{"id":16334,"date":"2022-08-08T02:49:31","date_gmt":"2022-08-08T02:49:31","guid":{"rendered":"https:\/\/www.booksofall.com\/?post_type=product&p=16334"},"modified":"2022-08-08T02:49:31","modified_gmt":"2022-08-08T02:49:31","slug":"complex-methods-for-the-sciences-chong","status":"publish","type":"product","link":"https:\/\/www.booksofall.com\/fr\/complex-methods-for-the-sciences-chong\/","title":{"rendered":"Complex Methods for the Sciences (Chong)"},"content":{"rendered":"

An introductory course in mathematical methods for science and engineering students. Topics covered include complex analysis, contour integration<\/a>, Fourier analysis<\/a>, and Green’s function methods. Mathematical methods are illustrated with examples drawn from physics, with a focus on oscillations and waves.<\/p>\n

Mathematical Functions<\/h3>\n

This is a course on complex methods in the physical sciences. Before dealing with complex numbers, however, let us undertake a brief review of real mathematical functions and their properties.<\/p>\n

The Complex Plane<\/h3>\n

A convenient way to conceptualize a complex number is to think of it as a point on a two-dimensional plane, called the complex plane, as shown in the figure below. The real and imaginary parts are the horizontal and vertical Cartesian coordinates in the plane. The horizontal (x) and vertical (y) coordinate axes are called the \u201creal axis\u201d and the \u201cimaginary axis\u201d, respectively.<\/p>\n

Complex Functions<\/h3>\n

When deriving Euler\u2019s formula in Section 4.3, we introduced complex functions that were defined by taking real mathematical functions<\/a>, like the exponential, and making them accept complex number inputs. Let us take a closer look at how these complex functions behave.<\/p>\n

Trajectories in the Complex Plane<\/h3>\n

If we have a function which takes a real input and outputs a complex number , it is often useful to plot a curve in the complex plane called the \u201cparametric trajectory\u201d of . Each point on this curve indicates the value of for a particular value of . We will give a few examples below.<\/p>\n

Why Complex Numbers?<\/h3>\n

Here are some questions that might have occurred to you:<\/p>\n