By Loomis, Lynn H. Loomis

This ebook is predicated on an honors Calculus path given within the Nineteen Sixties. The e-book includes extra fabric than was once regularly coated in anybody 12 months. it may be used (with omissions) for a year's direction in complex Calculus, or as a textual content for a 3-semester advent to research. There are workouts unfold in the course of the publication.

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Additional info for Advanced Calculus, Revised Edition

Example text

As the human brain matures, its plasticity declines, and so does its capacity for new forms of learning. Crucially, such decline intersects with what appears to be an epiphenomenal consequence of first language learning, namely that certain neural areas of the brain have become committed. Learning a second language, then, becomes imposing another system upon the existing neural template, hence parasitic in nature. In this context, transfer – primarily from the old system to the new system– is set to occur, not only due to the interconnected nature of the brain but importantly as a compensatory strategy for the loss of plasticity.

If such is the case, then it must be true that the only way that the avoided L2 elements may be produced subsequently by the L2 learner will have to be through ‘transfer’ of the L1 element to cover for the avoided L2 element. Therefore, one can expect the L2 user to continue producing the same deviant form for as long as the interlingual identification is maintained, granted that the L1 and L2 elements which have been (mis)perceived to be ‘identical’ are actually not identical. (Nakuma, 1998: 251) Thus, for Nakuma, fossilization arises from L2 learners’ individual perception of L1-L2 equivalents, the result of which may be positive or negative, depending on whether the form transferred from the L1 overlaps with the target L2 form.

Also automatic acquisition from mere exposure to a given language seems to disappear after this age, and foreign languages have to be taught and learned through a labored effort. Foreign accents cannot be overcome easily after puberty. However, a person can learn to communicate in a foreign language at the age of forty. (Lenneberg, 1967: 176) In simple terms, Lenneberg’s hypothesis predicts a rectangular function in the relationship between age of acquisition and ultimate performance. It is worth noting that the proposal evinces considerable vagueness.

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Advanced Calculus, Revised Edition by Loomis, Lynn H. Loomis
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