Mathematics Courses and Certifications

Professor Leonard

Calculus 3 - Finding Tangent Planes and Normal Lines to Surfaces

Learn to find tangent planes and normal lines to surfaces in multivariable calculus, using gradient functions to analyze complex three-dimensional geometries.

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

Professor Leonard

Calculus 3 - Finding Directional Derivatives and Gradients

Learn to calculate directional derivatives along any vector path and explore the concept of gradients, their applications, and fundamental principles in multivariable calculus.

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

Professor Leonard

Calculus 3 - Finding Differentials of Multivariable Functions

Explore differentials of multivariable functions, from basic concepts to advanced applications in word problems. Gain a deeper understanding of calculus principles and their real-world relevance.

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

Professor Leonard

Calculus 3 - The Chain Rule for Multivariable Functions

Explore the Chain Rule for multivariable functions, focusing on derivatives involving parametrics and compositions. Derive the rule and practice with examples.

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

Professor Leonard

Calculus 3 - Partial Derivatives - Derivatives of Multivariable Functions

Explore partial derivatives in multivariable calculus, including tangent line slopes, implicit differentiation, and higher-order derivatives. Gain a deep understanding through numerous examples.

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

Professor Leonard

Calculus 3 - Limits and Continuity of Multivariable Functions

Explore limits and continuity of multivariable functions, including the Squeeze Theorem. Learn techniques to determine limit existence and regions of continuity in this comprehensive lecture.

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

Professor Leonard

Intro to Multivariable Functions - Domain, Sketching, Level Curves

Explore multivariable functions, focusing on domain analysis, function sketching, and level curves. Gain practical skills in visualizing and interpreting complex mathematical concepts.

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

Professor Leonard

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

Explore TNB Frames, curvature, and torsion in vector calculus. Learn to compute Frenet-Serret frames, find osculating circles and planes, and perform vector encapsulation for 2D functions.

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

Professor Leonard

Calculus 3 - Velocity and Acceleration of Vector Functions

Explore velocity and acceleration of vector functions, including particle motion, integration for position, acceleration components, and projectile motion applications.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

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 - Derivatives and Integrals of Vector Functions

Explore derivatives and integrals of vector functions, focusing on tangent vectors, space curves, and initial value problems in this comprehensive mathematical lecture.

• YouTube
• 2 hours 42 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 - An Introduction to Vector Functions

Explore vector functions, their interpretation, and graphing techniques, with a focus on 3D representations. Learn to visualize and analyze complex mathematical concepts in multidimensional space.

• YouTube
• 2 hours 5 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