This lecture from M.I.T. is nearly 50 minutes long delivered by Professor David Jerison and covers the application of Taylor's series to a problem about stacking bricks. It is aimed at undergraduate students.
These lectures will give you some idea of how this subject is treated at university level.
Maclaurin was a Scottish mathematican who published the first systematic exposition of Newton's methods, written as a reply to Berkeley's attack on the calculus for its lack of rigorous foundations.
Software/Applets used on this page
There are widespread applications in science, economics, and engineering.
This question appears in the following syllabi:
|AP Calculus BC (USA)||5||Maclaurin and Taylor Series||Taylor series||-|
|AQA A2 Further Maths 2017||Pure Maths||Extra||Taylor Series||-|
|AQA AS/A2 Further Maths 2017||Pure Maths||Extra||Taylor Series||-|
|Edexcel A-Level (UK - Pre-2017)||FP2||Maclaurin and Taylor Series||Taylor series||-|
|Edexcel A2 Further Maths 2017||Further Pure 1||Methods in Calculus||Taylor Series||-|
|Edexcel AS/A2 Further Maths 2017||Further Pure 1||Methods in Calculus||Taylor Series||-|
|I.B. Higher Level||9||Maclaurin and Taylor Series||Taylor series||-|
|Methods (UK)||M10||Maclaurin and Taylor Series||Taylor series||-|
|OCR A2 Further Maths 2017||Pure Core||Extra||Taylor Series||-|
|OCR MEI AS Further Maths 2017||Numerical Methods||Extra||Taylor Series||-|
|Scottish Advanced Highers||M3||Maclaurin and Taylor Series||Taylor series||-|
|Scottish (Highers + Advanced)||AM3||Maclaurin and Taylor Series||Taylor series||-|
|Universal (all site questions)||M||Maclaurin and Taylor Series||Taylor series||-|
|WJEC A-Level (Wales)||FP3||Maclaurin and Taylor Series||Taylor series||-|