Browsing by Author "Leahy, J. (James)"
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MathsCast: Completing the Square
Leahy, J. (James) (Swinburne Commons, 2011)Explains the concept of completing the square with two practical examples resulting in trigonometric identities.

MathsCasts: Cyclical Integration by Parts
Leahy, J. (James) (Swinburne Commons, 2011)Applies the method of repeated integration by parts to an function containing the product of exponential and trigonometric terms resulting in a cyclical answer.

MathsCasts: Important Integral Properties
Leahy, J. (James) (Swinburne Commons, 2011)Discusses important integrand properties with simple examples.

MathsCasts: Integrating Exponents
Leahy, J. (James) (Swinburne Commons, 2011)Discusses how to integrate exponents with simple examples.

MathsCasts: Integration by Parts: Definition
Leahy, J. (James) (Swinburne Commons, 2011)Defines the concept of integration by Parts, when it is appropriate to use IBP, and how to determine u and dv.

MathsCasts: Integration by Parts: Integrating Arc Tan
Leahy, J. (James) (Swinburne Commons, 2011)Applies the method of integration by parts to integrate Arc Tan.

MathsCasts: Integration by Parts: Integrating Ln
Leahy, J. (James) (Swinburne Commons, 2011)Applies the method of integration by parts to integrate Ln.

MathsCasts: Integration by Parts: Simple Example
Leahy, J. (James) (Swinburne Commons, 2011)Applies the method of integration by parts to a simple function.

MathsCasts: Integration: The Power Rule
Leahy, J. (James) (Swinburne Commons, 2011)Definition and example of the power rule for integration. Includes exception to this power rule.

MathsCasts: Inverse Trigonometric Identities
Leahy, J. (James) (Swinburne Commons, 2011)Discusses inverse trigonometric identities with simple examples.

MathsCasts: Inverse Trigonometric Identities: When the XCoefficient is Not One
Leahy, J. (James) (Swinburne Commons, 2011)Discusses inverse trigonometric identities when the xcoefficient is not one.

MathsCasts: Iterative Reduction Formula: Part 1
Leahy, J. (James) (Swinburne Commons, 2011)Firstly discusses iterative functions and solutions while noting the usefulness of an Iterative Reduction Formula for multiple integration by parts. Then applies this to a simple indefinite case.

MathsCasts: Iterative Reduction Formula: Part 2
Leahy, J. (James) (Swinburne Commons, 2011)Continues the previous simple indefinite example noting the construction of a base case. Then considers the corresponding definite case.

MathsCasts: Maclaurin Series: Composite Functions
Leahy, J. (James) (Swinburne Commons, 2012)Calculates the MacLaurin series for a composite function e^{sinx}. Highlights the fact that this series must be a polynomial.

MathsCasts: Maclaurin Series: Exponential Functions
Leahy, J. (James) (Swinburne Commons, 2012)Calculates the MacLaurin series for the exponential function. Also discusses the MacLaurin series for e^2x derived from the corresponding series for e^x.

MathsCasts: Maclaurin Series: Trigonometric Functions
Leahy, J. (James) (Swinburne Commons, 2012)Calculates the MacLaurin series for the trigonometric function sine x. Comments on the pattern of the series.

MathsCasts: Newton's Method
Leahy, J. (James) (Swinburne Commons, 2012)Introduces Newton' Method and explains the procedure for finding a root.

MathsCasts: Partial Fractions: Definition
Leahy, J. (James) (Swinburne Commons, 2011)Explains the concept of Partial Fractions.

MathsCasts: Partial Fractions: Linear Roots Part 1
Leahy, J. (James) (Swinburne Commons, 2011)Explains the partial fraction expansion procedure when the denominator has linear roots, and applies this technique to a simple example.

MathsCasts: Partial Fractions: Linear Roots Part 2
Leahy, J. (James) (Swinburne Commons, 2011)Firstly double checks the expansion from Part 1. Then shows the use of partial fractions to conduct the integration. Uses substitution in the resulting integrals.