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. Ba1 is easily seen to be an isomorphism and hence is invertible, and thus that Ba2 is an isomorphism. Since Ba2a is an isomorphism, Ba2 is injective, and. This isomorphism is called the covariant exterior derivative. There is also a contravariant exterior derivative, given by the formula.
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. Ask and Answer the Calculus Problem of the Week You can print them out at home, and take the completed test in the office for feedback. Chapters 8 and 9 of this book are a collection of problem-solving exercises based on selected..
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