Created on: October 29, 2014

Website Address: https://library.curriki.org/oer/AD14-Geometric-interpretation-of-differential-equations-via-slope-fields-70634

TABLE OF CONTENTS

- Curriki Project Based Geometry
- Curriki Calculus: Applications of Derivatives
- Curriki Calculus: Integrals

- How Random Is My Life? Teacher Edition
- How Random Is My Life? Student Edition
- How Random Is My Life? Resources
- Curriki Geometry Tools and Resources

- Selling Geometry
- Designing a Winner
- What's Your Angle, Pythagoras?
- TED Talk: House of the Future
- The Art of Triangles
- How Random Is My Life?
- Introduction to Angles
- Lesson -- Drawing right triangles from word problems
- Accessing Curriki Geometry Projects
- Introduction to Curriki Geometry

- Integrals Table of Contents by Standard
- I.1: Use Rectangle Approximations to Find Approximate Values of Integrals.
- I.2: Calculate the Values of Riemann Sums.
- I.3: Interpret a Definite Integral as a Limit of Riemann Sums.
- I.4: Understand the Fundamental Theorem of Calculus
- I.5: Use the Fundamental Theorem of Calculus.
- I.6: Understand and Use the Properties of Definite Integrals.
- I.7: Understand and Use Integration by Substitution.
- I.8: Understand and Use Riemann Sums and Trapezoidal Sums.

- Applications of Derivatives Table of Contents by Standard
- AD.1: Find the slope of a curve at a point.
- AD.2: Find a tangent line to a curve at a point and a local linear approximation.
- AD.3: Decide where functions are decreasing and increasing.
- AD.4: Solve real-world and other mathematical problems involving extrema.
- AD.5: Analyze real-world problems modeled by curves.
- AD.6: Find points of inflection of functions.
- AD.7: Use first and second derivatives to help sketch graphs.
- AD.8: Compare the corresponding characteristics of the graphs of f, f', and f".
- AD.9: Solve optimization real-world problems with and without technology.
- AD.10: Find average and instantaneous rates of change.
- AD.11: Find the velocity and acceleration of a particle moving in a straight line.
- AD.12: Model rates of change, including related rates problems.
- AD.13: Interpret a derivative as a rate of change in applications.
- AD.14 Geometric interpretation of differential equations via slope fields

- Differential Equations
- Slope fields
- Slope Fields
- Slope Field: Example 1
- ODE | Slope fields
- Differential Equations & Slope Fields
- Slope Fields
- Differential Equations Exercises
- Introduction to Differential Equations Exercises
- Slope Fields Exercises
- Differential Equations; First-Order Linear Equations Exercises
- Separable Equations Exercises

Geometric interpretation of differential equations via slope fields and the relationship between slope fields and solution curves for differential equations

Mooculus Calculus Textbook Section 11.2 pp 193-195

It may be hard or even impossible to find an explicit solution to for some differential equations. Fortunately, if the DE is 1st order we can graph the differential equation’s slope field and see the solution curves, even if we cannot write down their exact equation.

A Firefly Lectures video on this topic.Video duration: 9:34

A Firefly Lectures video on this topic.Video duration: 9:56

A Youtube video on this topic.Video duration: 4:39

A Math League of America video on this topic.Video duration: 18:53

A calculus applet illustrating the topic. Requires security enabled Java.

Mooculus Calculus Textbook Exercises, Sect 11.2 p 196 (ex 9&10) (Ans p 253)This set of exercises supports the following Standards of Mathematical Practice1 Make sense of problems and persevere in solving them.2 Reason abstractly and quantitatively.5 Use appropriate tools strategically.6 Attend to precision.7 Look for and make use of structure.

This set of exercises supports the following Standards of Mathematical Practice1 Make sense of problems and persevere in solving them.2 Reason abstractly and quantitatively.4 Model with mathematics.5 Use appropriate tools strategically.6 Attend to precision.7 Look for and make use of structure.

This set of exercises supports the following Standards of Mathematical Practice1 Make sense of problems and persevere in solving them.2 Reason abstractly and quantitatively.4 Model with mathematics.5 Use appropriate tools strategically.6 Attend to precision.7 Look for and make use of structure.

This set of exercises supports the following Standards of Mathematical Practice1 Make sense of problems and persevere in solving them.2 Reason abstractly and quantitatively.5 Use appropriate tools strategically.6 Attend to precision.7 Look for and make use of structure.

This set of exercises supports the following Standards of Mathematical Practice1 Make sense of problems and persevere in solving them.2 Reason abstractly and quantitatively.4 Model with mathematics.5 Use appropriate tools strategically.6 Attend to precision.7 Look for and make use of structure.