Mathematics Courses and Certifications

Professor Leonard

Calculus 3 Lecture - The Cross Product

Explore vector cross products, determinants, orthogonal vectors, torque, and geometric applications. Master advanced calculus concepts with in-depth proofs and practical examples.

• YouTube
• 2 hours 11 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 3 - Using the Dot Product

Explore vector operations, angles, projections, and applications in physics using dot product. Master key concepts for advanced vector analysis and problem-solving in multivariable calculus.

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

Professor Leonard

Calculus 3 - Vectors in 3-D Coordinate System

Explore 3-D coordinate systems, position vectors, magnitude, and unit vectors. Master point relationships in three-dimensional space for advanced mathematical understanding.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Professor Leonard

Intermediate Algebra - Factoring the Greatest Common Factor

Master factoring techniques for algebraic expressions, focusing on identifying and extracting the Greatest Common Factor to simplify complex equations.

• YouTube
• 2 hours 18 minutes
• Self-Paced
• Free Video

Professor Leonard

Numerical Integration With Trapezoidal and Simpson's Rule

Learn to approximate definite integrals using the Trapezoidal and Simpson's Rules, powerful numerical methods for solving complex integration problems.

• YouTube
• 27 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