Why study infinite series? Not all mathematical problems can be solved exactly or have a solution that can be expressed in terms of a known function. In such cases, it is common practice to use an infinite series expansion to approximate or represent a solution. This informal introduction for undergraduate students explores the numerous uses of infinite series and sequences in engineering and the physical sciences. The material has been carefully selected to help the reader develop the techniques needed to confidently utilize infinite series. The book begins with infinite series and sequences before moving onto power series, complex infinite series and finally onto Fourier, Legendre, and Fourier-Bessel series. With a focus on practical applications, the book demonstrates that infinite series are more than an academic exercise and helps students to conceptualize the theory with real world examples and to build their skill set in this area.
An informal, plain language approach enables the student to get to grips with the material quickly
A focus on practical real-world examples ensures a complex topic is accessible for students
The early introduction of complex numbers allows the reader to apply infinite series to applications that are typically only addressed in high level mathematics courses
Bernhard W. Bach, Jr is the Director of Undergraduate Laboratories at the University of Nevada, Reno. His research interests focus on Gamma ray, X-ray and UV spectroscopy, and the manufacture of diffractive optics and spectroscopic instrumentation. He has contributed to the design and construction of scientific instruments for numerous space-flight missions and synchrotron light sources around the world.
1. Infinite sequences
2. Infinite series
3. Power series
4. Complex infinite series
5. Series solutions for differential equations
6. Fourier, Legendre, and Fourier-Bessel series