Mathematics Courses and Certifications

Professor Leonard

Introduction to Initial Value Problems - Differential Equations

Explore initial value problems in differential equations, transitioning from general to particular solutions. Learn their significance and practical applications.

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

Professor Leonard

Checking Solutions in Differential Equations

Learn to verify solutions for differential equations, enhancing your problem-solving skills and deepening your understanding of this fundamental mathematical concept.

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

Professor Leonard

Surface and Flux Integrals, Parametric Surf., Divergence-Stoke's Theorem: Calculus 3 Lecture

Comprehensive exploration of advanced calculus concepts including surface integrals, flux integrals, and theorems, with practical applications and problem-solving techniques.

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

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