MATH 4721 / 6721 Fall 2017
Numerical Analysis Dwiggins
Tuesdays Thursdays
Aug 29 §§ 5.1-2 Aug 31 §§ 5.2-3
Numerical Solutions to Euler's Method,
Ordinary Differential Equations: Runge-Kutta Methods,
Initial Value Problems and variations on those themes
Sep 5 §§ 5.4, 4.1-2 Sep 7 §§ 4.2-3
Multi-Step Methods for ODEs, Simpson's Rule
Introduction to and Beyond
Numerical Integration HW # 1 due (Chapter 5)
Sep 12 §§ 4.5-6 Sep 14 §§ 4.8-9
Gaussian Quadrature, Improper Integrals,
Adaptive Quadrature, Techniques for
Examples from Physics Numerical Differentiation
Sep 19 §§ 1.1-3 Sep 21 §§ 1.3-5
Floating-Point Arithmetic Error Analysis:
and Computational Error Estimating the total error, and
HW # 2 due (Chapter 4) algorithms for minimizing error
Sep 26 §§ 2.1-3 Sep 28 §§ 2.4-6
Classical Techniques of Newton's Method,
Approximate Computation Rates of Convergence,
(e.g. the Mechanic's Method) Müller's Method
Oct 3 §§ 3.1-2 Oct 5 § 3.2
Polynomial Interpolation, Recursion Relations
the Lagrange Polynomial for Interpolating
HW # 3 due (Chapters 1-2) Polynomials
Oct 10 § 3.3 Oct 12 §§ 3.4-5
Organizing your work: Hermite Polynomials,
Divided Difference Introduction to
Tables Spline Theory
Oct 17 FALL BREAK Oct 19  
   
No classes scheduled REVIEW
   
Oct 24   Oct 26 §§ 6.1-2
Mid-Term Exam Solving Linear Systems:
Chapters 1, 2, 4, 5 Gaussian Elimination and
  Backward Substitution
Oct 31 § 6.3 Nov 2 § 6.4
Matrix Inversion and Matrix Inverses and
Pivoting Schemes Determinants, and why we
HW # 4 due (Chapter 3) often don't really need them
Nov 7 § 6.5 Nov 9 § 6.6
Matrix Factorizations Problems involving
and their special types of matrices
Applications (Band Matrices, Tridiagonal Matrices)
Nov 14 §§ 7.2-3 Nov 16 §§ 7.3-4
Vector Norms and Methods for estimating
Matrix Norms Eigenvalues and
HW # 5 due (Chapter 6) Eigenvectors
Nov 21 § 7.6 Nov 23 THANKSGIVING
Matrix Factorizations  
and their No classes scheduled
Applications  
Nov 28 § 8.4 Nov 30 §§ 9.5-6
Interpolation using More on matrices:
Orthogonal Polynomials Householder's Method,
HW # 6 due (Chapter 7) the QR Decomposition
Dec 5   Dec 7 STUDY DAY
   
REVIEW No classes scheduled
   
Dec 12   Dec 14  
Final Exam Extra Credit
Chapters 3, 6, 7, plus Assignments Due
material from Mid-Term Exam  
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