Calculate the values of the differential 1-form dr^2 on the following vectors: (0,1); (-1,-1); (1,-1).
Calculate the values of the differential 1-form dr^2 on the following vectors: (0,1); (-1,-1); (1,-1).
Homework Answers
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Calculate the values of the differential 1-form dr^2 on the
following vectors: (0,1); (-1,-1); (1,-1).
2) Verifty that each of the following vectors X is a solution to the differential equation....
2) Verifty that each of the following vectors X is a solution to the differential equation. 3 -2 b) 0 -1 1 4
For which real values of x do the following vectors form a linearly dependent set in R3
For which real values of x do the following vectors form a linearly dependent set in R3?v1= (x, -1/9, -1/9)v2= (-1/9, x, -1/9) v3= (-1/9, -1/9, x)
2. Determine which of the following are subspaces of R3: (a) all vectors of the form...
2. Determine which of the following are subspaces of R3: (a) all vectors of the form (a,b,c)), where a - 2b = c. (b) all vectors of the form (a, b, -3)), (c) all vectors of the form (a, b,0)). Explain your answer.
II. Answer the following questions concerning the simultaneous differential equa- dac tions below. Here, à dt...
II. Answer the following questions concerning the simultaneous differential equa- dac tions below. Here, à dt dr -2- 3y 2, dt dt2 dy da (2) 2y, dt df x(0)0, (0)0, y(0) = 2. -- 1. Let us transform the simultaneous differential equations in Eq.(2) into. da Ax b, (0) dt Here ais defined as the form x(t) (t) y(t) x(t) (3) A is a constant matrix, and b and c are constant vectors. Obtain A, b and c Calculate all...
Problem 1. (25 points) Consider the following differential equation. 36 (a) Using the change of variable, 2 VT, write the differential equation in the form of Bessel's equation, 22y" zy(22- v...
Problem 1. (25 points) Consider the following differential equation. 36 (a) Using the change of variable, 2 VT, write the differential equation in the form of Bessel's equation, 22y" zy(22- v2)y 0. (b) Find the general solution of the differential equation (y(). (You do not need to find the value:s of Gamma functions.) (c) Find the term multiplying ? in the solution. (You do not need to find the values of Gamma functions.)
Problem 1. (25 points) Consider the following...
Fill in the blanks (1 point) A Bernoulli differential equation is one of the form dy...
Fill in the blanks
(1 point) A Bernoulli differential equation is one of the form dy + P()y= Q(Cy" (*) dr Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=yl-n transforms the Bernoulli equation into the linear equation du dac + (1 - n)P(x)u= (1 - nQ(2). Consider the initial value problem xy' +y= -6xy?, y(1) = -2. (a) This differential equation can be written in the form...
8. Let w be the differential form yzdydz + zxdzdx + xydrdy. (i) Show that w is closed. (ii) Is w exact? If it is, find η such that dr-w. If not, explain why not. 8. Let w be the differential for...
8. Let w be the differential form yzdydz + zxdzdx + xydrdy. (i) Show that w is closed. (ii) Is w exact? If it is, find η such that dr-w. If not, explain why not.
8. Let w be the differential form yzdydz + zxdzdx + xydrdy. (i) Show that w is closed. (ii) Is w exact? If it is, find η such that dr-w. If not, explain why not.
8. A parallelepiped is formed by the vectors a,1,0, b 0,1, 1 and c1,1 e the...
8. A parallelepiped is formed by the vectors a,1,0, b 0,1, 1 and c1,1 e the volume of the parallelepiped. etermin 9. Show that the four points A(1,3, 2), B(3,-1,6), C(5, 2,0) and D(3,6,-4) are copla- nar
8. Solve the following differential equation given the initial condition y(0) = -5: dy 2.c dr...
8. Solve the following differential equation given the initial condition y(0) = -5: dy 2.c dr 1+22 9. Solve the following differential equation using the method of separation of variables: dy = x²y. dic
HW 17, #5 For what values of a will the following vectors be linearly dependent? -2...
HW 17, #5
For what values of a will the following vectors be linearly
dependent?
-2 α 2 -1 5
2) Verifty that each of the following vectors X is a solution to the differential equation. 3 -2 b) 0 -1 1 4
2. Determine which of the following are subspaces of R3: (a) all vectors of the form (a,b,c)), where a - 2b = c. (b) all vectors of the form (a, b, -3)), (c) all vectors of the form (a, b,0)). Explain your answer.
II. Answer the following questions concerning the simultaneous differential equa- dac tions below. Here, à dt dr -2- 3y 2, dt dt2 dy da (2) 2y, dt df x(0)0, (0)0, y(0) = 2. -- 1. Let us transform the simultaneous differential equations in Eq.(2) into. da Ax b, (0) dt Here ais defined as the form x(t) (t) y(t) x(t) (3) A is a constant matrix, and b and c are constant vectors. Obtain A, b and c Calculate all...
Problem 1. (25 points) Consider the following differential equation. 36 (a) Using the change of variable, 2 VT, write the differential equation in the form of Bessel's equation, 22y" zy(22- v2)y 0. (b) Find the general solution of the differential equation (y(). (You do not need to find the value:s of Gamma functions.) (c) Find the term multiplying ? in the solution. (You do not need to find the values of Gamma functions.)
Problem 1. (25 points) Consider the following...
Fill in the blanks
(1 point) A Bernoulli differential equation is one of the form dy + P()y= Q(Cy" (*) dr Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=yl-n transforms the Bernoulli equation into the linear equation du dac + (1 - n)P(x)u= (1 - nQ(2). Consider the initial value problem xy' +y= -6xy?, y(1) = -2. (a) This differential equation can be written in the form...
8. Let w be the differential form yzdydz + zxdzdx + xydrdy. (i) Show that w is closed. (ii) Is w exact? If it is, find η such that dr-w. If not, explain why not.
8. Let w be the differential form yzdydz + zxdzdx + xydrdy. (i) Show that w is closed. (ii) Is w exact? If it is, find η such that dr-w. If not, explain why not.
8. A parallelepiped is formed by the vectors a,1,0, b 0,1, 1 and c1,1 e the volume of the parallelepiped. etermin 9. Show that the four points A(1,3, 2), B(3,-1,6), C(5, 2,0) and D(3,6,-4) are copla- nar
8. Solve the following differential equation given the initial condition y(0) = -5: dy 2.c dr 1+22 9. Solve the following differential equation using the method of separation of variables: dy = x²y. dic
HW 17, #5
For what values of a will the following vectors be linearly
dependent?
-2 α 2 -1 5
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