Differential Equations Teacher Resources
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Differential Equations and Slope Fields
Students solve differential equations. For this differential equations lesson, students use their TI-89 calculator to explore slope fields and find solutions to a differential equation. They graph their solutions.
Approxiamte Solutions to Differential Equations-Slope Fields (graphical) and Euler's Method (numeric)
Twelfth graders explore differential equations. In this calculus lesson, 12th graders explore Euler’s Methods of solving differential equations. Students use the symbolic capacity of the TI-89 to compare Euler’s Method of numeric solutions to a graphical solution.
Biological Models with Differential Equations
Explore differential equations by using models representing growth and decline. Using calculus, learners will investigate exponential and logistic growth in the context of several models representing the growth or decline of a population. Most of the models have a closed-form solutions. Problems and solutions are included.
Worksheet Seventeen: Differential Equations
In this differential equation worksheet, students solve differential equations and graph solutions. This two-page worksheet contains 8 multi-step problems.
Solving Differential Equations via the Fundamental Theorem of Calculus
Students use their TI-89 calculator to compute derivatives and anti-derivatives. In this differential equation lesson, students follow detailed directions to complete one table of derivative/anti-derivative values. They compute the anti-derivative of one equation and find the derivative of one equations.
The Spread of Disease with Differential Equations
Twelfth graders solve problems using differential equations. In this Calculus lesson, 12th graders analyze data regarding the spread of a flu virus. Students use the symbolic capacity of the TI-89 to develop a model and analyze the spread of the disease.
Differential Equations with the TI-86
Students explore how to graph differential equations using a TI calculator. In this math lesson, students solve systems of equations using the calculator. Students explore graphing and use it to interpret experimental data.
Linear Systems: Applications of Linear Algebra to Differential Equations
In this differential equations worksheet, learners solve systems of simultaneous differential equations using linear algebra. This six-page worksheet contains approximately six problems, with explanations and examples.
A Simple Model for Atmospheric Carbon Dioxide
In this atmospheric carbon dioxide worksheet, students use two diagrams to solve 6 problems about atmospheric carbon dioxide. One diagram shows the Keeling Curve and the other shows sources of carbon and the natural and anthropogenic flux. Students find sources and sinks of carbon dioxide, they write a differential equation describing the change in carbon dioxide in the atmosphere and they use the Keeling Curve to compare it to their equation for the rate of change.
Logistic Growth, Differential Equations, Slope Fields
Investigate differential equations with your class. They use the TI-89 to explore differential equations analytically, graphically, and numerically as the examine the relationships between each of the three approaches.
An Introduction to Solving Differential Equations
Twelfth graders investigate differential equations. For this calculus lesson, 12th graders are presented with a step-by-step illustrated review of the process used in solving differential equations and an application problem. Students solve differential equations and application of differential equations.
Differential Equations on the TI-92 PLUS
Students identify and familiarize themself with the features and capabilities of the TI-92 Plus calculator. They also find symbolic solutions of differential equations and general solutions or to find particular solutions of initial-value and boundary-value problems. Finally, students use TRACE to find numerical values for this phase-plane graph.
Using Slope Fields
Twelfth graders investigate slope fields. In this Calculus lesson, 12th graders identify whether a slope field appropriately reflects a differential equation by matching. TI-83 Plus/TI-84 Plus and appropriate programs are required to complete the lesson.
Students investigate differential equations and slope fields. In this differential equations and slope fields lesson, students determine how much time can pass before a cup of coffee is safe to drink. Students use a differential equation to solve the problem algebraically. Students create a slope field to represent the time at which it is safe to drink the coffee.
Newton's Law of Cooling
Twelfth graders investigate exponential decay. For this Calculus lesson, 12th graders explore Newton’s Law of cooling which can be modeled by a differential equation. Students use the model to solve a murder as they examine the temperature of a body to determine time of death.
Recovering a Function from its Derivative: A Graphical Approach
Students follow detailed instructions for using their TI-86 graphing calculator to find solutions to differential equations. In this lesson, students learn to use their graphing calculator to solve 12 differential equations.
Slope Fields and Euler's Method for AP Calculus
Twelfth graders investigate slope fields and Euler’s Method. In this calculus lesson, 12th graders explore the steps for programming slope fields on the TI-83 and Euler’s method for achieving a numerical solution to differential equations.
Introduction to Slope Fields
Students plot slope fields. In this introduction to slope fields lesson, students plot 12 slope fields for given differential equations.
Variational Calculus 3
In this methods of applied mathematics worksheet, students solve 5 various types of problems that relate to variational calculus equations. First, they determine a second order differential equation for the geodesic. Then, students write down Euler Lagrange equations for 2 dependent variables, and then determine a system of first order differential equations describing motion of an object.
Students solve derivatives of differential equations. For this calculus lesson, students solve equations using the derivative to obtain no differentials in the equation. They complete an assignment in the text book also.