Student's Guide to Infinite Series and Sequences

Infinite series are used to approximate solutions to mathematical problems that cannot be solved exactly. This introduction for undergraduate students explores their numerous applications in engineering and the physical sciences, helping students develop the techniques needed to utilize them confidently. The book covers infinite series, power series, complex infinite series, and Fourier, Legendre, and Fourier-Bessel series, with a focus on practical applications.

Format: Paperback / softback
Length: 198 pages
Publication date: 17 May 2018
Publisher: Cambridge University Press

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.

Infinite series and sequences play a crucial role in various fields of engineering and the physical sciences. They are used to approximate and represent solutions to complex problems that cannot be solved exactly. By expanding a series in terms of infinite terms, we can obtain an approximation that becomes increasingly accurate as the number of terms increases. This technique is particularly useful in fields such as physics, where we often encounter complex phenomena that cannot be modeled by simple functions.

One of the most important applications of infinite series is in the study of electricity and magnetism. Maxwell's equations, which describe the behavior of electric and magnetic fields, are expressed in terms of infinite series. By analyzing these series, we can understand the properties of electromagnetic waves, such as radio waves, light, and X-rays. Infinite series also play a role in the study of thermodynamics, where they are used to model the behavior of heat and temperature.

In addition to their applications in engineering and the physical sciences, infinite series and sequences have numerous other uses. They are used in computer science to analyze algorithms and optimize performance. Infinite series are also used in finance to model interest rates, stock prices, and other financial phenomena. They are even used in art and music to create complex melodies and harmonies.

Despite their usefulness, infinite series can be challenging to understand and apply. They require a solid foundation in mathematics, including algebra, trigonometry, and calculus. However, with practice and perseverance, anyone can develop the skills needed to utilize infinite series effectively.

In conclusion, infinite series and sequences are a powerful tool that can be used to approximate and represent solutions to complex mathematical problems. They have numerous applications in engineering and the physical sciences, as well as in computer science, finance, and art and music. While they may be challenging to understand, with practice and perseverance, anyone can develop the skills needed to utilize infinite series effectively.

Weight: 340g
Dimension: 154 x 229 x 14 (mm)
ISBN-13: 9781107640481