and electrical) modeled by linear second-order ODEs with constant coefficients. 4. Solve initial value problems for linear ODEs by Laplace transform techniques. 5. Compute solutions of linear first-order systems of ODEs with constant coefficients by the eigenvalue-eigenvector method. 6. Approximate solutions of IVPs for ODEs using Euler and Improved Euler methods. 7. Solve applied ODEs using MATLAB. |
| Course Competencies and Objectives OR Course Competencies and Outline: | Competency 1 Describe the basic terminology related to the field of differential equations.
Objective 1.1 Classify differential equations by order, linearity, and as ordinary or partial. Objective 1.2 Model simple physical processes using a first order linear differential equation. Objective 1.3 Describe solutions to differential equations qualitatively using direction fields. Objective 1.4 Use MATLAB dfield8 to plot direction fields. Objective 1.5 Solve simple differential equations using techniques from Calculus. Objective 1.6 Identify key personages in the historical development of differential equations. Objective 1.7 Use MATLAB to perform basic arithmetic and matrix operations, and to define and plot functions. Objective 1.8 Use scripts and function files in MATLAB to simplify repetitive processes and write programs involving conditions and looping procedures. Competency 2 Solve First Order Differential Equations Objective 2.1 Solve first order linear equations using the method of integrating factors. Objective 2.2 Solve first order linear and nonlinear equations using separation of variables. Objective 2.3 Model complex mixture problems and continuous compound interest using first order linear initial value problems. Objective 2.4 Distinguish between first order linear and nonlinear equations in regard to existence and uniqueness of a solution, the interval of definition, the existence of a general solution, and explicit solutions. Objective 2.5 Model population dynamics using the logistics growth equation. Objective 2.6 Describe qualitatively the solution of autonomous equations using phase line analysis. Objective 2.7 Solve exact differential equations. Competency 3 Solve differential equations using numerical techniques Objective 3.1 Apply Euler's Method to approximate solutions to differential equations using Excel. Objective 3.2 Apply the Improved Euler's Method to approximate solutions to differential equations using Excel. Objective 3.3 Apply the Runge-Kutta Method to approximate solutions to differential equations using Excel. Objective 3.4 Describe the order of the error involved with each of the previous techniques. Objective 3.5 Use a function file in MATLAB to apply Euler's and Improved Euler's methods to approximate and plot solutions to differential equations. Objective 3.6 Use MATLAB built in solver ode45 to solve linear and higher order initial value problems. Competency 4 Solve second order linear differential equations. Objective 4.1 Determine existence and uniqueness of second order linear differential equations. Objective 4.2 Apply the principle of superposition to solutions of second order linear equations. Objective 4.3 Apply the Wronskian determinant to determine if solutions form a fundamental set. Objective 4.4 Solve homogeneous equations with constant coefficients having real and different roots of the characteristic equation. Objective 4.5 Solve homogeneous equations with constant coefficients having complex roots of the characteristic equation. Objective 4.6 Solve homogeneous equations with constant coefficients having repeated roots of the characteristic equation. Objective 4.7 Use the method of reduction of order to find a second solution given one solution. Objective 4.8 Solve non-homogeneous equations using the method of undetermined coefficients. Objective 4.9 Solve non-homogeneous equations using variation of parameters. Objective 4.10 Model mechanical and electrical vibrations using second order linear equations. Objective 4.11 Solve damped and undamped free vibration problems and express solution as a single cosine function. Objective 4.12 Solve forced vibration problems with damping and express the solution as the sum of the steady state and transient solution. Objective 4.13 Use MATLAB to determine the effect of parameters on the solutions and behavior of a mass-spring system for both damped and undamped motion. Objective 4.14 Use MATLAB to explore the amplitude, resonance and beats of forced oscillations of a mass-spring system Competency 5 Apply the Laplace transform to solve differential equations. Objective 5.1 Compute the Laplace transform using the definition for various functions and step functions. Objective 5.2 Find the inverse Laplace transform for various functions and step functions. Objective 5.3 Solve initial value problems using the Laplace transform. Objective 5.4 Apply the Laplace transform to solve equations with discontinuous forcing functions. Competency 6 Solve systems of first order linear differential equations. Objective 6.1 Model two-mass, three-spring systems and complex mixture problems using a system of first order linear equations. Objective 6.2 Perform the following basic matrix operations: transpose, conjugate, adjoint, multiplication, inverse, row reduction, Gauss-Jordan elimination. Objective 6.3 Find the eigenvalues and eigenvectors of a square matrix. Objective 6.4 Determine the linear dependence of a set of eigenvectors. Objective 6.5 Solve homogeneous linear systems with constant coefficients having real eigenvalues. Objective 6.6 Solve homogeneous linear systems with constant coefficients having complex eigenvalues. Objective 6.7 Plot solution curves in the phase plane. Objective 6.8 Describe qualitatively the solution of a linear system using phase portraits. Objective 6.9 Use MATLAB pplane8 to plot phase portraits. Competency 7 Use power series to solve first and second order linear equations. Objective 7.1 Identify and classify ordinary points and singular points. Objective 7.2 Determine the existence and radius of convergence for power series solutions. Objective 7.3 Derive the series solutions for first and second order differential equations. Objective 7.4 Solve differential equations involving special functions of historical importance. |