Reading

As described in the syllabus, you are required to read each section and do a quiz prior to each class.

  • The reading assignments are listed below, and must be read prior to class on the date indicated.
  • Quizzes based on each reading must be completed on Canvas prior to the beginning of class on the date indicated.

I encourage you to work together on these problems.

Chapter 1 – Mathematical preliminaries

  • Introduction to logic, sets, and proofs: read Logic, Sets, and Proofs by D.A. Cox and C.C. McGeoch, due Aug 23
  • Section 1.1: Basic Concepts and Taylor’s Theorem, pp. 3-12, due Aug 28
  • Section 1.2: Orders of Convergence and Additional Basic Concepts, pp. 15-24, due Aug 30

Chapter 3 – Solution of nonlinear equations

  • Section 3.2: Newton’s Method, pp. 81-90, due Sep 4
  • Section 3.4: Fixed Points and Functional Iteration, pp. 100-105, due Sep 6

Chapter 6 – Approximating functions

  • Section 6.1: Polynomial Interpolation, pp. 308-323, due Sep 13
  • Section 6.2: Divided Differences, pp. 327-335, due Sep 18
  • Section 6.3: Hermite Interpolation, pp. 338-345, due Sep 20
  • Section 6.4: Spline Interpolation, pp. 349-358, due Sep 25
  • Section 6.8: Best Approximation: Least-Squares Theory, pp. 392-403, due Oct 2

Chapter 7 – Numerical differentiation and integration

  • Section 7.1: Numerical Differentiation and Richardson Extrapolation, pp. 465-476, due Oct 16
  • Section 7.2: Numerical Integration Based on Interpolation, pp. 478-488, due Oct 18
  • Section 7.3: Gaussian Quadrature, pp. 492-498, due Oct 23
  • Section 7.5: Adaptive Quadrature, pp. 507-512, due Oct 30

Chapter 8 – Numerical solution of ordinary differential equations

  • Section 8.2: Taylor-Series Method, pp. 530-535, due Nov 1
  • Section 8.3: Runge-Kutta Methods, pp. 539-546, due Nov 6
  • Section 8.4: Multistep Methods, pp. 549-554, due Nov 8
  • Section 8.5: Local and Global Errors: Stability, pp. 557-564, due Nov 13
  • Section 8.6: Systems and Higher-Order Ordinary Differential Equations, pp. 565-570, due Nov 15
  • Section 3.6: Homotopy and Continuation Methods, pp. 130-137, due Nov 20
  • Section 8.7: Boundary-Value Problems, pp. 572-578, due Nov 27
  • Section 8.9: Boundary-Value Problems: Finite-Differences, pp. 589-592, due Nov 29