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).
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
- Integration by substitution using hyperbolic functions
- …contour integration
- Cauchy’s Residue Theorem: Example 1
- Cauchy’s Residue Theorem: Example 2
- Cauchy’s Residue Theorem: Example 1
- …hyperbolic functions
- Integration by substitution using 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)
- Line integral (given in terms of dx, dy, dz)
- …over an area
- Calculation of surface area using integration
- 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
- Integration of sin x from 0 to π/2
- …partial fractions
- Integration using partial fractions
- Integration using partial fractions
- …repeated integration
- Calculation of surface area using 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
