# 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