Playlist of solved problems and examples from engineering mathematics, presented by Dr Chris Tisdell, UNSW, Sydney. Topics covered will include important aspects of applied mathematics used in engineering, such as: multivariable calculus; vector calculus; differential equations; Laplace transforms; Fourier series.
This presentation shows how to differentiate under integral signs via. Leibniz rule. Many examples are discussed to illustrate the ideas. A proof is also given of the most basic case of Leibniz rule. Such ideas are important in applied mathematics and engineering, for example, in Laplace transforms.
This video shows how to calculate and classify the critical points of functions of two variables. The ideas involve first and second order derivatives and are seen in university mathematics.
An introduction to the calculus of vector functions of one variable. Some simple problems are discussed, including differentiation, integration and how to determine the curve associated with a function (in this example, a helix). Such functions can be used to describe curves and motion in space.
A basic lecture discussing the divergence of a vector field. I show how to calculate the divergence and present some geometric explanation of what the divergence represents. Several examples are discussed. Such ideas have important applications in fluid flow and are seen in vector calculus.
I discuss and solve a "homogeneous" first order ordinary differential equation. The method involves a substitution. Such an example is seen in 1st and 2nd year university mathematics.
A basic lecture showing how to solve nonhomogeneous second-order ordinary differential equations with constant coefficients. The approach illustrated uses the method of undetermined coefficients. I present several examples and show why the method works.
This is a basic introduction to the Laplace transform and how to calculate it. Such ideas are seen in university mathematics.
How to solve the wave equation via Fourier series and separation of variables. Such ideas are have important applications in science, engineering and physics.