## Browsing by Author "Leahy, J. (James)"

Now showing items 1-20 of 37

• #### MathsCast: Completing the Square ﻿

(Swinburne Commons, 2011)
Explains the concept of completing the square with two practical examples resulting in trigonometric identities.

• #### MathsCasts: Cyclical Integration by Parts ﻿

(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 ﻿

(Swinburne Commons, 2011)
Discusses important integrand properties with simple examples.

• #### MathsCasts: Integrating Exponents ﻿

(Swinburne Commons, 2011)
Discusses how to integrate exponents with simple examples.

• #### MathsCasts: Integration by Parts: Definition ﻿

(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 ﻿

(Swinburne Commons, 2011)
Applies the method of integration by parts to integrate Arc Tan.

• #### MathsCasts: Integration by Parts: Integrating Ln ﻿

(Swinburne Commons, 2011)
Applies the method of integration by parts to integrate Ln.

• #### MathsCasts: Integration by Parts: Simple Example ﻿

(Swinburne Commons, 2011)
Applies the method of integration by parts to a simple function.

• #### MathsCasts: Integration: The Power Rule ﻿

(Swinburne Commons, 2011)
Definition and example of the power rule for integration. Includes exception to this power rule.

• #### MathsCasts: Inverse Trigonometric Identities ﻿

(Swinburne Commons, 2011)
Discusses inverse trigonometric identities with simple examples.

• #### MathsCasts: Inverse Trigonometric Identities: When the X-Coefficient is Not One ﻿

(Swinburne Commons, 2011)
Discusses inverse trigonometric identities when the x-coefficient is not one.

• #### MathsCasts: Iterative Reduction Formula: Part 1 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(Swinburne Commons, 2012)
Calculates the MacLaurin series for the trigonometric function sine x. Comments on the pattern of the series.

• #### MathsCasts: Newton's Method ﻿

(Swinburne Commons, 2012)
Introduces Newton' Method and explains the procedure for finding a root.

• #### MathsCasts: Partial Fractions: Definition ﻿

(Swinburne Commons, 2011)
Explains the concept of Partial Fractions.

• #### MathsCasts: Partial Fractions: Linear Roots Part 1 ﻿

(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 ﻿

(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.