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

Chapter 1 – Mathematical Preliminaries and Floating-Point Representation

  • Section 1.1: Introduction (due 8/30)

    • reading: pp. 2-14
    • homework: 3
  • Section 1.2: Mathematical Preliminaries (due 9/1)

    • reading: pp. 20-28
    • homework: 5
  • 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
  • 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

Chapter 3 – Nonlinear Equations

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

    • reading: pp. 114-123
    • homework: 1
  • Section 3.2: Newton’s Method (due 9/20)

    • reading: pp. 125-135
    • homework: 1
  • Section 3.3: Secant Method (due 9/22)

    • reading: pp. 142-149
    • homework: 3

Chapter 4 – Interpolation and Numerical Differentiation

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

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

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

    • reading: pp. 187-189, 194-198
    • homework: 1

Chapter 5 – Numerical Integration

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

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

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

    • reading: pp. 239-245
    • homework: 1

Chapter 6 – Spline Functions

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

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

    • reading: pp. 263-268, 275-276
    • homework: 6

Chapter 9 – Least Squares Methods and Fourier Series

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

    • reading: pp. 426-432
    • homework: 1

Chapter 7 – Initial Value Problems

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

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

    • reading: pp. 311-316
    • homework: 2

Chapter 8 – More on Linear Systems

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

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