Mathematics Courses and Certifications

Professor Leonard

Calculus 3 - Triple Integrals Over Regions with Cylindrical or Spherical Coordination

Set up and evaluate triple integrals over regions using cylindrical and spherical coordinates, with applications to center of mass and moments of inertia.

• YouTube
• 3 hours 20 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 3 - How to Solve Triple Integrals - Along with Center of Mass and Volume

Learn how triple integrals represent and calculate volume and mass in three-dimensional regions, with an introduction to center of mass.

• YouTube
• 3 hours 34 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 3 - Center of Mass and Moments of Mass and Inertia for Lamina in 2-D

Calculus-based methods for finding mass, center of mass, moments of mass and inertia, and radius of gyration for two-dimensional laminae.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 3 - Double Integrals Over Polar Regions

Learn to evaluate double integrals over polar regions and translate rectangular integrals into polar coordinates.

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

Professor Leonard

Calculus 3 - How to Solve Double-Repeated-Iterated Integrals

Explains how to solve double, repeated, and iterated integrals by constructing integrals over specified regions.

• YouTube
• 3 hours 24 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 3 - Finding Extrema of Functions of 2 Variables (Max and Min)

Learn to find relative and absolute extrema of functions of two variables, including optimization applications.

• YouTube
• 3 hours 38 minutes
• Self-Paced
• Free Video

Professor Leonard

Introduction to Double Integrals - Background Info

An introduction to the origins, meaning, and interpretation of double integrals.

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

Professor Leonard

Calculus 3 - Finding Tangent Planes and Normal Lines to Surfaces

Learn to find tangent planes and normal lines to surfaces using gradients at a point.

• YouTube
• 1 hour 42 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 3 - Finding Directional Derivatives and Gradients

Learn to find directional derivatives along vectors and understand the gradient and its basic uses.

• YouTube
• 2 hours 37 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 3 - Finding Differentials of Multivariable Functions

Derives differentials for multivariable functions and applies them to word problems.

• YouTube
• 1 hour 51 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 3 - The Chain Rule for Multivariable Functions

Derive and practice the multivariable chain rule for derivatives involving parametric functions and compositions.

• YouTube
• 2 hours 12 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 3 - Partial Derivatives - Derivatives of Multivariable Functions

How to find directional slopes on surfaces using partial derivatives, with implicit differentiation and higher-order partial derivatives.

• YouTube
• 2 hours 29 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 3 - Limits and Continuity of Multivariable Functions

Learn how to show when limits of multivariable functions exist or do not, apply the Squeeze Theorem, and determine regions of continuity.

• YouTube
• 2 hours 15 minutes
• Self-Paced
• Free Video

Professor Leonard

Intro to Multivariable Functions - Domain, Sketching, Level Curves

Learn to determine domains and visualize multivariable functions through domain sketches, function sketches, level curves, and contour plots.

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

Professor Leonard

Calculus 3 - TNB (Frenet-Serret) Frames, Curvature, Torsion, Encapsulation

Compute Frenet–Serret frames, curvature, torsion, and osculating geometry for vector-valued curves.

• YouTube
• 2 hours 37 minutes
• Self-Paced
• Free Video