Mathematics Courses and Certifications

Professor Leonard

Green's Theorem - Calculus 3 Lecture

Comprehensive exploration of Green's Theorem, its applications in line integrals, and its significance in vector calculus, with detailed explanations and practical examples.

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

Professor Leonard

Line Integrals on Conservative Vector Fields - Independence of Path: Calculus 3 Lecture

Explore line integrals on conservative vector fields, understanding independence of path and the Fundamental Theorem of Line Integrals in this comprehensive calculus lecture.

• YouTube
• 1 hour 54 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 3: How to Compute Line Integrals Over Non-Conservative Vector Fields

Learn advanced techniques for computing line integrals, including over non-conservative vector fields. Gain insights into their interpretation and practical applications in calculus.

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

Professor Leonard

Calculus 3 - How to Change Variables in Multiple Integrals Using the Jacobian

Learn to use the Jacobian for variable changes in multiple integrals, including finding transformations and applying substitutions in advanced calculus problems.

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

Professor Leonard

Introduction to Vector Fields - And What Makes Them Conservative

Explore vector fields, their graphical representations in 2D and 3D, and the concept of conservative vector fields in this comprehensive introduction.

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

Professor Leonard

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

Explore triple integrals using cylindrical and spherical coordinates, with applications to center of mass and moments of inertia in advanced calculus.

• 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

Comprehensive guide to solving triple integrals, exploring their applications in calculating mass, volume, and center of mass for 3D regions. Ideal for advanced calculus students seeking in-depth understanding.

• 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

Explore center of mass, moments, and inertia for 2D lamina. Learn to calculate mass, moments of mass, moments of inertia, and radius of gyration, with practical problem-solving applications.

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

Professor Leonard

Calculus 3 - Double Integrals Over Polar Regions

Comprehensive exploration of double integrals in polar coordinates, covering translation from rectangular to polar forms and practical applications in calculus.

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

Professor Leonard

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

Comprehensive guide to solving double integrals, covering construction techniques over various regions. Ideal for mastering advanced calculus concepts and enhancing problem-solving skills in multivariable integration.

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

Professor Leonard

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

Comprehensive guide to finding relative and absolute extrema of two-variable functions, covering optimization techniques for advanced calculus applications.

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

Professor Leonard

Introduction to Double Integrals - Background Info

Explore the origins, representations, and fundamental concepts of double integrals in this comprehensive introduction, laying the groundwork for advanced calculus applications.

• 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 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