506 results in Content created by Newcastle University  search across all projects.

Represent a linear map as a matrix with a given basis
Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$ with coefficients in the real numbers.
Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by:
$\phi(p(x))=ap(x) + (bx + c)p'(x) + (x ^ 2 + dx + f)p''(x)$
Using the standard basis for range and domain find the matrix given by $\phi$.
Question Ready to use
CC BY Published
Last modified 18/02/2019 19:22
 No subjects selected
 No topics selected
No ability levels selected

Represent a linear map as a matrix given a basis
Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$ with coefficients in the real numbers. Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by: \[\phi(p(x))=p(a)+p(bx+c).\]Using the standard basis for range and domain find the matrix given by $\phi$.
Question Ready to use
CC BY Published
Last modified 18/02/2019 19:14
 No subjects selected
 No topics selected
No ability levels selected

Question Ready to use
CC BY Published
Last modified 15/02/2019 19:26
 No subjects selected
 No topics selected
No ability levels selected

Solve a separable first order ODE,
Find the solution of a first order separable differential equation of the form $axyy'=b+y^2$.
Question Ready to use
CC BY Published
Last modified 15/02/2019 19:21
 No subjects selected
 No topics selected
No ability levels selected

Question Has some problems
CC BY Published
Last modified 15/02/2019 11:00
 No subjects selected
 No topics selected
No ability levels selected

Solve a separable first order ODE,
Find the solution of a first order separable differential equation of the form $(a+x)y'=b+y$.
Question Ready to use
CC BY Published
Last modified 12/02/2019 17:46
 No subjects selected
 No topics selected
No ability levels selected

PDF and CDF of continuous uniform random variable,
$X$ is a continuous uniform random variable defined on $[a,\;b]$. Find the PDF and CDF of $X$ and find $P(X \ge c)$.
Question Ready to use
CC BY Published
Last modified 08/02/2019 15:20
 No subjects selected
 No topics selected
No ability levels selected

Precedence of operators  everything except indices
Questions testing understanding of the precedence of operators using BIDMAS. These questions only test BDMAS. That is, they test Brackets, Division/Multiplication and Addition/Subtraction.
Question Ready to use
CC BY Published
Last modified 08/02/2019 15:14
 No subjects selected
 No topics selected
No ability levels selected

Precedence of operators  everything except brackets
Questions testing understanding of the precedence of operators using BIDMAS applied to integers. These questions only test IDMAS. That is Indices, Division/Multiplication and Addition/Subtraction.
Question Ready to use
CC BY Published
Last modified 08/02/2019 15:11
 No subjects selected
 No topics selected
No ability levels selected

Precedence of operators
Questions testing understanding of the precedence of operators using BIDMAS. That is, they test Brackets, Indices, Division/Multiplication and Addition/Subtraction.
Question Ready to use
CC BY Published
Last modified 08/02/2019 15:08
 No subjects selected
 No topics selected
No ability levels selected