# Homework¶

• As described in the syllabus, there are two sets of homework problems from each section:
• The pages marked “reading” must be read prior to class on the date indicated.
• The problems marked “homework” will be turned in for a grade at the beginning of class on the date indicated. The reading will be critical to completing these problems.
• The problems marked “practice” will not be turned in, but should be done after the indicated class in preparation for exams.
• The homework and practice problems are from Problems of a section (Not from Computer Problems).
• I highly recommend that you do all practice problems as we progress through the material, instead of waiting until just prior to each exam.
• I encourage you to work together on these problems

## Chapter 1 – Mathematical Preliminaries and Floating-Point Representation¶

• Section 1.1: Introduction (due 8/30)

 reading: pp. 2-14 homework: 3 practice: 6, 10, 12 (solutions)
• Section 1.2: Mathematical Preliminaries (due 9/1)

 reading: pp. 20-28 homework: 5 practice: 6, 15, 30, 37 (solutions)
• Section 1.3: Floating-Point Representation (due 9/6)

 reading: pp. 38-51 homework: 15 practice: none

## Chapter 2 – Linear Systems¶

• Section 2.1: Naive Gaussian Elimination (due 9/8)

 reading: pp. 69-80 homework: 2 practice: 5 (solutions)
• Section 2.2: Gaussian Elimination with Scaled Partial Pivoting (due 9/13)

In your reading and problems for this section, you can ignore the ‘scaling’ portion of the algorithm, focusing instead on only the Gaussian Elimination with Partial Pivoting algorithm.

 reading: pp. 82-93, 97 homework: 1 practice: 3, 17, 19, 20 (solutions)

## Chapter 3 – Nonlinear Equations¶

• Section 3.1: Bisection Method (due 9/15)

 reading: pp. 114-123 homework: 1 practice: 8, 12, 13, 17 (solutions)
• Section 3.2: Newton’s Method (due 9/20)

 reading: pp. 125-135 homework: 1 practice: 12, 17, 41 (solutions)
• Section 3.3: Secant Method (due 9/22)

 reading: pp. 142-149 homework: 3 practice: 4, 13 (solutions)

## Chapter 4 – Interpolation and Numerical Differentiation¶

• Section 4.1: Polynomial Interpolation (due 9/27)

 reading: pp. 153-160, 167-168 homework: 1 practice: 4, 10, 11, 45 (solutions)
• Section 4.2: Errors in Polynomial Interpolation (due 10/4)

 reading: pp. 178-183 homework: 6 practice: 10, 13 (solutions)
• Section 4.3: Estimating Derivatives and Richardson Extrapolation (due 10/13)

 reading: pp. 187-189, 194-198 homework: 1 practice: 8, 24a (solutions)

## Chapter 5 – Numerical Integration¶

• Section 5.1: Trapezoid Method (due 10/18)

 reading: pp. 201-209 homework: 1 practice: 9, 11, 14 (solutions)
• Section 5.3: Simpson’s Rules and Newton-Cotes Rules (due 10/20)

 reading: pp. 227-231, 235-237 homework: 1 practice: 2 (solutions)
• Section 5.4: Gaussian Quadrature Formulas (due 10/25)

 reading: pp. 239-245 homework: 1 practice: 3, 5 (solutions)

## Chapter 6 – Spline Functions¶

• Section 6.1: First-Degree and Second-Degree Splines (due 10/27)

 reading: pp. 252-258 homework: 1 practice: 9, 20 (solutions)
• Section 6.2: Natural Cubic Splines (due 11/1)

 reading: pp. 263-268, 275-276 homework: 6 practice: 8, 12, 40 (solutions)

## Chapter 9 – Least Squares Methods and Fourier Series¶

• Section 9.1: Method of Least Squares (due 11/10)

 reading: pp. 426-432 homework: 1 practice: 3, 19 (solutions)

## Chapter 7 – Initial Value Problems¶

• Section 7.1: Taylor Series Methods (due 11/15)

 reading: pp. 299-309 homework: 1a practice: 10, 12 (solutions)
• Section 7.2: Runge-Kutta Methods (due 11/17)

 reading: pp. 311-316 homework: 2 practice: 3, 9, 11 (solutions)

## Chapter 8 – More on Linear Systems¶

• Section 8.4: Iterative Solutions of Linear Systems (due 11/22)

 reading: handout homework: 2 (in handout) practice: 6,7 (in handout), 3-10 (in book) (solutions)