May 1, 2024
Updated May 9, 2025
17 minute read
At a high level, a Taylor series is a mathematical concept that allows us to represent a function as an infinite sum of terms. These terms are calculated from the function's derivatives at a single point. For many common functions, this infinite sum is equal to the original function near that chosen point. Think of it as a way to build a potentially very complex function using simpler building blocks – polynomials. The more terms you include from the series, the closer your approximation gets to the actual function.
z9keds|
Find a path to becoming a Taylor Series. Learn more at:
OpenCourser.com/topic/z9keds/taylor
Reading list
We've selected 30 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Taylor Series.
More specialized treatment of Taylor series. It covers a wide range of topics, including convergence, error estimation, and applications.
Covers a wide range of topics related to Taylor series, including numerical methods, asymptotic analysis, and applications in physics and engineering.
A rigorous and theoretical approach to calculus, this book delves deeply into the foundations of sequences, series, and power series, including a thorough treatment of Taylor Series. It's particularly valuable for undergraduate students seeking a deeper, proof-based understanding of the subject. is often used as a challenging textbook for honors calculus courses.
This comprehensive calculus text presents a unified approach to calculus and linear algebra. It includes a thorough treatment of sequences and series, with detailed explanations of Taylor series and their convergence. It's a strong resource for ambitious undergraduates seeking a deeper and broader mathematical foundation.
Provides a focused and detailed treatment of Taylor series and their connection to analytic functions. It explores advanced topics related to convergence, properties, and applications of Taylor series in complex analysis. Suitable for graduate students and researchers interested in the theoretical aspects.
Offers a clear and accessible introduction to real analysis, bridging the gap between calculus and more abstract analysis texts like Rudin. It covers sequences, series, and the theoretical basis for Taylor series in a way that is understandable for upper-level undergraduate students. It's a good resource for solidifying the theoretical concepts behind Taylor series.
Another highly-regarded introduction to real analysis for undergraduates, Abbott's book provides intuitive explanations alongside rigorous proofs. It covers the necessary background on sequences and series for understanding Taylor series convergence and properties. is valuable for students looking for a more conceptual understanding of analysis.
Known as "Big Rudin," this graduate-level text covers measure theory, functional analysis, and complex analysis. It builds upon the foundations of "Baby Rudin" and discusses Taylor series in the context of complex analytic functions and their properties. Essential for graduate students in mathematics.
A standard introductory textbook for numerical analysis, this book explains how Taylor series are used to approximate functions and derive numerical methods for solving problems. It's crucial for understanding the computational aspects of Taylor series and their role in numerical algorithms. Suitable for undergraduate and graduate students in STEM fields.
This widely-used calculus textbook provides a solid introduction to Taylor Series as part of its coverage of infinite sequences and series. It's an excellent resource for high school and early undergraduate students to gain a fundamental understanding of the topic and its basic applications. The book includes numerous examples and exercises to help solidify understanding.
A graduate-level text on complex analysis that provides a comprehensive and rigorous treatment of complex series, including detailed discussions of Taylor and Laurent series. is suitable for graduate students specializing in complex analysis or related fields.
A classic and comprehensive work that covers calculus and the beginnings of analysis. It includes a thorough treatment of sequences, series, and power series, with a strong emphasis on understanding the underlying concepts. Valuable for serious undergraduate students seeking a deep understanding.
Provides a comprehensive introduction to complex analysis with a strong emphasis on applications. It covers Taylor and Laurent series thoroughly, demonstrating their utility in solving problems in various scientific and engineering fields. It's a valuable resource for upper-level undergraduates and graduate students in applied disciplines.
This textbook provides an introduction to numerical methods, building upon calculus concepts like Taylor series for approximations and error analysis. It's a practical guide for students learning to implement numerical algorithms. Suitable for undergraduate students in mathematics, engineering, and computer science.
This advanced calculus text provides a rigorous treatment of sequences, series, and multivariable calculus, including the extension of Taylor series to functions of several variables. It's suitable for advanced undergraduate and graduate students looking to deepen their understanding of Taylor series in higher dimensions.
Provides a modern introduction to numerical methods, covering topics like Taylor series for approximations and error analysis. It emphasizes the mathematical foundations of numerical algorithms and is suitable for advanced undergraduate and graduate students in scientific computing and related fields.
Provides a comprehensive overview of calculus, including a section on Taylor series. It is well-written and accessible to students with a variety of backgrounds.
Covers a wide range of topics related to calculus of variations, including Taylor series. It well-written and accessible text.
Covers a wide range of topics related to partial differential equations, including Taylor series. It well-written and accessible text.
Covers a wide range of topics related to approximation theory, including Taylor series. It classic text in the field.
Covers a wide range of topics related to real analysis, including Taylor series. It well-written and accessible text.
Covers a wide range of topics related to mathematical methods in the physical sciences, including Taylor series. It well-written and accessible text.
Written with the student in mind, this real analysis textbook aims to be more approachable than some of the classic texts. It covers the theory of sequences and series necessary for understanding Taylor series convergence and properties, with clear explanations and motivation. Useful for undergraduates transitioning to rigorous mathematics.
For more information about how these books relate to this course, visit:
OpenCourser.com/topic/z9keds/taylor
Save
