Prof. Douglas Meade: New Applications
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en-us2021 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSat, 23 Oct 2021 09:05:50 GMTSat, 23 Oct 2021 09:05:50 GMTNew applications published by Prof. Douglas Meadehttps://www.maplesoft.com/images/Application_center_hp.jpgProf. Douglas Meade: New Applications
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Lesson 19 -- Application: Rocket Flight
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Models and solutions for rocket flight.<img src="https://www.maplesoft.com/view.aspx?si=4707//applications/images/app_image_blank_lg.jpg" alt="Lesson 19 -- Application: Rocket Flight" style="max-width: 25%;" align="left"/>Models and solutions for rocket flight.https://www.maplesoft.com/applications/view.aspx?SID=4707&ref=FeedWed, 01 Oct 2003 00:00:00 ZProf. Douglas MeadeProf. Douglas MeadeLesson 18: Finite Difference Method
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Overview of the Finite Difference Method and examples.<img src="https://www.maplesoft.com/view.aspx?si=4706//applications/images/app_image_blank_lg.jpg" alt="Lesson 18: Finite Difference Method" style="max-width: 25%;" align="left"/>Overview of the Finite Difference Method and examples.https://www.maplesoft.com/applications/view.aspx?SID=4706&ref=FeedWed, 01 Oct 2003 00:00:00 ZProf. Douglas MeadeProf. Douglas MeadeLesson 17: Shooting Method
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The Second-Order Boundary Value Problem
Overview of the Shooting Method<img src="https://www.maplesoft.com/view.aspx?si=4705//applications/images/app_image_blank_lg.jpg" alt="Lesson 17: Shooting Method" style="max-width: 25%;" align="left"/>The Second-Order Boundary Value Problem
Overview of the Shooting Methodhttps://www.maplesoft.com/applications/view.aspx?SID=4705&ref=FeedWed, 01 Oct 2003 00:00:00 ZProf. Douglas MeadeProf. Douglas MeadeLesson 16: Runge-Kutta Method
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Runge-Kutta Method<img src="https://www.maplesoft.com/view.aspx?si=4704//applications/images/app_image_blank_lg.jpg" alt="Lesson 16: Runge-Kutta Method" style="max-width: 25%;" align="left"/>Runge-Kutta Methodhttps://www.maplesoft.com/applications/view.aspx?SID=4704&ref=FeedWed, 01 Oct 2003 00:00:00 ZProf. Douglas MeadeProf. Douglas MeadeLesson 15: Improved Euler's Method
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Improved Euler's method<img src="https://www.maplesoft.com/view.aspx?si=4703//applications/images/app_image_blank_lg.jpg" alt="Lesson 15: Improved Euler's Method" style="max-width: 25%;" align="left"/>Improved Euler's methodhttps://www.maplesoft.com/applications/view.aspx?SID=4703&ref=FeedWed, 01 Oct 2003 00:00:00 ZProf. Douglas MeadeProf. Douglas MeadeLesson 13: Direction Fields and Phase Portraits
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A direction field for a two-dimensional system of first-order ODEs, drawn in the phase plane for the system, is similar to the direction field for a single first-order ODE.<img src="https://www.maplesoft.com/view.aspx?si=4702//applications/images/app_image_blank_lg.jpg" alt="Lesson 13: Direction Fields and Phase Portraits" style="max-width: 25%;" align="left"/>A direction field for a two-dimensional system of first-order ODEs, drawn in the phase plane for the system, is similar to the direction field for a single first-order ODE.https://www.maplesoft.com/applications/view.aspx?SID=4702&ref=FeedWed, 01 Oct 2003 00:00:00 ZProf. Douglas MeadeProf. Douglas MeadeLesson 12: Slope Fields
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slope fields<img src="https://www.maplesoft.com/view.aspx?si=4701//applications/images/app_image_blank_lg.jpg" alt="Lesson 12: Slope Fields" style="max-width: 25%;" align="left"/>slope fieldshttps://www.maplesoft.com/applications/view.aspx?SID=4701&ref=FeedWed, 01 Oct 2003 00:00:00 ZProf. Douglas MeadeProf. Douglas MeadeLesson 11: First-Order Linear Systems
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Equilibrium Analysis
Graphical Analysis
Analytic Solutions
Numerical Solutions<img src="https://www.maplesoft.com/view.aspx?si=4700//applications/images/app_image_blank_lg.jpg" alt="Lesson 11: First-Order Linear Systems" style="max-width: 25%;" align="left"/>Equilibrium Analysis
Graphical Analysis
Analytic Solutions
Numerical Solutionshttps://www.maplesoft.com/applications/view.aspx?SID=4700&ref=FeedWed, 01 Oct 2003 00:00:00 ZProf. Douglas MeadeProf. Douglas MeadeLesson 10: Substitution and Change of Variables
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Homogeneous Equations
Bernoulli Equations
Reduction to Separation of Variables
Riccati Equations<img src="https://www.maplesoft.com/view.aspx?si=4699//applications/images/app_image_blank_lg.jpg" alt="Lesson 10: Substitution and Change of Variables" style="max-width: 25%;" align="left"/>Homogeneous Equations
Bernoulli Equations
Reduction to Separation of Variables
Riccati Equationshttps://www.maplesoft.com/applications/view.aspx?SID=4699&ref=FeedWed, 01 Oct 2003 00:00:00 ZProf. Douglas MeadeProf. Douglas MeadeLesson 9: Application: Orthogonal Trajectories
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Trajectories Orthogonal to a Family of Circles<img src="https://www.maplesoft.com/view.aspx?si=4697//applications/images/app_image_blank_lg.jpg" alt="Lesson 9: Application: Orthogonal Trajectories" style="max-width: 25%;" align="left"/>Trajectories Orthogonal to a Family of Circleshttps://www.maplesoft.com/applications/view.aspx?SID=4697&ref=FeedWed, 01 Oct 2003 00:00:00 ZProf. Douglas MeadeProf. Douglas MeadeLesson 8: Exact Equations
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exact differential equations<img src="https://www.maplesoft.com/view.aspx?si=4696//applications/images/app_image_blank_lg.jpg" alt="Lesson 8: Exact Equations" style="max-width: 25%;" align="left"/>exact differential equationshttps://www.maplesoft.com/applications/view.aspx?SID=4696&ref=FeedWed, 01 Oct 2003 00:00:00 ZProf. Douglas MeadeProf. Douglas MeadeLesson 7: Application: The Spruce Budworm
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A classical example of bifurcation in nature is the interaction between the spruce budworm and balsam fir forests in North America.<img src="https://www.maplesoft.com/view.aspx?si=4695//applications/images/app_image_blank_lg.jpg" alt="Lesson 7: Application: The Spruce Budworm" style="max-width: 25%;" align="left"/>A classical example of bifurcation in nature is the interaction between the spruce budworm and balsam fir forests in North America.https://www.maplesoft.com/applications/view.aspx?SID=4695&ref=FeedWed, 01 Oct 2003 00:00:00 ZProf. Douglas MeadeProf. Douglas MeadeLesson 6: Bifurcations
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Graphical Approaches to Bifurcation
Analytic Determination of Bifurcation Points<img src="https://www.maplesoft.com/view.aspx?si=4694//applications/images/app_image_blank_lg.jpg" alt="Lesson 6: Bifurcations" style="max-width: 25%;" align="left"/>Graphical Approaches to Bifurcation
Analytic Determination of Bifurcation Pointshttps://www.maplesoft.com/applications/view.aspx?SID=4694&ref=FeedWed, 01 Oct 2003 00:00:00 ZProf. Douglas MeadeProf. Douglas MeadeLesson 5: Application: Mixing Problems
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One-Tank Mixing Problem
Variable Volume Mixing Problem
Two-Tank Mixing Problem<img src="https://www.maplesoft.com/view.aspx?si=4693//applications/images/app_image_blank_lg.jpg" alt="Lesson 5: Application: Mixing Problems" style="max-width: 25%;" align="left"/>One-Tank Mixing Problem
Variable Volume Mixing Problem
Two-Tank Mixing Problemhttps://www.maplesoft.com/applications/view.aspx?SID=4693&ref=FeedWed, 01 Oct 2003 00:00:00 ZProf. Douglas MeadeProf. Douglas MeadeLesson 4: First-Order Linear Equations
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Structure of Solutiosn to Linear ODEs
Integrating Factor for a First-Order Linear ODE<img src="https://www.maplesoft.com/view.aspx?si=4691//applications/images/app_image_blank_lg.jpg" alt="Lesson 4: First-Order Linear Equations" style="max-width: 25%;" align="left"/>Structure of Solutiosn to Linear ODEs
Integrating Factor for a First-Order Linear ODEhttps://www.maplesoft.com/applications/view.aspx?SID=4691&ref=FeedWed, 01 Oct 2003 00:00:00 ZProf. Douglas MeadeProf. Douglas MeadeLesson 3: Application: Exponential and Logistic Growth
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Solved problems:
Exponential Growth and Decay
Logistic Equation<img src="https://www.maplesoft.com/view.aspx?si=4690//applications/images/app_image_blank_lg.jpg" alt="Lesson 3: Application: Exponential and Logistic Growth" style="max-width: 25%;" align="left"/>Solved problems:
Exponential Growth and Decay
Logistic Equationhttps://www.maplesoft.com/applications/view.aspx?SID=4690&ref=FeedWed, 01 Oct 2003 00:00:00 ZProf. Douglas MeadeProf. Douglas MeadeLesson 2: Separable Equations
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General Solution Method for Separable ODEs<img src="https://www.maplesoft.com/view.aspx?si=4689//applications/images/app_image_blank_lg.jpg" alt="Lesson 2: Separable Equations" style="max-width: 25%;" align="left"/>General Solution Method for Separable ODEshttps://www.maplesoft.com/applications/view.aspx?SID=4689&ref=FeedWed, 01 Oct 2003 00:00:00 ZProf. Douglas MeadeProf. Douglas MeadeLesson 14: Euler's Method
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Euler's method for the solution of a first-order IVP<img src="https://www.maplesoft.com/view.aspx?si=1405/euler1502.gif" alt="Lesson 14: Euler's Method" style="max-width: 25%;" align="left"/>Euler's method for the solution of a first-order IVPhttps://www.maplesoft.com/applications/view.aspx?SID=1405&ref=FeedWed, 01 Oct 2003 00:00:00 ZProf. Douglas MeadeProf. Douglas MeadeLesson 1: Introduction to Differential Equations in Maple
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A differential equation can be entered in Maple using any of the methods for constructing algebraic, transcendental, or any other equation in Maple. It is a good idea to assign each differential equation to a unique, and descriptive, Maple name. Such assignments are typically done using an assignment statement . For example, the ordinary differential equation (ODE)
dx/dt = k*x
would be entered into Maple as
> ode := diff( x(t), t ) = k * x(t);<img src="https://www.maplesoft.com/view.aspx?si=1404/1505.gif" alt="Lesson 1: Introduction to Differential Equations in Maple" style="max-width: 25%;" align="left"/>A differential equation can be entered in Maple using any of the methods for constructing algebraic, transcendental, or any other equation in Maple. It is a good idea to assign each differential equation to a unique, and descriptive, Maple name. Such assignments are typically done using an assignment statement . For example, the ordinary differential equation (ODE)
dx/dt = k*x
would be entered into Maple as
> ode := diff( x(t), t ) = k * x(t);https://www.maplesoft.com/applications/view.aspx?SID=1404&ref=FeedWed, 01 Oct 2003 00:00:00 ZProf. Douglas MeadeProf. Douglas MeadeLesson 20 -- Application: Parachute Problem
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Models and solutions for a parachute problem.<img src="https://www.maplesoft.com/view.aspx?si=4708//applications/images/app_image_blank_lg.jpg" alt="Lesson 20 -- Application: Parachute Problem" style="max-width: 25%;" align="left"/>Models and solutions for a parachute problem.https://www.maplesoft.com/applications/view.aspx?SID=4708&ref=FeedWed, 01 Oct 2003 00:00:00 ZProf. Douglas MeadeProf. Douglas Meade