數值分析參考資料
Lectures
| Date | Topics | Assignments | Reading |
|---|---|---|---|
| Aug 19 | Introduction Notes: PDF | ||
| Aug 21 | Review of Calculus Notes: PDF | § 1.1 | |
| Aug 24 | Review of Calculus, cont'd Notes: PDF | § 1.1 | |
| Aug 26 | Round-off Errors and Computer Arithmetic Notes: PDF | § 1.2 | |
| Aug 28 | Round-off Errors and Computer Arithmetic, cont'd Notes: PDF | § 1.2 | |
| Aug 31 | Algorithms and Convergence Notes: PDF | § 1.3 | |
| Sep 2 | Algorithms and Convergence, cont'd Notes: PDF | § 1.3 | |
| Sep 4 | The Bisection Method Notes: PDF Code: bisect.m | § 2.1 | |
| Sep 7 | Labor Day Holiday, no class | ||
| Sep 9 | Fixed-Point Iteration Notes: PDF Code: fixedpt.m | § 2.2 | |
| Sep 11 | Newton's Method Notes: PDF Code: newton.m | § 2.3 | |
| Sep 14 | The Secant Method and Method of Regula Falsi Notes: PDF | § 2.3 | |
| Sep 16 | Error Analysis for Iterative Methods Notes: PDF | § 2.4 | |
| Sep 18 | Acclerating Convergence Notes: PDF | Exam Paper 1 Assigned | § 2.5 |
| Sep 21 | Exam 1 Review | ||
| Sep 23 | Interpolation and the Lagrange Polynomial Notes: PDF | § 3.1 | |
| Sep 25 | Interpolation and the Lagrange Polynomial, cont'd Notes: PDF | Exam Paper 1 Due | § 3.1 |
| Sep 28 | Divided Differences Notes: PDF | § 3.2 | |
| Sep 30 | Interpolation Using Equally Spaced Points Notes: PDF Code: runge_newton.m | § 3.2 | |
| Oct 2 | Osculatory Interpolation Notes: PDF | § 3.3 | |
| Oct 5 | Cubic Spline Interpolation Notes: PDF Code: runge_spline.m | § 3.4 | |
| Oct 7 | Cubic Spline Interpolation, cont'd Notes: PDF | § 3.4 | |
| Oct 9 | Fall Break, no class | ||
| Oct 12 | Cubic Spline Interpolation, cont'd Notes: PDF | § 3.4 | |
| Oct 14 | Numerical Differentiation Notes: PDF Code: diffrule.m | § 4.1 | |
| Oct 16 | Richardson Extrapolation Notes: PDF | § 4.2 | |
| Oct 19 | Numerical Differentiation, cont'd | § 4.1 | |
| Oct 21 | Elements of Numerical Integration Notes: PDF Code: quadtrap.m, quadsimp.m, quadinterp.m, quadinterpweights.m | § 4.3 | |
| Oct 23 | Composite Numerical Integration Notes: PDF Code: quadcomptrap.m, quadcompsimp.m, quadcomp.m, quadcompnodes.m,quadcompweights.m | Exam Paper 2 Assigned | § 4.4 |
| Oct 26 | Exam 2 Review | ||
| Oct 28 | Romberg Integration Notes: PDF Code: quadromberg.m | § 4.5 | |
| Oct 30 | Adaptive Quadrature Methods Notes: PDF Code: quadadapsimp.m | Exam Paper 2 Due | § 4.6 |
| Nov 2 | Gaussian Quadrature Notes: PDF Code: quadgauss.m, quadgaussnodes.m, quadcompgauss.m | § 4.7 | |
| Nov 4 | Multiple Integrals Notes: PDF | § 4.8 | |
| Nov 6 | Improper Integrals Notes: PDF | § 4.9 | |
| Nov 9 | Discrete Least Squares Approximation Notes: PDF | § 8.1 | |
| Nov 11 | Discrete Least Squares Approximation, cont'd Notes: PDF | § 8.1 | |
| Nov 13 | Orthogonal Polynomials and Least Squares Approximation Notes: PDF | § 8.2 | |
| Nov 16 | Orthogonal Polynomials and Least Squares Approximation, cont'd Notes: PDF | § 8.2 | |
| Nov 18 | Orthogonal Polynomials and Least Squares Approximation, cont'd Code: makeorthpolys.m, makelegendre.m, nestedmult.m | § 8.2 | |
| Nov 20 | Trigonometric Polynomial Approximation Notes: PDF | § 8.5 | |
| Nov 23 | Trigonometric Polynomial Approximation, cont'd Fast Fourier Transforms Notes: PDF | § 8.5-8.6 | |
| Nov 25 | Thanksgiving Holidays begin, no class | ||
| Nov 30 | Review | ||
| Dec 2 | Review | ||
| Dec 7 | Final Exam, 10:45am-1:15pm Practice Exam: PDF Practice Exam Solution: PDF | ||
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