Linear Compartment Models in Engineering & Medicine
Dr. John PaisLadue Horton Watkinspais.john@gmail.comLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=<Text-field style="Heading 1" layout="Heading 1">3x3 Eigenvalue & Eigenvector Examples: Flow Curves for Dynamical Systems </Text-field>
Example 1. Real Distinct EigenvaluesEnter the three rows of the matrix A and the initialization vector.
Click anywhere into the math area below and press [Enter].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Example 1. Real Distinct Eigenvalues (continued)Using the P matrix you computed by hand.
Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
Click anywhere into the math area below and press [Enter].LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEoJmFscGhhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEqJmNvbG9uZXE7RidGMkY1LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYmUTBmbG93Q3VydmVJbnB1dFBGJy9GMFEldHJ1ZUYnRjIvRjZRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiwtRiw2I1EhRictRiM2Ki1GVzYnLUYjNigtSSNtbkdGJDYlUSI0RidGMkY1LUY5Ni5RIixGJ0YyRjVGPC9GP0ZTRkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTlEsMC4zMzMzMzMzZW1GJy1GX282JVEiMEYnRjJGNUZiby1GX282JVEiMUYnRjJGNUY1RjJGNS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Ziby1GVzYnLUYjNiktRjk2LlEqJnVtaW51czA7RidGMkY1RjxGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GXnEtRl9vNiVRIjJGJ0YyRjVGYm9GXXBGYm9Gam9GNUYyRjVGYHBGY3BGYm8tRlc2Jy1GIzYpRmpwRmBxRmJvRmpvRmJvRl1wRjVGMkY1RmBwRmNwRmJvLUZXNictRiM2KEZeb0Ziby1GX282JVEiOEYnRjJGNUZiby1GX282JVEjMTJGJ0YyRjVGNUYyRjVGYHBGY3BGNUZlbkZiby1GVzYnLUYjNipGam9GYm9GanBGXXBGYm9GanAtSSZtZnJhY0dGJDYoRl1wLUYjNiZGYHFGUkYyRlQvJS5saW5ldGhpY2tuZXNzR0ZfcC8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zecy8lKWJldmVsbGVkR0YxRjVGMkY1RmBwRmNwRmJvLUZXNictRiM2KEZdcEZib0ZdcEZib0ZdcEY1RjJGNUZgcEZjcEZiby1GVzYnLUYjNihGam9GYm9GXXBGYm9GXXBGNUYyRjVGYHBGY3BGNUYyRjUtRjk2LVEiOkYnRjVGPEY+RkBGQkZERkZGSEZKRk0vJStleGVjdXRhYmxlR0YxRjU=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFHExample 2. Real Distinct EigenvaluesEnter the three rows of the matrix A and the initialization vector.
Click anywhere into the math area below and press [Enter].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 2. Real Distinct Eigenvalues (continued)Using the P matrix you computed by hand.
Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
Click anywhere into the math area below and press [Enter].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JSFHExample 3. Real Distinct EigenvaluesEnter the three rows of the matrix A and the initialization vector.
Click anywhere into the math area below and press [Enter].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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Example 3. Real Distinct Eigenvalues (continued)Using the P matrix you computed by hand.
Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
Click anywhere into the math area below and press [Enter].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JSFHExample 4. Complex EigenvaluesEnter the three rows of the matrix A and the initialization vector.
Click anywhere into the math area below and press [Enter].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JSFHExample 4. Complex Eigenvalues (continued)Using the P matrix you computed by hand.
Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
Click anywhere into the math area below and press [Enter].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JSFHExample 5. Complex EigenvaluesEnter the three rows of the matrix A and the initialization vector.
Click anywhere into the math area below and press [Enter].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Example 5. Complex Eigenvalues (continued)Using the P matrix you computed by hand.
Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
Click anywhere into the math area below and press [Enter].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JSFHExample 6. Complex EigenvaluesEnter the three rows of the matrix A and the initialization vector.
Click anywhere into the math area below and press [Enter].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JSFHExample 6. Complex Eigenvalues (continued)Using the P matrix you computed by hand.
Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
Click anywhere into the math area below and press [Enter].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JSFHExample 7. Real Repeated EigenvaluesEnter the three rows of the matrix A and the initialization vector.
Click anywhere into the math area below and press [Enter].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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFHExample 7. Real Repeated Eigenvalues (continued)Using the P matrix you computed by hand.
Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
Click anywhere into the math area below and press [Enter].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JSFHExample 8. Real Repeated EigenvaluesEnter the three rows of the matrix A and the initialization vector.
Click anywhere into the math area below and press [Enter].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Example 8. Real Repeated Eigenvalues (continued)Using the P matrix you computed by hand.
Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
Click anywhere into the math area below and press [Enter].LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEoJmFscGhhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEqJmNvbG9uZXE7RidGMkY1LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYmUTBmbG93Q3VydmVJbnB1dFBGJy9GMFEldHJ1ZUYnRjIvRjZRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNi4tRiw2I1EhRictRiM2J0Zlbi1GIzYpLUZXNictRiM2Ki1JI21uR0YkNiVRIjNGJ0YyRjUtRjk2LlEiLEYnRjJGNUY8L0Y/RlNGQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjMzMzMzMzNlbUYnLUY5Ni5RKiZ1bWludXMwO0YnRjJGNUY8Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmBwLUZhbzYlUSIxRidGMkY1RmRvLUZhbzYlUSIyRidGMkY1RjJGNUYyRjUvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGZG8tRlc2Jy1GIzYqRmBvRmRvRlxwRmJwRmRvLUZhbzYlUSI2RidGMkY1RjJGNUYyRjVGaHBGW3FGZG8tRlc2Jy1GIzYrRlxwRmVwRmRvRmVwRmRvRlxwRmVwRjJGNUYyRjVGaHBGW3FGMkY1RmVuRjJGNUZlbkZkby1GVzYnLUYjNigtRmFvNiVRIjRGJ0YyRjVGZG8tRmFvNiVRIjhGJ0YyRjVGZG8tRmFvNiVRIzEyRidGMkY1RjVGMkY1RmhwRltxRmRvLUZXNictRiM2KkZccC1JJm1mcmFjR0YkNihGYnAtRiM2JEZlcEY1LyUubGluZXRoaWNrbmVzc0dGZHAvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGY3MvJSliZXZlbGxlZEdGMUZkb0ZicEZkb0ZccEZlcEY1RjJGNUZocEZbcUZkby1GVzYnLUYjNilGXHAtRltzNihGYG8tRiM2JkZlcEZSRjJGVEZfc0Zhc0Zkc0Zmc0Zkb0ZicEZkby1GYW82JVEiMEYnRjJGNUY1RjJGNUZocEZbcUZkby1GVzYnLUYjNihGYnBGZG9GYHRGZG9GYnBGNUYyRjVGaHBGW3FGNUYyRjUtRjk2LVEiOkYnRjVGPEY+RkBGQkZERkZGSEZKRk0vJStleGVjdXRhYmxlR0YxRjU=JSFHExample 9. Real Repeated EigenvaluesHirsch and Smale Example 2, p. 112. Check new flowCurvePlus with one Eigenvalue with multiplicity 2 but S + N needed
since only one basis eigenvector, thus must find the kernel of Caley-Hamilton power operator for the basis.
Click anywhere into the math area below and press [Enter].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Example 9. Real Repeated Eigenvalues (continued)Using the P matrix you computed by hand.
Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
Click anywhere into the math area below and press [Enter].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JSFHExample 10. Real Repeated EigenvaluesEnter the three rows of the matrix A and the initialization vector.
Click anywhere into the math area below and press [Enter].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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Example 10. Real Repeated Eigenvalues (continued)Using the P matrix you computed by hand.
Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
Click anywhere into the math area below and press [Enter].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
<Text-field style="Heading 1" layout="Heading 1">3x3 Eigenvalue & Eigenvector Examples: Flow Curves for Brine Tank Dynamical Systems</Text-field>
Linear Compartment Model: Recall our previous Brine Tank (used in water softeners) Cascade Problem for an Open 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LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlIVEpRiotJS5CT1VORFNfSEVJR0hURzYjJCIlcUtGKi0lKUNISUxEUkVORzYiJSFHBrine Tank Cascade Problem 1. Real Distinct Eigenvalues
Enter the three rows of the matrix A and the initialization vector.
Click anywhere into the math area below and press [Enter].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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Brine Tank Cascade Problem 1. Real Distinct Eigenvalues (continued)Using the P matrix you computed by hand.
Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
Click anywhere into the math area below and press [Enter].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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFHLinear Compartment Model: Brine Tank Cascade Problem for a Closed 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LSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlIVEpRiotJS5CT1VORFNfSEVJR0hURzYjJCIlP0tGKi0lKUNISUxEUkVORzYiBrine Tank Cascade Problem 2. Complex Eigenvalues
Enter the three rows of the matrix A and the initialization vector.
Click anywhere into the math area below and press [Enter].LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnRjIvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZJLUYsNiVRLmZsb3dDdXJ2ZVBsdXNGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYsLUZUNiYtRiM2Ki1GNjYtUSomdW1pbnVzMDtGJ0YyRjlGO0Y9Rj9GQUZDRkUvRkhRLDAuMjIyMjIyMmVtRicvRktGam4tSSZtZnJhY0dGJDYoLUkjbW5HRiQ2JFEiMUYnRjItRiM2JS1GYG82JFEiMkYnRjIvJTBmb250X3N0eWxlX25hbWVHUSgyRH5NYXRoRidGMi8lLmxpbmV0aGlja25lc3NHRmJvLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl9wLyUpYmV2ZWxsZWRHRjEtRjY2LVEiLEYnRjJGOS9GPEZQRj1GP0ZBRkNGRS9GSFEmMC4wZW1GJy9GS1EsMC4zMzMzMzMzZW1GJy1GYG82JFEiMEYnRjJGZHAtRl1vNihGX28tRiM2JS1GYG82JFEjMTBGJ0YyRk9GUUZbcEZdcEZgcEZicEZob0YyRjIvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGZHAtRlQ2Ji1GIzYqRlxvRmRwRmZuLUZdbzYoRl9vLUYjNiUtRmBvNiRRIjVGJ0YyRmhvRjJGW3BGXXBGYHBGYnBGZHBGXHFGaG9GMkYyRmZxRmlxRmRwLUZUNiYtRiM2KkZccUZkcEZgckZkcEZmbi1GXW82KEZfby1GIzYlRmNxRmhvRjJGW3BGXXBGYHBGYnBGaG9GMkYyRmZxRmlxRmRwLUZUNiYtRiM2KS1GYG82JFEiNEYnRjJGZHAtRmBvNiRRIjhGJ0YyRmRwLUZgbzYkUSMxMkYnRjJGaG9GMkYyRmZxRmlxLUYsNiNRIUYnRmhvRjJGMi1GNjYtUSI6RidGMkY5RjtGPUY/RkFGQ0ZFRkdGSkYyJSFHJSFHJSFHBrine Tank Cascade Problem 2. Complex Eigenvalues (continued)Using the P matrix you computed by hand.
Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
Click anywhere into the math area below and press [Enter].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 Tank Cascade Problem 3. Complex Eigenvalues
Enter the three rows of the matrix A and the initialization vector.
Click anywhere into the math area below and press [Enter].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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Brine Tank Cascade Problem 3. Complex Eigenvalues (continued)Using the P matrix you computed by hand.
Enter the three rows of the matrix A, the initialization vector, and the three rows of your P matrix.
Click anywhere into the math area below and press [Enter].LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEoJmFscGhhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEqJmNvbG9uZXE7RidGMkY1LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYmUTBmbG93Q3VydmVJbnB1dFBGJy9GMFEldHJ1ZUYnRjIvRjZRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNi4tRiw2I1EhRictRiM2KS1GVzYnLUYjNiotRjk2LlEqJnVtaW51czA7RidGMkY1RjxGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GYm8tSSZtZnJhY0dGJDYoLUkjbW5HRiQ2JVEiMUYnRjJGNS1GIzYlLUZobzYlUSIyRidGMkY1RjJGNS8lLmxpbmV0aGlja25lc3NHRmpvLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmRwLyUpYmV2ZWxsZWRHRjEtRjk2LlEiLEYnRjJGNUY8L0Y/RlNGQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjMzMzMzMzNlbUYnLUZobzYlUSIwRidGMkY1RmlwRmRvRjJGNUYyRjUvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGaXAtRlc2Jy1GIzYqRmRvRmlwRl5vLUZlbzYoRmdvLUYjNiUtRmhvNiVRIjVGJ0YyRjVGMkY1RmBwRmJwRmVwRmdwRmlwRmFxRjJGNUYyRjVGZHFGZ3FGaXAtRlc2Jy1GIzYqRmFxRmlwRl5yRmlwRl5vRmRvRjJGNUYyRjVGZHFGZ3FGMkY1RmVuRmlwLUZXNictRiM2KC1GaG82JVEiNEYnRjJGNUZpcC1GaG82JVEiOEYnRjJGNUZpcC1GaG82JVEjMTJGJ0YyRjVGNUYyRjVGZHFGZ3FGaXAtRlc2Jy1GIzYqRmdvRmlwRl5vLUZlbzYoLUYjNiUtRmhvNiVRIjNGJ0YyRjVGMkY1LUYjNiZGXXBGUkYyRlRGYHBGYnBGZXBGZ3BGaXBGXm8tRmVvNihGZ29GYXRGYHBGYnBGZXBGZ3BGNUYyRjVGZHFGZ3FGaXAtRlc2Jy1GIzYpLUZlbzYoRmByLUYjNiRGXXBGNUZgcEZicEZlcEZncEZpcC1GZW82KC1GIzYkRl50RjVGW3VGYHBGYnBGZXBGZ3BGaXBGXm8tRmVvNihGZ29GW3VGYHBGYnBGZXBGZ3BGNUYyRjVGZHFGZ3FGaXAtRlc2Jy1GIzYoRmdvRmlwRmFxRmlwRmdvRjVGMkY1RmRxRmdxRjVGMkY1LUY5Ni1RIjpGJ0Y1RjxGPkZARkJGREZGRkhGSkZNLyUrZXhlY3V0YWJsZUdGMUY1JSFH
<Text-field style="Heading 1" layout="Heading 1">3x3 Eigenvalue & Eigenvector Examples: Flow Curves for Drug Absorption Model Dynamical Systems</Text-field>
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on the edge of the image below to see vcr controls (in the task bar above) to run the animation.
Drug Absorption Model Linear Solution Functions: General Percent Concentration Functions
Click anywhere into the math area below and press [Enter].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 Absorption Model Linear Solution Functions: Specific Percent Concentration Functions for start values of the animation above.
Click anywhere into the math area below and press [Enter].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Note that these Linear Solution Functions above can be found by soving the eigenvalue problem immediately below: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 Model Problem 1. Real Distinct Eigenvalues
Enter the three rows of the matrix A and the initialization vector.
Click anywhere into the math area below and press [Enter].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
<Text-field style="Heading 1" layout="Heading 1">Drug Absorption Model</Text-field><Text-field style="Normal" layout="Normal">Define general model for first-order absorption with metabolite concentration, which specializes</Text-field><Text-field style="Normal" layout="Normal">to the first-order absorption model with metabolite elimination when k4 = 0, and to the standard
first-order absorption model when k3 = k4 = 0.</Text-field>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<Text-field 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style="Heading 1" layout="Heading 1">Flow Curve Code with P as 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style="Heading 1" layout="Heading 1">Vector Calculus APIs </Text-field>
JSFH<Text-field style="Heading 1" layout="Heading 1">Various Useful Examples</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=<Text-field bookmark="examples" style="Heading 2" layout="Heading 2">Examples-plots</Text-field>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Plot a sequence of related arrows.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Plot three points with various 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three points using various 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a sequence of arrows of differing sizes.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Display the eigenvectors of a given 3x3 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a directional plot for a given vector-valued 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triads at a number of 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bookmark="examples" style="Heading 2" layout="Heading 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bookmark="examples" style="Heading 2" layout="Heading 2">Examples-map</Text-field>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map(proc(x,y) x^2+y end proc, [1,2,3,4], 2);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The following example counts the number of finite Abelian groups of the order n by using the map and map2 commands.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtRiw2JVE2TnVtYmVyT2ZBYmVsaWFuR3JvdXBzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GOlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUy1GIzYpRistRiM2Jy1GLDYlUSJuRidGNkY5LUY9Ni1RIzo6RidGQEZCRkVGR0ZJRktGTUZPL0ZSUSYwLjBlbUYnL0ZVRltvLUYsNiVRJ3Bvc2ludEYnRjZGOS8lK2V4ZWN1dGFibGVHRkRGQC1GPTYtUSgmIzg1OTQ7RidGQEZCRkVGR0ZJRktGTUZPRmpuRlxvLUYjNictRiw2JVEkbXVsRidGNkY5LUY9Ni1RMCZBcHBseUZ1bmN0aW9uO0YnRkBGQkZFRkdGSUZLRk1GT0ZqbkZcby1JKG1mZW5jZWRHRiQ2JC1GIzYoLUYsNiVRImtGJ0Y2RjktRj02LVEiLEYnRkBGQi9GRkY4RkdGSUZLRk1GT0Zqbi9GVVEsMC4zMzMzMzMzZW1GJy1GIzYoRmJwLUY9Ni1RIj1GJ0ZARkJGRUZHRklGS0ZNRk9GUUZULUYjNictRiw2JVEkbWFwRidGNkY5RmpvLUZecDYkLUYjNilGKy1GIzYnLUYsNiVRKWNvbWJpbmF0RidGNkY5LUY9Ni1RIzotRidGQEZCRkVGR0ZJRktGTUZPRmpuRlxvLUYsNiVRKW51bWJwYXJ0RidGNkY5RmBvRkBGZXAtRiM2Jy1GLDYlUSVtYXAyRidGNkY5RmpvLUZecDYkLUYjNiktRiw2JVEjb3BGJ0Y2RjlGZXAtSSNtbkdGJDYkUSIyRidGQEZlcC1JJW1zdWJHRiQ2JS1GIzYnLUYsNiVRKWlmYWN0b3JzRidGNkY5RmpvLUZecDYkLUYjNiVGWkZgb0ZARkBGYG9GQC1GIzYlRmBzRmBvRkAvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Zgb0ZARkBGYG9GQEYrRmBvRkBGQEZgb0ZARitGYG9GQEYrRmBvRkBGQEZgb0ZARitGYG9GQEYrRmBvRkBGK0Zgb0ZARitGYG9GQA==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVE2TnVtYmVyT2ZBYmVsaWFuR3JvdXBzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjpRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZELyUpc3RyZXRjaHlHRkQvJSpzeW1tZXRyaWNHRkQvJShsYXJnZW9wR0ZELyUubW92YWJsZWxpbWl0c0dGRC8lJ2FjY2VudEdGRC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlMtSShtZmVuY2VkR0YkNiQtRiM2JS1JI21uR0YkNiRRIjRGJ0ZALyUrZXhlY3V0YWJsZUdGREZARkBGaW5GQEYrRmluRkBGK0ZpbkZALUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVE2TnVtYmVyT2ZBYmVsaWFuR3JvdXBzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjpRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZELyUpc3RyZXRjaHlHRkQvJSpzeW1tZXRyaWNHRkQvJShsYXJnZW9wR0ZELyUubW92YWJsZWxpbWl0c0dGRC8lJ2FjY2VudEdGRC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlMtSShtZmVuY2VkR0YkNiQtRiM2JS1JI21uR0YkNiRRIjZGJ0ZALyUrZXhlY3V0YWJsZUdGREZARkBGaW5GQEYrRmluRkBGK0ZpbkZALUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVE2TnVtYmVyT2ZBYmVsaWFuR3JvdXBzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjpRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZELyUpc3RyZXRjaHlHRkQvJSpzeW1tZXRyaWNHRkQvJShsYXJnZW9wR0ZELyUubW92YWJsZWxpbWl0c0dGRC8lJ2FjY2VudEdGRC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlMtSShtZmVuY2VkR0YkNiQtRiM2JS1JI21uR0YkNiRRJDc2OEYnRkAvJStleGVjdXRhYmxlR0ZERkBGQEZpbkZARitGaW5GQEYrRmluRkA=The map command can be used with type atomic.sum_to_product:=proc(expr)
if expr::atomic then
expr;
elif expr::`+` then
`*`(op(expr));
else
map(procname,expr); end if;
end proc: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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=