# Errata

## for: Dynamic Equations on Time Scales: An Introduction With Applications, Birkhauser, Boston (2001) (with Martin Bohner)

• Page 4, line 15-: Replace "is closed and nonempty" by "is nonempty and $\T$ is closed"
• Page 11, line 19: Replace "$(fg)^{\Delta}$" by "$(fg)^{\Delta\Delta}$"
• Page 20, line 5-: There should be a minus sign in front of the right hand side of this equation.
• Page 40, line 2: Replace "\Delta s" by "\Delta\tau"
• Page 60, line 7-: Replace "less than" by "less than or equal to"
• Page 60, line 1-: Replace "<" by "$\leq$"
• Page 61, line 3: Add $s\neq t$
• Page 61, line 8: Replace "<" by "$\leq$"
• Page 63, line 4-: Replace "C_{rd}" by "\mathcal{R}"
• Page 70, line 14-: Replace "$e_1(\cdot,0)$" by "$e_1(\cdot,\alpha_0)$"
• Page 71, line 16-: Right before "Let N(t)" insert "Example 2.58."
• Page 73, line 1-: Replace $\infty$ by $L$.
• Page 74: The last exponetial in Table 2.3 on page 74 should be $\frac{(n+\alpha)^{(n-n_0)}}{n^{(n-n_0)}}$.
• Page 76, line 19: Replace "y" by "x".
• Page 93, line 11: Interchange the two columns of this matrix.
• Page 95, line 6: Replace "\mu\frac{\alpha^2}{4}" by "-\alpha+\mu\frac{\alpha^2}{4}".
• Page 97, line 4: Omit the last "$e_p(t,t_0)$".
• Page 102. In lines 4-8 we assume that $q$ is a constant.
• Page 117. In the integral in the table replace "r" by "$\alpha$".
• Page 125, line 2: Omit the first "5".
• Page 125, line 7: Replace the "x(2)" by "x^{\Delta}(1)".
• Page 126, line 10: Omit the second "(1+hz)".
• Page 127, line 3: Replace the first "9" by "13".
• Page 127, line 6: Replace the last "\frac{3}{1+2\mu}" by "$2$" and replace the last "3" by "\frac{3}{1+2\mu}".
• Page 127, line 3: Replace "sin_7(t,0)" by "e_7(t,0)".
• Page 129, line 7-: Replace "h_3(t,0)" by "h_2(t,0)" and replace "h_2(t,\sigma(s))" by "h_1(t,\sigma(s))".
• Page 138, 1ine 19-: Replace "$(n+1)^2$" in numerator of second term by "$(n+1)^3$."
• Page 138, 1ine 15-: Replace "$(n+1)^2$" in numerator of second term by "$(n+1)^3$."
• Page 139, 1ine 2: Replace "$p(t_0)$" by "$\frac{p(t_0)}{p(t)}$."
• Page 158, 1ine 14: Replace "$\sigma^2(t)$" by "$\sigma(t)$."
• Page 162, 1ine 1: In two places replace "$v$" by "$v_0$."
• Page 171, 1ine 14: Replace "50" by "49"
• Page 171, 1ine 15: In the upper limit of integration in the second integral replace "50" by "49"
• Page 171, 1ine 16: In the upper limit of summation in the second sum replace "49" by "48"
• Page 192, 1ine 22: Interchange "A" and "B" on right hand side of this equation.
• Page 208, 1ine 8-: Replace "$2\alpha^*X^{-1}u$" by "$2\Re(\alpha^*X^{-1}u)$."
• Page 209, 1ine 14-: Replace "$2\alpha^*X^{-1}u$" by "$2\Re(\alpha^*X^{-1}u)$."
• Page 209, 1ine 13-: Replace "$2\alpha^*(X^{\sigma})^{-1}X^{\Delta}X^{-1}u$" by "$2\Re(\alpha^*(X^{\sigma})^{-1}X^{\Delta}X^{-1}u)$."
• Page 209, 1ine 12-: Replace "$2\alpha^*(X^{\sigma})^{-1}u^{\Delta}$" by "$2\Re(\alpha^*(X^{\sigma})^{-1}u^{\Delta})$."
• Page 305, line 8-: By a dense point $t$ here we mean either $t$ is right dense or left dense. (this is not consistent with the definition on page 2.) My recommendation for the definition of a dense point is that it is either left dense or right dense.
• Page 317, 1ine 1-: Replace "$f_n(t)$" by "$f_n^{Delta}(t)$."
• Page 319, 1ine 8: In two places replace "$\sigma(t)$" by "$t$."
• Page 319, 1ine 4-: Replace "$D_{nt}$" by "$[t_0,t]$."
• Page 320, 1ine 13-: Replace "$(t,r]$" by "$(t,r]^{\kappa}$."
• Page 321, 1ine 3: Replace "$\nu(s,t)$" by "$\nu(s,r)$."
• Page 335, 1ine 7: Replace "$x(t,s)$" by "$k(t,s)$."
• Page 338. In the answer to Exercise 1.100 replace $t$ by $2t$.
• Page 338. The answer to Exercise 1.106 should be $\frac{t^{n+1}}{\sum_{\nu=0}^nq^{\nu}}$.
• Page 338, line 4-: Replace "$e_1(t_n,0)$" by "$e_1(t_n,\alpha_0)$".
• Page 338, line 2-: Replace "$\Gamma(\lambda)$" by "$\Gamma(\lambda+1)$".
• Page 339, line 12: Replace "$e_{ip}(t,t_0)$" by "$e_{ip}(t,s)$".
• Page 339, line 13: Replace "$e_{-ip}(t,t_0)$" by "$e_{-ip}(t,s)$".
• Page 339, line 18: Replace "$\cos_1=_\frac{e_i-e_{-i}}{2}$" by "$\cos_1=_\frac{e_i+e_{-i}}{2}$".
• Page 339, line 13: Replace "$e_{-ip}(t,t_0)$" by "$e_{-ip}(t,s)$"."$\frac{(t+\alpha-1)^{(\alpha)}}{\alpha!}$".
• Page 339, line 11-: Replace "$e^{-\frac{3}{2}t^2}$" by "$e^{\frac{3}{2}t^2}$".
• Page 339, line 11-: Replace "$c_2$" by "$c_2 t!$".
• Page 339, line 8-: Replace "$(t+\alpha-1)^{(\alpha)}$" by $"\frac{(t+\alpha-1)^{(\alpha)}}{\alpha !}$".
• Page 339, line 4-: Replace "$x(t)=c_12^t+c_2(-2)^t$" by "$x(t)=c_1t^2+c_2t^{-2}$".
• Page 342, 1ine 1: Replace last "$A$" by "$B$".
• Page 342, 1ine 4: Answer is $e_A(t,1)=\prod_{k=0}^{\frac{\ln(t)}{\ln(2)}-1}(I+2^kA).$
• Page 342, 1ine 5: Replace last "$3$" by "$2$".