MATHS 340

Real and Complex Calculus

Tutorial one

The first two exercises below do not require the symbolic capabilities of matlab.

1. Enter the vector u = [1, 2, 3] by typing

u = [1,2,3]

beside the matlab prompt. Enter the vectors v = [−1, 5, 6] and w = [0, 1, 2] in a similar way.Then find u · v. To do this, type

dot(u,v’)

2. Now find v × w. To do this, type

cross(v,w’);

3. Suppose u = [t, cos(2t), exp(t)]. Use the diff command to find du/dt. You can find out aboutthe diff command by typing help sym/diff.

4. If u = [t, cos(2t), exp(t)], v = [−t, 0, (1 + t)−1], what is d(u× v)/dt?

5. Use the taylor command to find the Taylor series expansion of tan(x) about x = 0 up to andincluding the x7 term.

6. Use the int command to evaluate the indefinite integral

∫cos6(x)dx

7. Use matlab to find the tangent plane for x6yz + exp(z) = 0 at (2,− exp(1)/64, 1).

8. Use the scalar triple product to find the volume of the parallelopiped with vertices at

(0, 0, 0), (5, 0, 0), (1, 4, 0), (6, 4, 0), (1, 1, 2), (6, 1, 2), (2, 5, 2), (7, 5, 2)