Taylor Series Teacher Resources
Find Taylor Series educational ideas and activities
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Polynomial Approximations--An Introduction to the Taylor Series
Twelfth graders examine the Taylor Series. In this calculus lesson, 12th graders explore the representation of a function as an infinite sum of terms calculated form the values of its derivatives at a single point, hence the Taylor Series. Students use a TI-89 to explore the patterns and the command to compute the Taylor series.
Convergence of Taylor Series
Students analyze taylor series for convergence. In this calculus lesson, students analyze the graph of a taylor series as it relates to functions. They use the TI calculator to graph and observe the different series.
In this calculus worksheet, students find the Taylor series for each function adn give the interval where the series converges. The two page worksheet contains nine questions. Answers are not included.
Taylor Series: Natural Number
In this calculus learning exercise, students apply the Taylor Series to exponential functions based at either zero or one. There are 2 questions with multiple parts.
Introduction to Taylor Series
In this Taylor Series worksheet, students explore functions with an infinite series. They complete an integral of convergence and explore the degree of the polynomials. This four-page worksheet contains four multi-step problems.
In this calculus learning exercise, students solve various functions for the Taylor Series using a variety of solving methods including the double angle formula, partial fractions, and u substitution. There are 8 questions.
Sequences and Series on a Calculator
Students find patterns in a sequence. In this sequences and series lesson, students use their calculator to find the sequence of partial sums. They graph functions and explore convergent series. Students approximate alternating series.
Worksheet 13 - Derivative
For this derivative of a power worksheet, students compare derivatives of functions, and graph functions. This one-page worksheet contains five multi-step problems.
Numeral Analysis: Rate of Convergence
In this rate of convergence learning exercise, students use three different methods to compute an order of convergence of a function. This four-page learning exercise contains approximately 10 problems, with examples.
Worksheet 5. Math 222. Intervals
In this interval worksheet, students determine the interval and radius of convergence of given equations. They use the Taylor series to identify points and the radii of convergence. This two-page worksheet contains 8 multi-step problems.
Error and Power Series
In this college level calculus learning exercise, students compare two series to compute the error given the number of terms added. Students write the Maclaurin and Taylor series for the given functions. The two page learning exercise contains seven problems. Answers are not provided.
Introduction to Taylor Series
In this Taylor series worksheet, students determine the difference between a Taylor series and a Taylor polynomial. They solve function problems. This two-page worksheet contains seven problems.
Basic Complex Analysis
This video gives an excellent overview of the different representations of a complex number. First, Sal reviews a pictorial representation of a complex number as an Argand diagram, then shows how to find the modulus and the argument of a complex number and write a complex number in the form z = r (cos _+isin_), and finally, how to write a complex number in exponential form using EulerÕs relations.
Forces Acting on a Spring
Teaching elastic forces in your physics class is a snap with this resource! Scholars compare the stretch of rubber bands with differing width, then measure the stretch of a spring and calculate force. In a whole-class experiment, wire is attached to the ceiling and stretched by adding weights to the loose end. When the weights are removed, does the wire return to its original length? Materials lists, procedures, background information and assessments are all provided for your convenience.
Help your pupils define a Taylor polynomial approximation to a function f of degree n about a point x = a. After completing several problems with guided practice, individuals graph convergence of Taylor polynomials and use them to approximate function values.
Infinite Sequences and Series
Students investigate sequences and series numerically, graphically, and symbolically. For this sequences and series lesson, students use their Ti-89 to determine if a series is convergent. Students find the terms in a sequence and series and graph them. Students use summation notation to determine the sum of a sequence.
Taylor and Maclaurin Series
In this Taylor and Maclaurin series worksheet, students answer 10 questions about Taylor and Maclaurin series. Students find the Taylor and Maclaurin series for trigonometric, exponential, and inverse functions at a given value.
AP Calculus Practice Exam: BC Version - Part A
In this calculus worksheet, students solve 28 multiple choice problems. Students find derivatives, volumes, limits, convergent series, etc.
Calculus Practice BC
In this calculus worksheet, students solve functions using the derivatives. They calculate the volume where the graph is revolving around the x-axis, a line, the y-axis and where x=e. There are 28 questions.
AP Calculus Practice Exam
In this calculus activity, students solve functions by taking the derivative of the equations. There are 28 questions using logs and trig functions.