## Resources

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Resource Type (20)

Modeling Scenario(11) Technique Narrative(2) Potential Scenario(4) Free Online Textbook(2) General Resource(1)

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Differential Equation Type (20)

ODE(20) Integral(1) First(9) Second(4) Higher(2) Linear(10) Nonlinear(2) System(9) Constant Coeff(3) Homogeneous(1) Nonhomogeneous(2)

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Technique (757)

Boundary Value Problems(71) Eigen Methods(15) Exact Equations(1) Fourier Series(1) Initial Value Problems(557) Integrating Factor(21) Laplace Transform(20) Linear Algebra(10) Matrices(9) Numerical Methods(104) Parameter Estimation(286) Qualitative Behavior(59) Separable(51) Separation of Variables(83) Series(3) Substitution Methods(4) Theory (general)(4) Undetermined Coefficients(2) Variation of Parameters(2) Other(65)

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Chemistry(2) Economics(3) Engineering(12) Life Sciences(3) Mathematics(9) Modeling (general)(12) Physics(6) Social Sciences(2)

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Calculus 2(6) Differential Equations(20) Modeling(17)

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Asking a question(12) Formulating hypotheses(8) Predicting outcomes(2) Gathering data/making observations(2) Analyzing data(3) Interpreting results/data(6) Displaying/modeling results/data(7) Communicating results(4)

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Computer Model(1) Physical Model(1) Guided inquiry/investigation(9)

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Vision and Change Core Competencies - Ability (13)

Create and develop models(11) Use quantitative reasoning(9) Tap into interdisciplinary study(8) Communicate and collaborate with mathematics community(2) Communicate and collaborate with other disciplines(3) Understand the relationship between material and society(1)

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Motivates student to learn material(14) Focuses student on the material to be learned(12) Reveals prior knowledge(1)

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Includes clear efforts on Issues (0)

###### Applied Filters

General Resource

##### Instructor Solutions Second Edition SIMIODE Textbook HTML Version

This is material we make available for instructors teaching a modeling-first approach to differential equations when using the Second Edition of SIMIODE Textbook, Differential Equations: A Toolbox for Modeling the Real World in HTML Version.Modeling Scenario

##### 1-027-StochasticProcesses-ModelingScenario

We build the infinite set of first order differential equations for modeling a stochastic process, the so-called birth and death equations. We will only need to use integrating factor solution strategy or DSolve in Mathematica for success.Modeling Scenario

##### 1-155-CruiseControl-ModelingScenario

In this project we illustrate the design of a proportional-integral-derivative (PID) cruise control algorithm for an automobile. PID control is one of the most common techniques in control engineering.Potential Scenario

##### 2018-LA_Peletier-Ordinary Differential Equations in Pharmacodynamics

Good mix of theory, application, solution technique in a number of areas of applications of differential equations. Develops qualitative behavior issues. Exercises, but not about models, more about the mathematics only.Potential Scenario

##### 2016-Roberto_Camporesi-A fresh look at linear ordinary differential equations with constant coefficients

We present an approach to the impulsive response method for solving linear constant-coefficient ordinary differential equations of any order based on the factorization of the differential operator.Potential Scenario

##### 2015-Carl_Lutzer-Using Expected Value to Introduce the Laplace Transform

We propose an introduction to the Laplace transform in which Riemann sums are used to approximate the expected net change in a function, assuming that it quantifies a process that can terminate at random.Potential Scenario

##### 2009-Martinez-Luaces-Modelling Applications Inverse Modelling

The discussion in this paper will deal with non-typical inverse problems and how they can be used in engineering courses.Free Online Textbook

##### 2016-Simon_Malham-Differential_Equations_and_Linear_Algebra

This is a nice set of notes on which a course can be based. There is ample material on first and second order, linear systems, and Laplace Transform methods for setting up and solving differential equations.Free Online Textbook

##### 2011-Steven_Desjardins-Remi_Vaillancourt-Ordinary_Differential_Equations_Laplace_Transforms_and_Numerical_Methods_for_Engineers

This text is packed with worked out presentations, problems, and exercises (with solutions) and MatLab code. There is sufficient detail and attention to topics to more than address interests/needs in an introductory course.Modeling Scenario

##### 9-125-BeamModeling-ModelingScenario

This modeling scenario examines the deflection of a cantilever beam under two different distributed loads. Students will have the opportunity to conduct experiments with their own cantilever beam or use data provided to build a model.Modeling Scenario

##### 7-011-CoupledSystemLaplace-ModelingScenario

Differential equations and Laplace transforms are an integral part of control problems in engineering systems. We consider a baby warming device.Technique Narrative

##### 7-006-LaplaceTransformBirth-TechniqueNarrative

We present a way of introducing the Laplace Transform as the continuous analogue of a power series expression of a function.Technique Narrative

##### 7-005-OverViewLaplaceTransforms-TechniqueNarrative

This is a specialized overview of Laplace Transform application to solving differential equations in Mathematica.Modeling Scenario

##### 3-092-WirelessPower-ModelingScenario

We present an engineering application (wireless power transmission) modelled by a coupled system of two linear second-order differential equations with constant coefficients. One equation is homogeneous while the other one is non-homogeneous.Modeling Scenario

##### 5-036-HalfCarVibration-ModelingScenario

Vibration vehicle models provide an opportunity to integrate vehicle-based vibrations into a mechanical engineering vibrations course. The project is on a multiple-degree-of-freedom (MDOF) including pitch and bounce of vehicle body on suspension...Modeling Scenario

##### 7-020-ThermometerInVaryingTempStream-ModelingScenario

We present a first order differential equation model for the temperature of a mercury thermometer which is sitting in a stream of water whose temperature oscillates. We suggest a solving strategy which uses Laplace Transforms.Modeling Scenario

##### 7-040-TankInterruptMixing-ModelingScenario

We present a first order differential equation model for the interrupted mixing of a tank with salt water. We offer two solution strategies (1) two step approach and (2) Laplace Transforms.Modeling Scenario

##### 7-010-MultipleDoses-ModelingScenario

Two multiple dose drug administration regimens are offered. A drug is to maintain a certain level (above a set minimum and below a set maximum) in the blood stream and one regimen involves bolus injections and another involves steady drip flow...Modeling Scenario

##### 4-023-MysteryCircuit-ModelingScenario

Students to build a system of differential equations which model a circuit. We give each student a unique input voltage frequency parameter and ask for system response (gain) to that input as a voltage over one of the resistors.Modeling Scenario