February  2022, 2(1): 73-83. doi: 10.3934/steme.2022005

Streamlining applications of integration by parts in teaching applied calculus

School of Engineering and Technology, Central Queensland University, Bruce Highway, North Rockhampton, QLD 4702, Australia

* Correspondence: Email: w.guo@cqu.edu.au; Tel: +61-7-49309687

Academic Editor: Gaifang Dong

Received  November 2021 Revised  January 2022 Published  March 2022

Integration by parts can be applied in various ways for obtaining solutions for different types of integrations and hence it is taught in all calculus courses in the world. However, the coverage and discourse of various applications of integration by parts in most textbooks, often packed into one section, lack a cohesion of progression for solving different types of integrals. Students may be confused by such incohesive presentation of the method and applications in the textbooks. Based on the author's experiences and practices in teaching applied calculus for undergraduate engineering and education students since 2013, a streamlined approach in teaching integration by parts has been gradually developed to the current state and ready to be shared with the mathematics teaching and learning communities. This streamlined approach allows integration by parts to be applied to solve complicated and integrated problems in a progressive way so that students can improve efficacy in their use of integration by parts gradually. This approach also makes communications easier with students on particular problems involving integration by parts.

Citation: William Guo. Streamlining applications of integration by parts in teaching applied calculus. STEM Education, 2022, 2 (1) : 73-83. doi: 10.3934/steme.2022005
References:
[1]

Guo, W., Unification of the common methods for solving the first-order linear ordinary differential equations. STEM Education, 2021, 1(2): 127‒140. https://doi.org/10.3934/steme.2021010 doi: 10.3934/steme.2021010.

[2]

Zill, D.G., A First Course in Differential Equations with Modeling Applications, 10th ed. 2013, Boston, USA: Cengage Learning.

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Kreyszig, E., Advanced Engineering Mathematics, 10th ed. 2011, USA: Wiley.

[4]

Croft, A., Davison, R., Hargreaves, M. and Flint J., Engineering Mathematics, 5th ed. 2017, Harlow, UK: Pearson.

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Stewart, J., Calculus: Concepts and Contexts, 4th ed. 2019. USA: Cengage.

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Trim, D., Calculus for Engineers. 4th ed. 2008, Toronto, Canada: Pearson.

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Guo, W.W., Essentials and Examples of Applied Mathematics. 2018, Melbourne, Australia: Pearson.

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Massingham, P. and Herrington, T., Does attendance matter? An examination of student attitudes, participation, performance and attendance. Journal of University Teaching and Learning Practice, 2006, 3: 82–103. https://doi.org/10.53761/1.3.2.3 doi: 10.53761/1.3.2.3.

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Henry, M.A., Shorter, S., Charkoudian, L., Heemstra, L.M. and Corwin, L.A., FAIL is not a four-letter word: A theoretical framework for exploring undergraduate students' approaches to academic challenge and responses to failure in STEM learning environments. CBE Life Sciences Education, 2019, 18: 1–17. https://doi.org/10.1187/cbe.18-06-0108 doi: 10.1187/cbe.18-06-0108.

[10]

Guo, W., Li, W. and Tisdell, C.C., Effective pedagogy of guiding undergraduate engineering students solving first-order ordinary differential equations. Mathematics, 2021, 9(14):1623. https://doi.org/10.3390/math9141623 doi: 10.3390/math9141623.

show all references

References:
[1]

Guo, W., Unification of the common methods for solving the first-order linear ordinary differential equations. STEM Education, 2021, 1(2): 127‒140. https://doi.org/10.3934/steme.2021010 doi: 10.3934/steme.2021010.

[2]

Zill, D.G., A First Course in Differential Equations with Modeling Applications, 10th ed. 2013, Boston, USA: Cengage Learning.

[3]

Kreyszig, E., Advanced Engineering Mathematics, 10th ed. 2011, USA: Wiley.

[4]

Croft, A., Davison, R., Hargreaves, M. and Flint J., Engineering Mathematics, 5th ed. 2017, Harlow, UK: Pearson.

[5]

Stewart, J., Calculus: Concepts and Contexts, 4th ed. 2019. USA: Cengage.

[6]

Trim, D., Calculus for Engineers. 4th ed. 2008, Toronto, Canada: Pearson.

[7]

Guo, W.W., Essentials and Examples of Applied Mathematics. 2018, Melbourne, Australia: Pearson.

[8]

Massingham, P. and Herrington, T., Does attendance matter? An examination of student attitudes, participation, performance and attendance. Journal of University Teaching and Learning Practice, 2006, 3: 82–103. https://doi.org/10.53761/1.3.2.3 doi: 10.53761/1.3.2.3.

[9]

Henry, M.A., Shorter, S., Charkoudian, L., Heemstra, L.M. and Corwin, L.A., FAIL is not a four-letter word: A theoretical framework for exploring undergraduate students' approaches to academic challenge and responses to failure in STEM learning environments. CBE Life Sciences Education, 2019, 18: 1–17. https://doi.org/10.1187/cbe.18-06-0108 doi: 10.1187/cbe.18-06-0108.

[10]

Guo, W., Li, W. and Tisdell, C.C., Effective pedagogy of guiding undergraduate engineering students solving first-order ordinary differential equations. Mathematics, 2021, 9(14):1623. https://doi.org/10.3390/math9141623 doi: 10.3390/math9141623.

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