Taylor and Maclaurin series is very useful in higher engineering mathematics. We can expand functions like exponential, sine and cosine functions. Functions can be approximated up to certain terms of Taylor and Maclaurin series. of course, there will be some error in truncated series but that error can be minimized by considering more number of terms. We will discuss the Tayor as well as Maclaurin series with the help of video lectures.
1. Taylor ‘s Theorem and Series
Expansion of function up to n terms is called Taylor’s Theorem. If n tends to infinity, we will have an infinite number of terms and then the theorem is called a series. We can expand a function about any point using Taylor series. Watch the video lecture attentively to learn the use of Taylor series. We have also discussed the examples to make you understand the concepts easily.
2. Maclaurin Theorem and Series
If function contain a definite number of terms (say n terms), it is called Maclaurin theorem and if n tends to infinity, the theorem is called Maclaurin series. Maclaurin series is also called the Taylor series expansion about x = 0. With the help of the Maclaurin series, we have expanded various functions like sine, cosine, and exponential functions. Watch the video tutorial to learn this topic.
Keep revising the concepts by doing exhaustive examples. We will add more examples on Taylor and Maclaurin series on our later videos. If you do not get the topic, watch the video lectures repeatedly until you grab the concepts. Practice makes the student smarter, hence, practice as much questions as you can.