An Introduction to Differential Equations: Order

An Introduction to Differential Equations: OrderAn Introduction to Differential Equations: Order and Chaos

by Florin Diacu (First edition, 2000)

Corrections

page position corrected text comment

inside Integration table - ``ln|·|'' not ``ln(·)''
cover right side of equations (10 occurrences)
p.10 5th line from bottom ``f(r) = 1/r for r > 0 and f(0) = 0''
p.11 Problem 11, line 3 ``inverse seventh power'' insert ``inverse''
p.11 Problem 11, line 4 ``inverse ninth power'' insert ``inverse''
p.11 Problem 11, col. 2, top line ``fahn der vahls'' omit extra ``s''
p.33 Step 5, line 1 ``c into x in step 2'' not ``u''
p.34 Step 5, line 1 ``function x in step 2'' not ``u''
p.39 Problem 10 ``t²v -3t²'' sign of exponent
p.39 Problem 16 ``(t+2)q+t³'' ``t³'', not ``3t''
p.48 2nd para., line 6 ``10¹ kg/m³'' insert ``kg/m³''
p.50 Problem 33, equation ``P^¢ = kP([P/( n₁)]-1)(1-[P/( n₂)])-N'' insert ``P''
p.50 Problem 34, lines 5-6 ``amount of glucose present'' not ``injected''
p.50 Problem 34, line 9 ``a differential equation'' not ``logistic''
p.50 Problem 36, line 2 ``force per unit mass'' insert phrase
p.50 Problem 37, line 2 ``forces per unit mass'' insert phrase
p.60 line 2 after Problem 20 ``through 28, apply the'' delete phrase
p.60 Problem 26 ``x^¢ = x²ln(t+1)'' replace equation
p.79 Problem 28, line 1 ``[0,0.5]'' change interval
p.81 last line, equation ``P^¢ = kP([P/( n₁)]-1)(1-[P/( n₂)])-AcosBt'' insert ``P''
p.91 Problem 17, line 2 ``w^¢(e) = [3/( Öe)]'' denominator
p.91 Problem 20, line 2 ``y^¢(1) = 0'' repeated (delete 1)
p.93 Step 3, line 1 ``r₁ = r₂ = -b/2'' minus
p.100 Problem 20 ``x^¢¢ = -¹/₂(x^¢)²+x^¢'' replace equation
p.100 Problem 27 ``x^¢¢ = ⁴/_tx^¢-[6/( t²)]x'' replace equation
p.107 Line 5 from bottom ``variable source (as shown...'' not ``resistor''
p.107 Line 2 from bottom ``an electromagnetic force...'' not ``a resistance...''
p.107 Last line ``variance of the source at the...'' not ``resistor''
p.108 Line 4 ``mx^¢¢ = F_weight+F_{electromagnetic}'' not ``resistance''
p.108 Line 6 ``F_{electromagnetic}'' not ``resistance''
p.108 Figure 3.3.1 ``source'' not ``resistor''
p.109 Lines 4-3 before Problems ``shows that the electromagnetic force'' delete, replace
p.109 Lines 3-2 before Problems ``so the bar is pushed'' delete ``finally''
p.110 Problem 36, 1st equation ``x^¢¢ = -^k/_mx^¢-[2g/ L]x'' minus
p.110 Problem 36, 2nd equation ``x^¢¢ = -^k/_mx^¢-[2g/ L]x+[1/ 10]cos8pt'' minus

page position corrected text comment

p.121 Problem 28, line 7 ``m = 1kg, n = ¹/₅kg/sec, k = 1N/m, replace
a = 1m, w₀ = 1Hz'' parameters
p.137 Applications, line 15 `` n = 0.1kg/sec'' add units
p.137 Last paragraph, line 2 `` n = 0.1kg/sec'' add units
p.137 Last paragraph, line 2 ``cords with coef-'' delete ``damping''
p.141 Problems, line 2 after (d) ``t = 0.1 (a,c) or t = 0.05 (b,d)''
p.142 Problem 9, line 5 ``Table 3.6.2'' not ``3.4.2''
p.142 Problem 12, line 1 ``x(0) = x^¢(0) = 0.1'' not ``0''
p.142 Problem 13, line 1 ``x^¢¢ = -x^¢-x'' replace equation
p.142 Problem 14, line 1 ``x^¢¢ = x^¢-x ,    x(0) = x^¢(0) = 1'' delete p's, change IC
p.142 Problem 15, line 1 ``x^¢¢ = -x^¢-x'' replace equation
p.142 Problem 16, line 1 ``x^¢¢ = ¹/_tx^¢-^x/_t  ,'' minus (note comma)
p.142 Problem 17, line 1 ``x^¢¢ = -[(e^-t)/( t-2)]x^¢-[(4t²)/( t²-4)]x+2(1-t)'' replace equation
p.142 Problem 18, line 1 ``x^¢¢ = [1/( 1-t)]x^¢-[x/( 1-t)]  ,'' replace (note comma)
p.142 Problem 18, line 2 ``[2,10]'' not ``[2,100]''
p.146 program,lines 13,14 ``t=t+h: M:=(M,[t,x]):'' reverse order
p.155 Problem 15 ``x^¢¢ = x^¢+x+cost'' replace equation
p.156 Problem 21 ``x^¢¢ = ¹/₄x^¢+x+t'' numerator
p.156 Problem 22 ``x^¢¢ = -¹/₃x^¢-x-t'' minus
p.156 Problem 27 ``x^¢¢ = tx^¢+2x'' denominator
p.156 Problem 35, line 2 ``[1,2.5]'' not ``[1,4]''
p.169 Problem 30, line 1 ``Example 9'' not ``8''
p.169 Problem 30, lines 2,3,5 u₁, u₂, u₃ not x₁, x₂, x₃
p.173 Proof, line 6 ``f(t) = c₁u+c₂v+c₃w'' not ``j(t)''
p.173 Proof, line 6 ``solution of (7)'' not ``(5)''
p.173 Proof, 3rd last line ``solution of (7)'' not ``(5)''
p.187 Problem 18, line 8 ``(asinbt+bcosbt)e^at'' 2nd expression
p.193 line 4 ``(d) a = 1/2, b = -1/2, c = 1'' change a,b values
p.199 Problem 31, line 3 ``z^¢ = ¹/₂z'' change z equation
p.199 Problem 32, line 1 ``u^¢ = 5v'' change u equation
p.199 Problem 32, line 2 ``v^¢ = -5u+6v'' change v equation
p.199 Problem 32, line 3 ``r^¢ = 5r'' change r equation
p.199 Problem 33, line 1 ``w^¢ = -w+r'' change w equation
p.199 Problem 33, line 2 ``r^¢ = -2w+r'' change r equation
p.199 Problem 33, line 3 ``q^¢ = -2q'' change q equation
p.199 Problem 35, line 1 ``U^¢ = -U-2V'' change U equation
p.199 Problem 35, line 2 ``V^¢ = U-2V'' change V equation
p.199 Problem 35, line 3 ``W^¢ = -W'' change W equation
p.204 Equation for I_n+1 ``-Q_n+1^E'' change last term
p.204 Equation for Q_n+1 ``Q_n+^h/₂(I_n-Q_n+I_n+1^E-Q_n+1^E)'' change equation
p.207 Definition 6.1.2, line 2 ``u^¢ = -u-2v'' delete ``p''

page position corrected text comment

p.225 last line ``Figure 5.1.1(a)'' not ``5.1(a)''
p.226 Example 2, line 5 ``Figure 5.1.1(b)'' not ``5.1(b)''
p.240 Problem 9 ``y^¢ = x+y(1-x²-y²)'' change last ``+'' to ``-''
p.255 Example 5, line 6 ``l₂ = iÖ2, l₃ = -iÖ2'' not 2i and -2i
p.272 Problem 18, line 1 ``into intervals'' delete ``several''
p.275 Inverse Transform, lines 8-9 ``set of continuous functions'' insert ``continuous''
p.282 Example 8, last equation ``4, for t ³ 4,'' not ``2, for t ³ 4,''
p.347 Section 2.1, after 29. ``31. x₁ = 1, x₂ = -1'' insert
p.348 Section 2.2, answer 29. ``11.00 years''
p.349 Section 2.3, answer 27. ``x(t) = ±Ö{[a/( b+ke^-2t)]}'' ``±'' in front
p.349 Section 2.3, answer 39. ``lnt -2'' denominator
p.354 Section 2.4, answer 37. ``1 £ a < 2''
p.354 Section 2.5, answer 17. ``f_n = 4å_{k = 2}ⁿ(^t/₂)^k[1/ k!]'' 2 terms wrong
p.355 Section 2.5, answer 21. ``f₁(t) = f₂(t) = f₃(t) = 1-cost-t''
p.355 Section 2.6, answer 9(a). ``... all n. x(t) = 3 is an equilibrium.''
p.355 Section 2.6, 9(b), line 2. ``x(t) = [(3(1-e^-t))/( 3e^-t+1)]'' replace equation
p.355 Section 2.6, 11. ``(a) 0 (b) 0''
p.355 Section 2.6, 13. ``(a) 0 (b) 0''
p.357 Section 3.2, answer 5. ``[([Ö11])/ 2]'' replace ``[Ö11]'' twice
p.357 Section 3.2, answer 19. ``x(t) = -tan^-1(^t/₂)+1'' minus
p.357 Section 3.2, after 35. ``39. T = 2pÖ{[(gr_box)/( Lr_water)]}'' insert
p.358 Section 3.4, answer 11. ``x(t) = A(t)cos[((w+w₀)t)/ 2] with replace
A(t) = -[2a/( (w²-w₀²))]sin(w-w₀)^t/₂''
p.365 Section 3.5, answer 39. ``perpendicular to the x-axis.'' not ``at''
p.366 Section 4.1, answer 15. ``form identical planes.'' replace ``two parallel''
p.368 Section 4.3, answer 13. ``y(t) = c₁e^at(acosbt-bsinbt) insert b's in y
+c₂e^at(asinbt+bcosbt)'' equation for l_1,2
p.368 Section 4.3, answer 19. ``e^-0.0089'' not ``e^-0.089''
p.383 Section 6.3, answer 11. ``q(t)'' not ``Q(t)''

File translated from T_EX by T_TH, version 1.92.
On 22 Mar 2002, 11:05.


page	position	corrected text	comment

inside	Integration table -	``ln\|·\|''	not ``ln(·)''
cover	right side of equations		(10 occurrences)
p.10	5th line from bottom	``f(r) = 1/r for r > 0 and f(0) = 0''
p.11	Problem 11, line 3	``inverse seventh power''	insert ``inverse''
p.11	Problem 11, line 4	``inverse ninth power''	insert ``inverse''
p.11	Problem 11, col. 2, top line	``fahn der vahls''	omit extra ``s''
p.33	Step 5, line 1	``c into x in step 2''	not ``u''
p.34	Step 5, line 1	``function x in step 2''	not ``u''
p.39	Problem 10	``t²v -3t²''	sign of exponent
p.39	Problem 16	``(t+2)q+t³''	``t³'', not ``3t''
p.48	2nd para., line 6	``10¹ kg/m³''	insert ``kg/m³''
p.50	Problem 33, equation	``P^¢ = kP([P/( n₁)]-1)(1-[P/( n₂)])-N''	insert ``P''
p.50	Problem 34, lines 5-6	``amount of glucose present''	not ``injected''
p.50	Problem 34, line 9	``a differential equation''	not ``logistic''
p.50	Problem 36, line 2	``force per unit mass''	insert phrase
p.50	Problem 37, line 2	``forces per unit mass''	insert phrase
p.60	line 2 after Problem 20	``through 28, apply the''	delete phrase
p.60	Problem 26	``x^¢ = x²ln(t+1)''	replace equation
p.79	Problem 28, line 1	``[0,0.5]''	change interval
p.81	last line, equation	``P^¢ = kP([P/( n₁)]-1)(1-[P/( n₂)])-AcosBt''	insert ``P''
p.91	Problem 17, line 2	``w^¢(e) = [3/( Öe)]''	denominator
p.91	Problem 20, line 2	``y^¢(1) = 0''	repeated (delete 1)
p.93	Step 3, line 1	``r₁ = r₂ = -b/2''	minus
p.100	Problem 20	``x^¢¢ = -¹/₂(x^¢)²+x^¢''	replace equation
p.100	Problem 27	``x^¢¢ = ⁴/_tx^¢-[6/( t²)]x''	replace equation
p.107	Line 5 from bottom	``variable source (as shown...''	not ``resistor''
p.107	Line 2 from bottom	``an electromagnetic force...''	not ``a resistance...''
p.107	Last line	``variance of the source at the...''	not ``resistor''
p.108	Line 4	``mx^¢¢ = F_weight+F_{electromagnetic}''	not ``resistance''
p.108	Line 6	``F_{electromagnetic}''	not ``resistance''
p.108	Figure 3.3.1	``source''	not ``resistor''
p.109	Lines 4-3 before Problems	``shows that the electromagnetic force''	delete, replace
p.109	Lines 3-2 before Problems	``so the bar is pushed''	delete ``finally''
p.110	Problem 36, 1st equation	``x^¢¢ = -^k/_mx^¢-[2g/ L]x''	minus
p.110	Problem 36, 2nd equation	``x^¢¢ = -^k/_mx^¢-[2g/ L]x+[1/ 10]cos8pt''	minus