About

These screencasts were produced by mathematicians at The Open University in conjunction with Swinburne University of Technology, kindly funded by The Higher Education Academy Maths, Stats and OR Network .

Making screencasts for teaching mathematics

This material was produced as part of a HEA MSOR-funded project, ”Supporting students studying advanced calculus using screencasts” to produce and evaluate the effectiveness of mathematical screencasts.

Project team: Camilla Jordan, Tim Lowe, and Ben Mestel from the Open University (UK), and Birgit Loch from Swinburne University of Technology (Australia).

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Screencasts By Topic

Cauchy’s Residue Theorem

• Example 1
• Example 2

Complex variable (function of)

• Taylor Series of a function of a complex variable
• Cauchy’s Residue Theorem: Example 1
• Cauchy’s Residue Theorem: Example 2
• Rouche’s Theorem

Differential Equations: First Order

• Solution of first order ODE using an integrating factor
  
• Solution of first order ODE by separation of variables

Differential Equations: Second Order

• Introduction to the Frobenius method for solving a second order linear ordinary differential equation
• Solution of a second order ordinary differential equation with constant coefficients
• Solution of Euler’s Equation (a second order nonlinear ordinary differential equation)
  
• Solution of a second order linear ordinary differential equation using the Frobenius method

Differentiation

• Differentiation of an integral
  
• Logarithmic differentiation

Forces

• Resolution of forces
  

Integration

• …by substitution
  • Integration by substitution using hyperbolic functions
    
• …contour integration
  • Cauchy’s Residue Theorem: Example 1
  • Cauchy’s Residue Theorem: Example 2
• …hyperbolic functions
  • Integration by substitution using hyperbolic functions
• …line integrals
  • Line integral (given in terms of dx, dy, dz)
  • Line integral (given in terms of dr)
• …over an area
  • Calculation of surface area using integration
• …trigonometric functions
  • Integration of sin x from 0 to π/2
  • Integration involving sin² x
  • Integration involving sin³ x
  • Integration involving tan³ x
  • Integration involving products of sin x and cos x
• …partial fractions
  • Integration using partial fractions
• …repeated integration
  • Calculation of surface area using integration

Lagrange multipliers

• Lagrange multipliers for optimisation with constraints
  

Legendre polynomials

• Legendre polynomials and generating functions

Limits

• Evaluation of limits using L’Hospital’s rule
  

Partial differentiation

• Partial differentiation using the chain rule

Partial fractions

• Partial fractions

Rouche’s Theorem

• Rouche’s Theorem

Surface area

• Calculation of surface area using integration

Taylor Series

• Taylor Series of a function of two variables
• Taylor Series of a function of a complex variable

Vectors

• Resolution of forces