Defines the Laplace transform. Briefly describes the uses of a Laplace transform then deals with technical issues such as what is meant by infinity integration limit. Concludes with explanation of the restrictions on the ...

Explains graphically what it means to multiply a matrix and a vector. Then introduces eigenvectors as vectors belonging to the matrix with a special property in matrix vector multiplication. Eigenvalues are also explained ...

We continue the theme of half range series and examine how the integrations can be simplified using the symmetry of the function. Here we examine a half-range cosine series for a linear f(t).

We explain what is meant by an odd function in terms of symmetry, then give a rule satisfied by the function. We show how to test for oddness then discuss the area under the graph of an even function between points an equal ...

We explain what is meant by an even function in terms of symmetry, then give a rule satisfied by the function. We show how to test for evenness then discuss the area under the graph of an even function between points an ...

Shows how to use known Laplace transforms to evaluate infinite integrals involving exponentials in product with other functions. We extend the idea to products of an exponential with another fctn and with t using the ...

Defines the factorial function and shows examples where it is used: e.g. in the MacLaurin series for exp(x), for cos(x), but also in nCr (n choose r). It concludes with a proof that 0!=1, using the Gamma function.

Introduction to the Sigma notation for sums, with examples. Also highlights that infinity is not a number.

We examine the integration involved in calculating some Fourier coefficients and discuss the approach to be taken when one has a formula sheet in comparison with having to calculate the integral on paper.

We introduce geometric series in which the variable is a quantity other than x or the constant is not 1. Convergence is discussed and we show how to get a series that converges when the absolute value of x is greater than ...