Amber C. Sumner, William Carey University

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- Preliminaries
- What is Numerical Analysis?
- Understanding Error

- Numerical Linear Algebra
- Direct Methods for Linear Systems
- Least Squares Problems
- Iterative Methods for Linear Systems
- Eigenvalue Problems

- Data Fitting and Function Approximation
- Polynomial Interpolation
- Approximation of Functions
- Differentiation and Integration

- Nonlinear Equations and Optimization
- Zeros of Nonlinear Functions
- Optimization

- Differential Equations
- Initial Value Problems
- Two-Point Boundary Value Problems
- Partial Differential Equations

- Review of Calculus
- Review of Linear Algebra

- Page 5: First paragraph, ``is is'' should be ``it is''
- Page 30: First paragraph, should say ``next innermost loop,
with index variable
`i`

'' - Page 52, Explorations 2.1.10 and 2.1.11: Equation reference (2.1.4) should actually be to un-numbered equation at the bottom of page 51
- Page 108, Explorations 3.3.9 and 3.3.10: The hint provided for 3.3.10 actually applies to 3.3.9
- Page 117, Algorithm 3.4.3: After the algorithm, the phrase ``test convergence'' should be ``convergence test''
- Page 127, Equation (4.3): $\hat{\bf x}$ should be ${\bf x}$
- Page 132, Equation (4.8): $s$ should have $\mathrm{sgn}(b)$ in the numerator
- Page 132, Equation (4.9): $c$ should have $\mathrm{sgn}(a)$ in the numerator
- Page 143, Algorithm 4.2.5: On third line from the bottom, a right parenthesis is missing at the end of the line
- Page 143, Algorithm 4.2.5: On second line from the bottom, all references to $Q$ should use rows $1:m$, not $j:m$
- Page 152, Explorations 4.3.3 and 4.3.5: ``Modify your function'' should be ``Use your function''
- Page 157, Exploration 4.4.9: It should be stated that $A$ is assumed to be a square, invertible matrix
- Page 164, Exploration 4.5.5: ``4.25'' should be in parentheses
- Page 166, Chapter 4, Exercise 1(b): Equation should be $A^T A = R^T R$
- Page 177: It needs to be explicitly stated that $k$ is a positive integer
- Page 178: All references to
**b**on this page, except for the equation for the residual at the bottom, should be**r**_{1} - Page 180: Should read ``$\tilde{T}_k$ has the $LDL^T$ factorization...''
- Page 180: Middle of the page, end of equation should be ``$= \beta_0 L_k^{-1}{\bf e}_1$''
- Page 181: Middle of the page, ``multiple of the initial'' should be ``multiple of the initial residual''
- Page 182: In Algorithm 5.2.3, the statement $k=1$ is not needed
- Page 184: In Algorithm 5.2.4, the statement $k=1$ is not needed
- Page 185-6: All references to ${\mathcal K}({\bf b},A,k)$ should be ${\mathcal K}({\bf r}_1,A,k)$, and ${\bf b}$ within $\langle f, g \rangle$ should also be ${\bf r}_1$
- Page 187: In Algorithm 5.3.1, $\beta_0$ should be $h_{10}$
- Page 214, Exploration 6.2.3: The matrix P should be a
*right*stochastic matrix - Page 218: After Algorithm 6.3.1, the expression $I - c{\bf vv}^T$ must be in parentheses
- Page 230, Exploration 6.4.8: The phrase ``Use your proof of the result in Exploration 6.4.7 to'' should be removed
- Page 234, Equation (6.10): This formula needs to be rewritten to avoid cancellation error; it should be μ =
*t*-_{nn}*t*_{n,n-1}^{2}/(*d*+ sign(*d*) (*d*^{2}+*t*_{n,n-1}^{2})^{1/2}) - Page 264: In computation of
*p*_{3}(*x*), second step, last two binomial coefficients should have lower indices of 2 and 3, respectively - Page 280: In formula for
*s*(*x*), first piece, -184/7 should be the coefficient of*x*, not*x*^{2} - Page 281: Not-a-knot boundary conditions are incorrectly described as being synonymous with natural boundary conditions. The MATLAB function
`spline`

supports not-a-knot, but not natural - Page 281, Exploration 7.6.7: ``members of
`p`

'' should be ``members of`pp`

'' - Page 286, Chapter 7, Exercise 9: ``output
`p`

'' should be ``output`pp`

'' - Page 286, Chapter 7, Exercise 6: $\pi_n'(x)$ should be $\pi_n'(x_j)$
- Page 300, Example 8.2.1: In the normal equations,
*n*should be 4 - Page 303: Above last equation, should be:
*p*_{-1}(*x*)≡0 - Page 373, Exploration 9.7.2: There is no
`makelegendre`

function from Section 8.2; instead, should use equation (8.9) - Page 386, Chapter 9, Exercise 6: The error formula for the Corrected Trapezoidal Rule should include the 4th derivative of f, not the 5th
- Page 394, Figure 10.1, right plot: Error should be 0.707, not 1.707
- Page 407, Example 10.3.6: should be ``containing
*x*=3/4.'' - Page 419, Exploration 10.4.6: ``What was wrong'' should be ``What happens''
- Page 477: In description of
`ode23`

, should be ``the second output`y`

is an (*n*+1)×*m*matrix'' and ``The (*i*+1)st row of`y`

consists of the values of*y*(*t*), for_{i}*i*=0,1,2,...,*n*.'' - Page 483: In definition of
*F*(*y*), the second summation should have a terminal index of*m*, not*s* - Page 484: In sequence of steps above equation (12.24), = should be ≈ in each step
- Page 487: Definition of α
_{i}should have a factor of*h*on the right side of the equation - Page 490: In computation of τ
_{n}(*h*),*f*(*t*,_{n}*y*(*t*)) is missing its closing right parenthesis in two places_{n} - Page 491: Above Exploration 12.4.3, the formula for
τ
_{n}(*h*) needs to be negated - Page 494, Equation (12.32): sum should have initial index of 1, not 0
- Page 495: Upper bound on |
*e*| is missing a factor of δ_{n} - Page 510, Exploration 12.6.3: ``use'' should be ``modify''
- Page 516, Exploration 13.1.2: should be ``condition
*y*_{2}(*b*) ≠ 0 is guaranteed'' - Page 520, Figure 13.1: Labels in the legend should be switched
- Page 521, Exploration 13.1.8: should be ``input argument
`f`

'' - Page 522, Equation (13.9):
*y*(*x*) should be_{i}*y*(*x*_{i-1}) - Page 526, Equation (13.14): Each entry in the
*i*th row of*J*_{F}(**y**) is a partial derivative of*F*, not_{i}*f*_{i} - Page 525, Figure 13.2: ``with circles'' should be ''with diamonds''
- Page 533, Example 13.3.1: The plot produced by the code is not the same as Figure 13.3. Also, in the caption of Figure 13.3, ``circles'' should be ``diamonds''
- Page 569, Exploration 14.4.1: ``second input arguments'' should be ``second and third input arguments''
- Page 573: In definition of
*u*,_{M}*u*should be_{j}*c*_{j} - Page 574, Exploration 14.5.1: (14.61) should be (14.60)