Mathematics Video Courses and Playlists

I have more than 300 mathematics videos available on my YouTube channel, including complete courses, developing course series, and shorter topic-based playlists.

Browse all mathematics playlists on YouTube

Calculus

MA 241: Single Variable Calculus II

Full-semester Calculus II course covering applications and techniques of integration, sequences and series, power series, and differential equations.

▶ Complete MA 241 Single Variable Calculus II playlist

Topic playlists

• Applications of Integration
  • Arc length
  • Average value of a function
  • Work done lifting objects
  • Work done pulling up a rope
  • Springs and Hooke's Law
  • Work done pumping fluid from a tank
  • Force due to hydrostatic pressure
  • Center of mass
• Techniques of Integration
  • Substitution
  • Integration by parts
  • Trigonometric integrals
  • Trigonometric substitution
  • Partial fractions
  • Trapezoidal Rule
  • Simpson's Rule
  • Improper integrals
• Sequences and Series
  Topics include sequences, convergence, infinite series, convergence tests, absolute convergence, power series, and Taylor series.
• Ordinary Differential Equations
• Second-Order Differential Equations and the Method of Undetermined Coefficients

MA 242: Multivariable Calculus / Calculus III

Full-semester multivariable calculus course, beginning with vectors and extending through the major theorems of vector calculus.

▶ Complete MA 242 Multivariable Calculus playlist

Written index to the complete Multivariable Calculus course

Topic playlists

• Introduction to Vectors
• Calculus on Parametric Curves
• Differential Multivariable Calculus
• Double and Triple Integration
• Line Integrals
• Surface Integrals

Differential Equations

MA 341: Applied Differential Equations

These videos are intended primarily as a supplement to an undergraduate differential equations course.

• First-Order Ordinary Differential Equations
• Second-Order Differential Equations and the Method of Undetermined Coefficients
• Laplace Transforms

Real Analysis and Advanced Calculus

MA 425 / MA 511: Real Analysis I / Advanced Calculus I

This developing series introduces rigorous single-variable analysis and proof writing. Topics include the real numbers, sequences, convergence, infinite series, topology of the real line, continuity, differentiation, and integration.

▶ Real Analysis I / Advanced Calculus I playlist

This series is currently under development.

MA 426: Mathematical Analysis II / Real Analysis II

This upper-level real analysis course develops multivariable analysis in Euclidean space. Topics include metric and topological ideas, multivariable differentiation, the inverse and implicit function theorems, Taylor's theorem, integration in several variables, Fubini's theorem, and change of variables.

▶ Complete Real Analysis II playlist

Mathematical Modeling

MA 510: Mathematical Modeling for Secondary Teachers

This course uses mathematical models to study real-world problems and was developed especially for teachers and others interested in strengthening their use of mathematics in applied settings.

▶ MA 510 Mathematical Modeling playlist

More Mathematics Videos

My channel also includes videos on proof writing, linear algebra, MATLAB, differential equations, mathematical modeling, and other undergraduate and graduate mathematics topics.

Browse all mathematics playlists on YouTube