Math Fundamentals Courses and Certifications

Professor Leonard

Calculus 3 - Arc Length/Parameterization, TNB (Frenet-Serret) Intro

Explore arc length, parameterization, and Frenet-Serret frames in vector functions. Learn to calculate, reparameterize, and understand movable frames in space curves.

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

Professor Leonard

Calculus 3 - Cylinders and Surfaces in 3-D

Comprehensive guide to identifying and hand-sketching 3D geometric shapes, including cylinders, ellipsoids, hyperboloids, cones, paraboloids, and hyperbolic paraboloids in calculus.

• YouTube
• 2 hours 32 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 3 - Using Cylindrical and Spherical Coordinates

Master coordinate system conversions and equations in 3D space, enhancing your ability to solve complex calculus problems and visualize mathematical concepts.

• YouTube
• 1 hour 40 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 3 - Lines and Planes in 3-D

Comprehensive exploration of 3D geometry, covering parametric and symmetric line equations, plane equations, normals, and spatial relationships between lines, planes, and objects.

• YouTube
• 3 hours 21 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 2 - Using Polar Coordinates and Polar Equations

Explore polar coordinates and equations in this comprehensive lecture, learning to graph and analyze curves in the polar system for advanced mathematical understanding.

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

Professor Leonard

Calculus of Polar Equations

Explore polar equations in calculus, focusing on areas bound by polar curves and between two polar curves. Gain insights into advanced mathematical concepts and problem-solving techniques.

• YouTube
• 1 hour 13 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus of Parametric Equations

Explore the calculus of parametric equations, learning to analyze and manipulate curves defined by parameter-dependent functions. Gain insights into advanced mathematical concepts and problem-solving techniques.

• YouTube
• 1 hour 34 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 2 - Introduction to Parametric Equations

Explore parametric equations in calculus, learning their applications and how to graph and analyze them for a deeper understanding of mathematical relationships.

• YouTube
• 1 hour 38 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 2 - Approximation of Functions by Taylor Polynomials

Explore the approximation of functions using Taylor polynomials, a powerful mathematical tool for estimating complex functions with simpler polynomial expressions.

• YouTube
• 1 hour 34 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 2 - Representation of Functions by Taylor Series and Maclaurin Series

Explore Taylor and Maclaurin series for representing functions, enhancing your understanding of advanced calculus concepts and their practical applications.

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

Professor Leonard

Calculus 2 - Power Series, Calculus of Power Series, Ratio Test for Interval of Convergence

Explore power series, their calculus applications, and use the ratio test to determine convergence intervals in this comprehensive mathematics lecture.

• YouTube
• 2 hours 30 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 2 - Absolute Convergence, Ratio Test and Root Test for Series

Explore absolute convergence, ratio test, and root test for series in this comprehensive lecture, enhancing your understanding of advanced calculus concepts.

• YouTube
• 1 hour 46 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 2 - Showing Convergence With the Alternating Series Test, Finding Error of Sums

Explore convergence using the Alternating Series Test and learn to calculate error in sums. Master advanced calculus concepts with clear explanations and practical examples.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 2 - The Comparison Test for Series and The Limit Comparison Test

Explore advanced series convergence techniques: Comparison Test and Limit Comparison Test. Master these powerful tools for analyzing infinite series in calculus.

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

Professor Leonard

Calculus 2 - Using the Integral Test for Convergence-Divergence of Series, P-Series

Learn to apply the Integral Test to determine series convergence/divergence, with a focus on P-Series. Gain practical skills for analyzing infinite series in calculus.

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video