Use synthetic division (Hormer's method) to find P(c).ġ5. 4 for cach funciiun expanded about tt»ġ3. Find the Taylor polynamial of degree n =.
Find the numberts c referred to in Rolle's thcorem for cach function over the indi-įind lhe numberts) e referred to in the mean value theorem for each function over theġ2. given any e > U, there exislsa 5 > U such thai, whcneverx e S,0 5x Zoverusingįind the upper and lower buunds referred to in the extreme value theorem for each Said to have the Emit L aux = xo, and we write assume thal f(x) is defined on a set $ of rzal numbers, Then f is Le undergraduate calculus sequence, This should have included the topics of limits.Ĭontinaity, differentiation, integration, sequences, and series. It is assumeu that the reader is tamiliar with the notation and subject matter covered in Thus we can view lhe sequence fenJX, = (xy - LYX, às an error sequence, The Thailx, - Lj Lasn - 39” Fquation (4) is equivalent to If, given any e > 0, there exista a positive integer N = N(e) such that r > 4 implics Supposc that (zn)££, is an infinite sequence, Then the sequence is LS) = (4/94 3 is not continnons at x = 0. As an example, consider Me function f(x) = x! on (pe inter.
The notation €"($) stands for he set of all funcliors / such that f and às first nĭerivatives are continuous on S. The function / is sai to be continuous on 5 if it is continuous at each point x e S. Then f is said to be continuons ai X = xo it These are some uT lhe results that we will necd to use from calculus.ĭefinition 1.2, Assume thar f (x) is defined on à set S of rcal nutabers and lerxg € 5. ħ3 Recursive Rules and Romberg Integration 368 Answers to Selected Exercises 631ħ5 GaussLegendre Integration (Optional) 389 Index 655
Some Suggested References for Reports 616ħ1 Introduction to Quedrature 343 Bibliography and References 619ħ2 Composite Trapezcidal ano Simpson's Rulc 354.
“4 Fourier Series amu Trigonomenie Podynomizis 297 ELi Homogêneous Systems: The Eigenvaloe Problem 556Ħ Numerical Differentiation 318 11,4 Eigenvalues of Syrametric Matricet, sáĦ.2 Numerica: Differentiation Formulas 329 Appendix: An Introduction to MATLAB 60% Įbyshev Polynomials (Optional) 230 10 Solution of Partial Differential Equations 514ĥ Curve Fitting 252 103 Elipiic Equativos 9%ĥ3 Curve Fiting 263 11 Eigenvalues and Eigenvectors 555ĥ3 interpolation by Spline Functions 279. Pproximation 96 Predictor-Corector Methods 474Ĥ1 Taylor Series and Culcularion of Functions 187 92 Systems of Differentia! Eguations 487Ĥ2 Introduction to Inlerpolaton 159 9.8 Boundary Velue Problems 497ģ3 Lagrange Approximaion 206 99 Finite-dilTerence Method 505Ĥs Chebyshev Polynomials (Optional a : a. Newton's Methods (Optional) 167 92 Euers Method 433Ĥ -nterpolation and Polynomish 05 Rampekme Menem 50 The Solution of Linear Systems AX = B 102ģ2 Properties ot Vectors and Matrices 109 8 Numerical Optimization 399ģ3 Uppeciriangular Lincar Systems 420 81 Minimization of 2 Fuacrion 460ģ6 lerative Methods for Linear Systems 156 9 Solution of Differential Equations 426Ģ7 Iteraon for Nontinear Systeris: Seidel and 91 Introduction to Diffesential Eguarions 427 Initia: Approximation and Convergence Criteria -62
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