Part I Review Questions
... A hot-air balloon is tied to the ground with two taut (straight) ropes, as shown in the diagram below. One rope is directly under the balloon and makes a right angle with the ground. The other rope forms an angle of 50º with the ground. ...
... A hot-air balloon is tied to the ground with two taut (straight) ropes, as shown in the diagram below. One rope is directly under the balloon and makes a right angle with the ground. The other rope forms an angle of 50º with the ground. ...
![[2012 question paper]](http://s1.studyres.com/store/data/008881815_1-f519c09d51fa08989c44092ef48b677c-300x300.png)
[2012 question paper]
... consider the exponential of a matrix A through the Taylor expansion for ex . Evaluate Exp[iασ 1 ] and reduce it to a simple expression, where α is a constant, i2 = −1, and σ 1 = (01 10 ) is one of the Pauli matrices. [4.2] The wavefunction for a certain system satisfies the partial differential equa ...
... consider the exponential of a matrix A through the Taylor expansion for ex . Evaluate Exp[iασ 1 ] and reduce it to a simple expression, where α is a constant, i2 = −1, and σ 1 = (01 10 ) is one of the Pauli matrices. [4.2] The wavefunction for a certain system satisfies the partial differential equa ...
Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. (A special case are ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.) PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a relevant computer model.PDEs can be used to describe a wide variety of phenomena such as sound, heat, electrostatics, electrodynamics, fluid flow, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalised similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. PDEs find their generalisation in stochastic partial differential equations.