due on September 12

Home assignment 1 on the Refresher course for the ICEF Master Degree students

due on September 12

Part I. Solve problems on Linear Algebra.

1. Calculate the determinant of the n-th order .
2. Solve the system of equations by the Gauss elimination procedure
3. A linear subspace is spanned by the three vectors , , . Find the system of linear equations whose solution set represents .
4. Let be the subspace spanned by the vectors , and the subspace spanned by the vectors , where , , , , , . Find and .

Part II. Solve problems on Calculus.

1. Determine whether the function

is differentiable at (0,0).

2. Solve the partial differential equation by introducing the new variables .

3. Equation in x and y variables is given by (1) , where for y values . Prove that in the neighborhood of there exists a unique function that satisfies equation (1) and y(0)=0.

4. Find the directional derivative of the function in 3d space at (1,2,-2), where the vector is a unit vector pointing along the tangent line drawn to the curve at .

Date: 2015-02-03; view: 1201