Recommended Textbooks
Introduction to Analysis
A more advanced text that provides rigorous treatment of sequences, series, and convergence. Excellent for students who want to deepen their understanding of the theoretical foundations.
Find on AmazonCalculus
A classic calculus textbook that emphasizes theoretical understanding. Chapter 23 covers infinite series with a focus on power series and their applications.
Find on AmazonAdvanced Calculus
A more advanced treatment of calculus topics, including a thorough discussion of power series and their applications in solving differential equations.
Free PDF VersionOnline Courses
Calculus 2: Sequences and Series
A comprehensive course covering sequences, series, convergence tests, and power series. Includes lecture videos, problem sets, and exams with solutions.
Course WebsiteSeries, Taylor Series and Fourier Series
A free online course with video tutorials covering sequences, series, convergence tests, power series, and Taylor series. Includes practice exercises with immediate feedback.
Course WebsiteVideo Lectures
Sequences and Series
A series of visually stunning videos that provide intuitive understanding of sequences, series, and their convergence properties. Excellent for visual learners.
YouTube ChannelInfinite Series
Engaging videos that explore fascinating aspects of infinite series, including the Basel problem, Ramanujan's work, and other interesting series.
YouTube ChannelMIT OpenCourseWare: Calculus II
Complete lecture videos from MIT's Calculus II course, with several lectures dedicated to sequences, series, and power series.
Video LecturesInteractive Tools
Desmos Graphing Calculator
A powerful online graphing calculator that can be used to visualize sequences, series, and power series approximations. Excellent for exploring convergence visually.
Use DesmosGeoGebra: Series Applets
A collection of interactive applets that demonstrate sequences, series, and Taylor polynomials. Users can adjust parameters and see the effects in real-time.
GeoGebra MaterialsTaylor Series Explorer
An interactive 3D visualization tool that allows users to explore Taylor series approximations of various functions. Users can adjust the number of terms and see the approximation improve.
Use Taylor Series ExplorerWolframAlpha
A computational knowledge engine that can compute series sums, test convergence, find Taylor series, and much more. Excellent for checking your work or exploring complex series.
Use WolframAlphaPractice Sites
Paul's Online Math Notes
Comprehensive notes, examples, and practice problems for sequences, series, and power series. Includes detailed solutions to all practice problems.
Visit WebsiteMIT OpenCourseWare Problem Sets
Problem sets from MIT's Calculus II course, with several sets focusing on sequences, series, and power series. Includes solutions for self-assessment.
Access Problem SetsBrilliant.org: Sequences and Series
Interactive courses and problem sets on sequences, series, and power series. Problems range from basic to advanced and include hints and detailed solutions.
Visit BrilliantResearch Papers
Historical Development of the Concept of Convergence
A paper exploring the historical development of the concept of convergence, from early work by Newton and Leibniz to the rigorous definitions by Cauchy and Weierstrass.
Fernando Gouvêa WebsiteApplications of Power Series in Solving Differential Equations
A collection of papers discussing the application of power series methods in solving ordinary and partial differential equations, with examples from physics and engineering.
arXiv MathematicsReal-world Applications
Power Series in Signal Processing
Resources explaining how power series and Fourier series are used in signal processing, including applications in audio processing, image compression, and telecommunications.
IEEE ResourcesTaylor Series in Computational Physics
Resources explaining how Taylor series are used in computational physics for numerical methods, approximating solutions to differential equations, and error analysis.
APS Publications