Matlab and Hand Calculation Help
Project 1: Power series expansion of A cos(at) Overview In this project you will apply calculus to write a soldal function of time as a truncated power series using the Taylor se expansion Along the way you will learn about robust methods of developing scripts. Once you are finished, you will learn about the limitations of a power series expansion. It is strongly recommended to complete each phase before moving on the next phase. This means you need to get started early Consider the functiont)=12 cas(40) where the efficient of tisinrads and is in seconds We can write this function as an infinite power series Phase 1. Getting a relatively simple script working fes quickly as possible). 20pts. Plata truncated power series for from t o t=0.25. starting with the first one term, then the sum of the first two s te p t o the first terms DESIGN SPECIFICATIONS 1. You should find a general expression for the mo re coefficients, s, include your hand calculation when you upload your solution) 2. You should use an array for the coeficients . These coefficients should be output to the Command Window in a way that is relatively easy to read and understand even though the 3. You should create functions to plat. These should be defined as effidently as possible without using a FOR loop (Using a POR loop will come bater) 4. The chart should have a meaningful title and proper and labels 5. Change the vertical axis to cut of some of the very high and very low values but still make sense in terms of the given function 6. For now, you should not be concerned with font sizes or a legend. These are coming next) For Spec 01, you should use a Taylor series expansion about t=0 te. where is the nth derivative of t)evaluated att . (Do not change the definition of You should end up with an expression for over, and another for e dit) For Spees 2 and you should set up an array of values corresponding to the non- confident. Note that there is an efficient way of creating the array of values Usedot operations to create the array of values. Then you should use the format a n d near the beginning of the script so that the output is meaningful for this wide range of values (continued) Phase 1 (continued Ale for Spec you will see think about a way o f the functions without FOR It will help to have the array of swak as you will be the cording the co n tence for the the coefficients in the functions you are Creating and once for the exponent of t ime when you are creating the si functions) For Spec a meaningful title should include the function being approximated by the power series and the number of the truncat si The should "Phase 1", so that this can be changed as you proceed through this project. You might weda For Spec . we are expecting the truncated series to eventually become something that looks like the given function, 12 cos Thero wse the AXIS OF YLENGO to choose Ylimits from -15 15. s ehing similar in other words without changing the limits on the hard for impossible to all whether your fire is correct but with one of these command you should just start to see the last function looking like the given function as for the first sors UPLOAD: Mand collation seript Command Window, one figure with all 6 graph) Project 1: Power series expansion of A cos(at) Overview In this project you will apply calculus to write a soldal function of time as a truncated power series using the Taylor se expansion Along the way you will learn about robust methods of developing scripts. Once you are finished, you will learn about the limitations of a power series expansion. It is strongly recommended to complete each phase before moving on the next phase. This means you need to get started early Consider the functiont)=12 cas(40) where the efficient of tisinrads and is in seconds We can write this function as an infinite power series Phase 1. Getting a relatively simple script working fes quickly as possible). 20pts. Plata truncated power series for from t o t=0.25. starting with the first one term, then the sum of the first two s te p t o the first terms DESIGN SPECIFICATIONS 1. You should find a general expression for the mo re coefficients, s, include your hand calculation when you upload your solution) 2. You should use an array for the coeficients . These coefficients should be output to the Command Window in a way that is relatively easy to read and understand even though the 3. You should create functions to plat. These should be defined as effidently as possible without using a FOR loop (Using a POR loop will come bater) 4. The chart should have a meaningful title and proper and labels 5. Change the vertical axis to cut of some of the very high and very low values but still make sense in terms of the given function 6. For now, you should not be concerned with font sizes or a legend. These are coming next) For Spec 01, you should use a Taylor series expansion about t=0 te. where is the nth derivative of t)evaluated att . (Do not change the definition of You should end up with an expression for over, and another for e dit) For Spees 2 and you should set up an array of values corresponding to the non- confident. Note that there is an efficient way of creating the array of values Usedot operations to create the array of values. Then you should use the format a n d near the beginning of the script so that the output is meaningful for this wide range of values (continued) Phase 1 (continued Ale for Spec you will see think about a way o f the functions without FOR It will help to have the array of swak as you will be the cording the co n tence for the the coefficients in the functions you are Creating and once for the exponent of t ime when you are creating the si functions) For Spec a meaningful title should include the function being approximated by the power series and the number of the truncat si The should "Phase 1", so that this can be changed as you proceed through this project. You might weda For Spec . we are expecting the truncated series to eventually become something that looks like the given function, 12 cos Thero wse the AXIS OF YLENGO to choose Ylimits from -15 15. s ehing similar in other words without changing the limits on the hard for impossible to all whether your fire is correct but with one of these command you should just start to see the last function looking like the given function as for the first sors UPLOAD: Mand collation seript Command Window, one figure with all 6 graph)
