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In each of 1 through 5, (a) verify that the given

Advanced Engineering Mathematics | 7th Edition | ISBN: 9781111427412 | Authors: Peter V. O'Neill ISBN: 9781111427412 173

Solution for problem 10.1 Chapter 10

Advanced Engineering Mathematics | 7th Edition

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Advanced Engineering Mathematics | 7th Edition | ISBN: 9781111427412 | Authors: Peter V. O'Neill

Advanced Engineering Mathematics | 7th Edition

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Problem 10.1

In each of 1 through 5, (a) verify that the given functions satisfy the system, (b) write the system in matrix form X= AX for an appropriate A, (c) write n linearly independent n 1 matrix solutions 1, , n , for appropriate n, (d) use the determinant test of Theorem 10.2(2) to verify that these solutions are linearly independent, (e) form a fundamental matrix for the system, and (f) use the fundamental matrix to solve the initial value problemx 1 = 5x1 + 3x2, x 2 = x1 + 3x2, x1(t)= c1e2t + 3c2e6t , x2(t) = c1e2t + c2e6t , x1(0)= 0, x2(0) = 4

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PSY 340 Chapter 6: Acquiring Language Components of Language  Arbitrariness  Productivity o Infinite number of combinations are possible from a finite number of parts  Regularity o Sentences follow a system of rules (grammar)  Semanticity  Displacement Theoretical Perspectives on Language  Nativist Theory o Idealized grammar o Impoverished input o Rudimentary learning mechanism o Domain specific (encapsulated)  Learning Theory o Real language is messy o Rich input o Powerful learning mechanism o Domain General mechanisms Critical Period  Period of language learning that is suggested to be biologic determinants of acquiring language  Statistically regular patterns in learning native language Mass Exposure to language: makes it impossible to rule out learning  Tomasello (2006)  Children 2-3 hearing 5000-7000 words a day  Argues for repetition helping toddlers learn statistically regular patterns of native language We have impressive learning ability  Saffran experiment(1996)  8 month olds can track transitional probabilities between syllables  paditobukuboktidofo How quickly do we learn language  Milestones o Reduplicated, canonical babbling (6-7) o Common words (6-9) o Jargon babbling (9-18) o First words (9-15) o Vocab explosion (18-24) o Two-word combinations (24) o Complex sentences (30-48) Aspects of Language  Phonology o Perceiving speech is hard because we don’t break in speech o Prototypes and Language  CATEGORICAL PERCEPTION  Language occurs on continuum, we only LEARN phoneme divisions through our conditioned discrimination between sounds  /d/-/t/ contrast o Critical period of perception of phonemes, (8-10 months they lose ability to discriminate NON NATIVE phonemes)  Synaptic pruning  More attuned to native language o Starts out as domain general, categorical perception is NOT encapsulated  **Encapsulation: a process specialized for a specific purpose, encapsulated processes are domain specific (processing is specific for a particular domain of perception such as speech or vision) o Production  Stages:  Cooing: vowels only  Babbling: repeated syllables  Intersubjectivity: interacting to produce shared meaning (infants who don’t have the words to make requests use gestures) Semantics  Early vocabulary  Comprehension  Precedes production  Children can use gestures to convey more complex meanings than words alone  Vocabulary size  16 months: produce 55 words  23 months: produce 225 words  30 months: produce 573 words  6 years: produce 6000 words  By 6 years, children comprehend approximately 14,000 words  Word Growth:  General nominals: nouns (dog, ball)  Specific nominals: names (Mommy, Daddy, Rover)  Action words: verbs (go, up, look)  Modifiers: (big, all gone)  Others: personal social words (no, want, please), function words (the, is, for) spurt  Individual differences: although general nouns dominate the first 50 words there is variability in which words children  learn within the first 50. Some children focus on specific names for objects. Other children focus on social words. o Naming insight Underextensions and Overextensions  Underextension – using a word in an overly narrow context  Using the word ‘dog’ to refer to only one dog ‘Spot’ and no other dogs, or using the word shoes to refer to ‘sneakers’ but not Mom’s sandals.  Overextension – using a word in an overly broad context  Using the word ‘dog’ to refer to all furry creatures  Constraints on word learning  Fast mapping and the word spurt  The whole object assumption  Labels refer to the whole thing, not the thing’s parts  The taxonomic assumption  Words refer to things of the same kind or general category (not things that merely tend to occur with that object)  The mutual exclusivity assumption  If a word already exists for an object a new label will refer to an object part Fast Mapping - the ability to hear a novel phonological string once and map it to an object or action -early language: By the age of 2 years, children are acquiring 10 new words per day -Often they hear a novel phonological string once, and learn it = “fast mapping” Morphology  Morpheme: the smallest unit of meaning in a language  Free and bound morphemes  Free morphemes (words) stand alone  Bound morphemes cannot (e.g. un-, -s, -ed, -ing)  Wug test o Gleason Syntax - Knowing rules about how words may form legal combinations in sentences - We see evidence of syntax as earlier as 18-24 months of age in children’s productions - Two-word stage o Pivot grammars Pragmatics  Pragmatic knowledge: understanding the communicative functions of language  Discourse knowledge: understanding the mechanics of conversation (e.g. that people take turns when speaking)  Sociolinguistic knowledge: knowing how language differs as a function of the social class or status of the conversational partner or the formality of the setting.  Pragmatic principles  Quantity: be as informative as is required  Quality: be truthful, don’t make false statements, only make statements for which you have adequate evidence  Relation: be relevant  Manner: be clear, brief, unambiguous  Take turns: don’t interrupt, don’t monopolize conversation

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Chapter 10, Problem 10.1 is Solved
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Textbook: Advanced Engineering Mathematics
Edition: 7
Author: Peter V. O'Neill
ISBN: 9781111427412

This textbook survival guide was created for the textbook: Advanced Engineering Mathematics, edition: 7. Since the solution to 10.1 from 10 chapter was answered, more than 273 students have viewed the full step-by-step answer. The answer to “In each of 1 through 5, (a) verify that the given functions satisfy the system, (b) write the system in matrix form X= AX for an appropriate A, (c) write n linearly independent n 1 matrix solutions 1, , n , for appropriate n, (d) use the determinant test of Theorem 10.2(2) to verify that these solutions are linearly independent, (e) form a fundamental matrix for the system, and (f) use the fundamental matrix to solve the initial value problemx 1 = 5x1 + 3x2, x 2 = x1 + 3x2, x1(t)= c1e2t + 3c2e6t , x2(t) = c1e2t + c2e6t , x1(0)= 0, x2(0) = 4” is broken down into a number of easy to follow steps, and 107 words. This full solution covers the following key subjects: . This expansive textbook survival guide covers 23 chapters, and 1643 solutions. The full step-by-step solution to problem: 10.1 from chapter: 10 was answered by , our top Math solution expert on 12/23/17, 04:48PM. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9781111427412.

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In each of 1 through 5, (a) verify that the given