Sheet One¶

## Line Integrals¶

Over a

scalarfield

Over avectorfield

## Definition of a Differential Equation¶

A differential equation is a mathematical equation that relates

some functionwith itsderivatives.

# Mathematics: Question One¶

Evaluate the integral:

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

Along the curve:

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

within the first quadrant.

# 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?