ield ENGL 2110-01 Midterm You must write an essay for each of the following prompts. Part I: Write a 1500 word essay (you may go over this word count, but you should not fall short of this word count) on the following prompt: Many of the readings that we have covered up to this point in the class have considered the native population that explorers encountered when they came to the “New World.” For this essay, you should examine the readings from any two of the explorers that we have encountered to this point to compare and contrast the similarities and differences between the ways that these two explorers interacted with the indigenous peoples. The thesis for this essay should make an argumentative claim as to which approach was/is more effective, and the writer should use quotations in each body paragraph (formatted correctly according to MLA style guidelines, with attributive tags to introduce the quotations and in-text citations following each quotation) to support the argument the writer is making. Please note that you should avoid summarizing the texts. Instead, your focus should be on making an argument about the ways that these explorers deal with the indigenous populations. Part II: Write a 1000 word essay (you may go over this word count, but you should not fall short of this word count) on the following prompt: Now that you have considered how the explorers interacted with the indigenous populations that they encountered, it then becomes necessary to examine how the native population viewed the explorers. Choose one of the readings that we covered in the creation/emergence accounts from Native American authors. You will then make an argumentative claim for your thesis statement about the way that this writer presents the relationship between the indigenous peoples and the European explorers. Is this a positive relationship, according to this writer? Does the writer think this is a negative relationship? You should also use quotations in each body paragraph (formatted correctly according to MLA style guidelines, with attributive tags to introduce the quotations and in-text citations following each quotation) to support the argument you are making. Please note that you should only discuss one text, and that you should avoid summarizing the text and instead focus on building and supporting an argument about the way that the author views the effect that the explorers have had or will have on the native population. Due: A typed Midterm Exam is due at the beginning of class on Wednesday, September 30th. Format: The exam should be formatted according to MLA guidelines, and it should be stapled in the upper left hand corner. It has to be from the book: The Concise Health Anthology of American Literature!!!!!!

ield ENGL 2110-01 Midterm You must write an essay for each of the following prompts. Part I: Write a 1500 word essay (you may go over this word count, but you should not fall short of this word count) on the following prompt: Many of the readings that we have covered up to this point in the class have considered the native population that explorers encountered when they came to the “New World.” For this essay, you should examine the readings from any two of the explorers that we have encountered to this point to compare and contrast the similarities and differences between the ways that these two explorers interacted with the indigenous peoples. The thesis for this essay should make an argumentative claim as to which approach was/is more effective, and the writer should use quotations in each body paragraph (formatted correctly according to MLA style guidelines, with attributive tags to introduce the quotations and in-text citations following each quotation) to support the argument the writer is making. Please note that you should avoid summarizing the texts. Instead, your focus should be on making an argument about the ways that these explorers deal with the indigenous populations. Part II: Write a 1000 word essay (you may go over this word count, but you should not fall short of this word count) on the following prompt: Now that you have considered how the explorers interacted with the indigenous populations that they encountered, it then becomes necessary to examine how the native population viewed the explorers. Choose one of the readings that we covered in the creation/emergence accounts from Native American authors. You will then make an argumentative claim for your thesis statement about the way that this writer presents the relationship between the indigenous peoples and the European explorers. Is this a positive relationship, according to this writer? Does the writer think this is a negative relationship? You should also use quotations in each body paragraph (formatted correctly according to MLA style guidelines, with attributive tags to introduce the quotations and in-text citations following each quotation) to support the argument you are making. Please note that you should only discuss one text, and that you should avoid summarizing the text and instead focus on building and supporting an argument about the way that the author views the effect that the explorers have had or will have on the native population. Due: A typed Midterm Exam is due at the beginning of class on Wednesday, September 30th. Format: The exam should be formatted according to MLA guidelines, and it should be stapled in the upper left hand corner. It has to be from the book: The Concise Health Anthology of American Literature!!!!!!

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MA 3351 – Fall 2015 Homework #3 Due Friday 18 September 1. Find eigenvalues and eigenvectors of the following matrices  1 2 2 4   3 1 1 2   3 0 0 4   1 2 1 3   0 −1 1 0   −2 1 0 1 −2 0 0 0 1   0 1 0 −1 0 0 0 0 1  . Do calculations by hand, though you can use Mathematica to check your results. 2. Find eigenvectors and eigenvalues of A =  2 0 1 1 2 −1 0 0 3  . Show that one of the eigenvalues is defective. Do calculations by hand, though you can use Mathematica to check your results. 3. Solve the initial value problem y′ = Ay, y (0) = y0 for the following cases (a) A =  −4 1 1 −4  y0 =  1 2  (b) A =  −1 1 0 −2  y0 =  −1 3  (c) A =  1 0 0 0 −2 1 0 1 −2  y0 =  1 0 2  Do all calculations by hand. 4. Repeat problem 3 using Mathematica to do all calculations. MORE PROBLEMS ON BACK OF PAGE 1 5. Use Mathematica’s Eigensystem function to find eigenvalues and eigenvectors of A =  −2 1 0 0 0 1 −2 1 0 0 0 1 −2 1 0 0 0 1 −2 1 0 0 0 1 −2  . Suppose you are interested in solutions to y′ = Ay. Without constructing the full solution, answer the following questions: (a) Does the solution grow or decay in time (or a mix of both)? (b) What is the smallest (in magnitude) rate constant? (c) What is the largest (in magnitude) rate constant? (d) As t → ¥, the solution will be dominated by one eigenvector times an exponen- tial. Which eigenvector, and what is the rate constant of the exponential? 6. Use diagonalization to compute (Is − A)−1, where A =  −2 1 0 1 −2 1 0 1 −2  . You may use Mathematica. I suggest running FullSimplify on your result. 2

MA 3351 – Fall 2015 Homework #3 Due Friday 18 September 1. Find eigenvalues and eigenvectors of the following matrices  1 2 2 4   3 1 1 2   3 0 0 4   1 2 1 3   0 −1 1 0   −2 1 0 1 −2 0 0 0 1   0 1 0 −1 0 0 0 0 1  . Do calculations by hand, though you can use Mathematica to check your results. 2. Find eigenvectors and eigenvalues of A =  2 0 1 1 2 −1 0 0 3  . Show that one of the eigenvalues is defective. Do calculations by hand, though you can use Mathematica to check your results. 3. Solve the initial value problem y′ = Ay, y (0) = y0 for the following cases (a) A =  −4 1 1 −4  y0 =  1 2  (b) A =  −1 1 0 −2  y0 =  −1 3  (c) A =  1 0 0 0 −2 1 0 1 −2  y0 =  1 0 2  Do all calculations by hand. 4. Repeat problem 3 using Mathematica to do all calculations. MORE PROBLEMS ON BACK OF PAGE 1 5. Use Mathematica’s Eigensystem function to find eigenvalues and eigenvectors of A =  −2 1 0 0 0 1 −2 1 0 0 0 1 −2 1 0 0 0 1 −2 1 0 0 0 1 −2  . Suppose you are interested in solutions to y′ = Ay. Without constructing the full solution, answer the following questions: (a) Does the solution grow or decay in time (or a mix of both)? (b) What is the smallest (in magnitude) rate constant? (c) What is the largest (in magnitude) rate constant? (d) As t → ¥, the solution will be dominated by one eigenvector times an exponen- tial. Which eigenvector, and what is the rate constant of the exponential? 6. Use diagonalization to compute (Is − A)−1, where A =  −2 1 0 1 −2 1 0 1 −2  . You may use Mathematica. I suggest running FullSimplify on your result. 2

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