Infinite series Courses and Certifications

Applied Math for Materials Science and Engineering

Master fundamental calculus, power series, and differential equations for materials science and engineering applications, building a strong mathematical foundation for physical science research.

• Coursera
• 7 hours 21 minutes
• Self-Paced
• Paid Course

Applied Math for Materials Science and Engineering (Part 2)

Master multivariable calculus, infinite series, and complex numbers with direct applications to materials science, including coordinate transformations, convergence tests, and LCR circuit analysis.

• Coursera
• 13 hours
• Self-Paced
• Paid Course

Real Analysis

Explore mathematical analysis fundamentals: convergence, continuity, differentiability, and Riemann integral. Develop abstract thinking and proof construction skills while studying real numbers and limit operations.

• MIT OpenCourseWare
• Self-Paced
• Free Online Course

Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra

Master complex variables, differential equations, and linear algebra through 20 MIT videos and study guides, building on calculus foundations with topics like conformal mappings, eigenvectors, and Laplace transforms.

• MIT OpenCourseWare
• Self-Paced
• Free Online Course

Steve Brunton

Infinite Dimensional Function Spaces and Fourier Series

Explore infinite dimensional function spaces and Fourier series, covering inner product spaces, orthogonal functions, and complex functions in engineering mathematics.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

Michael Penn

An Interesting Infinite Sum, Featuring Fourier Series

Explore the derivation of a closed form for the infinite sum cos(n)/n^4 using Fourier series, featuring integration by parts and coefficient analysis.

• YouTube
• 25 minutes
• Self-Paced
• Free Video

3Blue1Brown

What Makes the Natural Log "Natural"

Explore the natural logarithm's unique properties, its relationship with prime numbers, exponentials, and derivatives. Gain insights into mathematical concepts through engaging explanations and visual demonstrations.

• YouTube
• 1 hour 15 minutes
• Self-Paced
• Free Video

Mathologer

Ramanujan - Making Sense of 1+2+3+... = -1/12 and Co.

Explore the mathematical paradox of infinite sums equaling unexpected values, delving into Ramanujan's work, summation rules, and connections to the Riemann Zeta function.

• YouTube
• 35 minutes
• Self-Paced
• Free Video

TED

Paper Towns and Why Learning Is Awesome

John Green explores the joy of learning outside traditional classrooms, highlighting online communities as vibrant spaces for intellectual growth and shared curiosity about diverse topics.

• YouTube
• 18 minutes
• Self-Paced
• Conference Talk

Math with Professor V

Sequences and Series - Complete Calculus and Precalculus Course

Master sequences and series fundamentals through comprehensive coverage of convergence tests, power series, Taylor polynomials, and practical problem-solving strategies.

• YouTube
• 1 day 6 hours 32 minutes
• Self-Paced
• Free Video

TabletClass Math

Can You Find the Sum of This Infinite Geometric Series?

Master infinite geometric series convergence conditions and sum formulas through step-by-step examples for Algebra 2 and Precalculus success.

• YouTube
• 11 minutes
• Self-Paced
• Free Video

Great Thinkers, Great Theorems

132 ratings at The Great Courses Plus

<p>Rub shoulders with towering mathematical geniuses of history in this fun and compelling course that takes you inside the mechanics of some of math's greatest and most awe-inspiring achievements.</p>

• The Great Courses Plus
• 12 hours 15 minutes
• Self-Paced
• Free Trial Available

Ross Dynamics Lab

Hamiltonian Normal Forms, Lie Series Method for Transformations - Infinite-Dimensional Hamiltonians

Explore Hamiltonian normal forms, Lie series transformations, and infinite-dimensional systems. Learn to simplify complex dynamics and analyze PDEs like shallow water equations.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

QuantumTopology

V. Tarkaev - The Complexity of an Infinite Series of Knots in the Thickened Torus

Explore the intricacies of knot theory as V. Tarkaev delves into the complexity of infinite knot series within a thickened torus, offering insights into advanced topological concepts.

• YouTube
• 1 hour 26 minutes
• Self-Paced
• Free Video

Kerala School of Mathematics;  NPTEL

Complex Analysis

1 rating

Explore holomorphic functions, Cauchy's theorem, residues, and singularities in this comprehensive study of complex analysis, suitable for advanced undergraduates and graduate students.

• Swayam
• 12 weeks
• Self-Paced
• Free Online Course