# AMP Sheet 1

Sheet One

## Line Integrals¶

Over a scalar field Over a vector field ## Definition of a Differential Equation¶

A differential equation is a mathematical equation that relates some function with its derivatives.

# Mathematics: Question One¶

Evaluate the integral:

\$\$ \ int_{C}(3x+2xy^2) ds \$\$

Along the curve:

\$\$ \ C: quad x^2+y^2 = 3 \$\$

# Mathematics: Question Two¶

Evaluate the integral:
\$\$ int big(x^2-y big) dx + big( y^2+x big) dy \$\$

Along \$C\$, the straight line from (0,1) \$rightarrow\$ (1,2)

# Physics: Question One¶

(a) What is the name of the following equation?

\$\$ ihbar frac{dphi}{dt} = E phi(t) \$\$

(b) Solve the differential equation for \$phi(t)\$:

\$\$ ihbar frac{dphi}{dt} = E phi(t) \$\$

Such that:

\$ i=sqrt{-1}\$

\$ h = 6.626 times 10^{-34} m^{2}kg/s \$

\$ hbar = h / 2pi \$

\$E \$ is a constant

# Physics: Question Two¶

(a) What is the formula for the Heisenberg Uncertainty Principle?

(b) If you have \$Delta x = 0 \$ (that is, you have no uncertainty in the position of a particle) then what is your uncertainty in the momentum (\$Delta p\$)?

(c) A particle of mass \$10^{-6}\$ kg moves on a straight path with velocity (\$326\$ × \$10^4\$ ± \$0.75\$) m/s. What would be the uncertainty in displacement?