Math Fundamentals Courses and Certifications

The Taylor Series, Complex Numbers, and Simple Harmonic Motion - Lecture 16

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Explores Taylor series, complex numbers in polar form, and their connection to trigonometric functions before applying them to simple harmonic motion.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Imaginary Numbers Are Real

An accessible journey from imaginary numbers and the complex plane to complex multiplication, functions, and Riemann surfaces.

• YouTube
• 1 hour 30 minutes
• Self-Paced
• Free Video

Insights into Mathematics

Wild Trig - An Introduction to Rational Trigonometry

Rational trigonometry replaces angles and trigonometric functions with algebraic quantities called quadrance and spread.

• YouTube
• 19 hours 47 minutes
• Self-Paced
• Free Video

Tom Rocks Maths

Oxford Calculus - Partial Differentiation, Critical Points, PDEs, and Fourier Series

Derives the heat equation and Fourier series, then uses separation of variables to solve heat equation examples.

• YouTube
• 6 hours 28 minutes
• Self-Paced
• Free Video

Math with Professor V

Calculus 2 - Complete Video Lecture Series

Step-by-step worked examples show how to choose integration methods and convergence tests across a broad Calculus II sequence.

• YouTube
• 2 days 19 hours 27 minutes
• Self-Paced
• Free Video

Math with Professor V

Sequences and Series - Complete Calculus and Precalculus Course

A Calculus II problem-solving course centers on choosing the right test for convergence, then builds toward power series and Taylor approximations.

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

3Blue1Brown

Essence of Calculus

A visuals-first tour of calculus builds intuition through geometric explanations of derivatives, integrals, and their connections.

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

Eddie Woo

Using Complex Numbers - Comprehensive Course on De Moivre's Theorem, Argand Diagrams, and Complex Analysis

Explore complex numbers geometrically on the plane, then use De Moivre’s theorem to solve for roots and derive trigonometric identities.

• YouTube
• 1 day 5 hours 22 minutes
• Self-Paced
• Free Video

Eddie Woo

Trigonometry and Measure of Angles

Develops trigonometry from right-triangle ratios to unit-circle functions, graphs, radian measure, and challenging 3D problems.

• YouTube
• 9 hours 31 minutes
• Self-Paced
• Free Video

Eddie Woo

Introduction to Complex Numbers

Explore how complex numbers extend algebra, then use modulus-argument form and the complex plane to understand multiplication, roots, and Euler’s formula.

• YouTube
• 13 hours 47 minutes
• Self-Paced
• Free Video

Krista King

Calculus II - Integrals, Applications, Polar and Parametric Equations, Sequences and Series

Worked integration techniques are carried into problems in geometry, motion, force, and other applications.

• YouTube
• 1 day 8 hours 9 minutes
• Self-Paced
• Free Video

Krista King

Applications of Integrals - Area, Volume, Work, Physics, Economics, and Biology Applications

Use definite integrals to calculate areas, arc lengths, volumes, centroids, work, and other quantities in geometric and physical systems.

• YouTube
• 6 hours 13 minutes
• Self-Paced
• Free Video

Krista King

Limits and Continuity

Builds intuition for limits through graphical and algebraic methods, then connects the formal epsilon-delta definition to continuity and the Intermediate Value Theorem.

• YouTube
• 2 hours 58 minutes
• Self-Paced
• Free Video

Krista King

Calculus I - Complete Course with Functions, Limits, Derivatives and Applications

Work through derivative applications such as geometric optimization, related rates, particle motion, and marginal cost, revenue, and profit.

• YouTube
• 17 hours 52 minutes
• Self-Paced
• Free Video

Krista King

Calculus Integrals - Complete Course on Antiderivatives, Definite Integrals, and Integration Techniques

Builds integration from Riemann sums and the Fundamental Theorem through a broad range of methods for evaluating definite and indefinite integrals.

• YouTube
• 11 hours 2 minutes
• Self-Paced
• Free Video