DIVERGENCE by Corinne Manogue Copyright 1997 Corinne Manogue 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Note: arrows are scaled in Maple plots so that the longest arrow in a given graph has length equal to the grid unit. 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 Now try another vector field: 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 Now try another vector field: 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

Now try another vector field: 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 Now try another vector field: 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 Now try another vector field: 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2JUYrLUYjNiUtRiw2JlEncGxvdDNkRicvJSVib2xkR1EmZmFsc2VGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUTAmQXBwbHlGdW5jdGlvbjtGJ0Y2L0Y9USdub3JtYWxGJy8lJmZlbmNlR0Y4LyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlUtSShtZmVuY2VkR0YkNiUtRiM2Li1GLDYmUSNmNkYnRjZGOUY8LUZANi5RIixGJ0Y2RkNGRS9GSEY7RklGS0ZNRk9GUUZTL0ZXUSwwLjMzMzMzMzNlbUYnLUYjNiYtRiw2JlEieEYnRjZGOUY8LUZANi5RIj1GJ0Y2RkNGRUZHRklGS0ZNRk9GUS9GVFEsMC4yNzc3Nzc4ZW1GJy9GV0Zpby1GIzYmRistRiM2JC1GQDYuUSomdW1pbnVzMDtGJ0Y2RkNGRUZHRklGS0ZNRk9GUS9GVFEsMC4yMjIyMjIyZW1GJy9GV0ZjcC1JI21uR0YkNiVRIjJGJ0Y2RkMtRkA2LlEjLi5GJ0Y2RkNGRUZHRklGS0ZNRk9GUUZicEZWRmVwRitGam4tRiM2Ji1GLDYmUSJ5RidGNkY5RjxGZW9GW3BGK0Zqbi1GIzYlLUYsNiZRJnN0eWxlRidGNkY5RjxGZW8tRiw2JlEtcGF0Y2hjb250b3VyRidGNkY5RjxGam4tRiM2JS1GLDYmUSxvcmllbnRhdGlvbkYnRjZGOUY8RmVvLUZZNictRiM2JkYrLUYjNiRGX3AtRmZwNiVRIzkwRidGNkZDRmpuLUZmcDYlUSIwRidGNkZDL0Y9USVib2xkRicvJStmb250d2VpZ2h0R0Zbcy8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Zqbi1GIzYlLUYsNiZRKHNoYWRpbmdGJ0Y2RjlGPEZlby1GLDYmUSV6aHVlRidGNkY5RjxGK0ZqckZcc0YrRis=

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