Streamlining applications of integration by parts in teaching applied calculus

<abstract> Based on the tutorial cases accumulated in the past several years, by reclassifying the arithmetic functions (A) in LIATE into the polynomial function (<italic>P</italic>), the standard power function (<italic>Po</italic>), and the integer power function (<italic>nPo</italic>), a new guide, comprising three sub-guides, <italic>Pet</italic>, <italic>LoPo</italic> and <italic>InPo</italic>, or <italic>Pet-LoPo-InPo</italic>, is summarized in this note to guide practicing integration by parts. This new guide removes many incompatible combinations included in LIATE, rationalizes the relationship between the exponential and trigonometric functions in LIATE, and expands the coverage of the <italic>P</italic>-functions beyond the traditional definitions. Hence, the new guide can reduce potential confusions that students may experience in using LIATE for their practices of integration by parts. The advantages of this new guide are demonstrated by many worked examples in this note. </abstract>

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Solving problems involving numerical integration (I): Incorporating different techniques

Guo

2023

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<abstract> Numerical integration plays an important role in solving various engineering and scientific problems and is often learnt in applied calculus commonly through the trapezium and Simpson's methods (or rules). A common misconception for some students is that Simpson's method is the default choice for numerical integration due to its higher accuracy in approximation over the trapezium method by overlooking the requirement for using Simpson's method. As learning progressed to other numerical methods scheduled later in advanced mathematics, such as interpolations and computational modelling using computing tools like MATLAB, there is a lack of articulation among these numerical methods for students to solve problems solvable only by combining two or more approaches. This classroom note shares a few teaching and learning practices the author experienced in lectures, tutorials, and formal assessments on comparing or combining different numerical methods for numerical integration for engineering students in applied calculus and advanced mathematics over the past decade at Central Queensland University (CQU), a regional university in Australia. Each case represents a common concern raised or a mistake made by some students in different times. These efforts helped not only correct the misconception on the use of Simpson's method by some students, but also develop students' strategic thinking in problem solving, particularly involving decision-making for choosing the best possible method to produce a more appropriate solution to a problem that does not have an analytical solution. </abstract>

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Streamlining applications of integration by parts in teaching applied calculus

Cited by 4 publications

References 4 publications

The Teaching and Learning of Tertiary Mathematics

The Teaching and Learning of Tertiary Mathematics

A guide for using integration by parts: <i>Pet-LoPo-InPo</i>

Solving problems involving numerical integration (I): Incorporating different techniques

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