# 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

## Linux/HPC Introduction¶

- Do the Linux tutorial: (due 8/25)
- Do sessions from the 2015 SMU HPC Winter workshop: (due 8/30)
- Session 2: Introduction to Scripts and Programs: Write your script in Python (not BASH)
- Session 3: More Programming: Skip the section on “Modules”
- Session 4: Advanced Programming: Do the C++ version of the exercises

## 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¶

## 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`

)