The four decimal approximated value of y ( 0.5 ) for the differential equation y ′ = x + y 2 by improved Euler’s method when h = 0.1 and h = 0.05 .

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Answer 1

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Chapter 9.1, Problem 6E

To determine

The four decimal approximated value of y(0.5) for the differential equation y′=x+y2 by improved Euler’s method when h=0.1 and h=0.05.

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please answer the questions below ands provide the required codes in PYTHON. alsp provide explanation of how the codes were executed. Also make sure you provide codes that will be able to run even with different parameters as long as the output will be the same with any parameters given. these questions are not graded. provide accurate codes please

(1) Let F be a field, show that the vector space F,NEZ* be a finite dimension. (2) Let P2(x) be the vector space of polynomial of degree equal or less than two and M={a+bx+cx²/a,b,cЄ R,a+b=c),show that whether Mis hyperspace or not. (3) Let A and B be a subset of a vector space such that ACB, show that whether: (a) if A is convex then B is convex or not. (b) if B is convex then A is convex or not. (4) Let R be a field of real numbers and X=R, X is a vector space over R show that by definition the norms/II.II, and II.112 on X are equivalent where Ilxll₁ = max(lx,l, i=1,2,...,n) and llxll₂=(x²). oper (5) Let Ⓡ be a field of real numbers, Ⓡis a normed space under usual operations and norm, let E=(2,5,8), find int(E), b(E) and D(E). (6) Write the definition of bounded linear function between two normed spaces and write with prove the relation between continuous and bounded linear function between two normed spaces.

ind → 6 Q₁/(a) Let R be a field of real numbers and X-P(x)=(a+bx+cx²+dx/ a,b,c,dER},X is a vector space over R, show that is finite dimension. (b) Let be a bijective linear function from a finite dimension vector ✓ into a space Yand Sbe a basis for X, show that whether f(S) basis for or not. (c) Let be a vector space over a field F and A,B)affine subsets of X,show that whether aAn BB, aAU BB be affine subsets of X or not, a,ẞ EF. (12 Jal (answer only two) (6) Let M be a non-empty subset of a vector space X and tEX, show that M is a hyperspace of X iff t+M is a hyperplane of X and tЄt+M. (b) State Jahn-Banach theorem and write with prove an application of Hahn-

Answer 2

Question

Chapter 9.1, Problem 6E

To determine

The four decimal approximated value of y(0.5) for the differential equation y′=x+y2 by improved Euler’s method when h=0.1 and h=0.05.

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Answer 3

Question

Chapter 9.1, Problem 6E

To determine

The four decimal approximated value of y(0.5) for the differential equation y′=x+y2 by improved Euler’s method when h=0.1 and h=0.05.

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Answer 4

Question

Chapter 9.1, Problem 6E

To determine

The four decimal approximated value of y(0.5) for the differential equation y′=x+y2 by improved Euler’s method when h=0.1 and h=0.05.

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Answer 5

Chapter 9.1, Problem 6E

To determine

The four decimal approximated value of y(0.5) for the differential equation y′=x+y2 by improved Euler’s method when h=0.1 and h=0.05.

Answer 6

Chapter 9.1, Problem 6E

To determine

The four decimal approximated value of y(0.5) for the differential equation y′=x+y2 by improved Euler’s method when h=0.1 and h=0.05.

Answer 7

Chapter 9.1, Problem 6E

To determine

The four decimal approximated value of y(0.5) for the differential equation y′=x+y2 by improved Euler’s method when h=0.1 and h=0.05.

Answer 8

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Answer 9

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Answer 10

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Answer 11

The four decimal approximated value of y ( 0.5 ) for the differential equation y ′ = x + y 2 by improved Euler’s method when h = 0.1 and h = 0.05 .

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The four decimal approximated value of y(0.5) for the differential equation y′=x+y2 by improved Euler’s method when h=0.1 and h=0.05.

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