 Chapter 1.1:
 Chapter 1.1: DEFINITIONS AND TERMINOLOGY
 Chapter 1.2:
 Chapter 1.2: INITIALVALUE PROBLEMS
 Chapter 1.3:
 Chapter 1.3: DIFFERENTIAL EQUATIONS AS MATHEMATICAL MODEL
 Chapter 1.R:
 Chapter 2.1:
 Chapter 2.1: SOLUTION CURVES WITHOUT A SOLUTION
 Chapter 2.2:
 Chapter 2.2: SEPARABLE EQUATIONS
 Chapter 2.3:
 Chapter 2.3: LINEAR EQUATIONS
 Chapter 2.4:
 Chapter 2.4: EXACT EQUATIONS
 Chapter 2.5:
 Chapter 2.5: SOLUTIONS BY SUBSTITUTIONS
 Chapter 2.6:
 Chapter 2.6: A NUMERICAL METHOD
 Chapter 2.R:
 Chapter 3.1:
 Chapter 3.1: LINEAR MODELS
 Chapter 3.2:
 Chapter 3.2: NONLINEAR MODELS
 Chapter 3.3:
 Chapter 3.3: MODELING WITH SYSTEMS OF FIRSTORDER DEs
 Chapter 3.R:
 Chapter 4.1:
 Chapter 4.1: PRELIMINARY THEORYLINEAR EQUATIONS
 Chapter 4.10:
 Chapter 4.2:
 Chapter 4.2: REDUCTION OF ORDER
 Chapter 4.3:
 Chapter 4.3: HOMOGENEOUS LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS
 Chapter 4.4:
 Chapter 4.4: UNDETERMINED COEFFICIENTSSUPERPOSITION APPROACH
 Chapter 4.5:
 Chapter 4.5: UNDETERMINED COEFFICIENTSANNIHILATOR APPROACH
 Chapter 4.6:
 Chapter 4.6: VARIATION OF PARAMETERS
 Chapter 4.7:
 Chapter 4.7: CAUCHYEULER EQUATION
 Chapter 4.8:
 Chapter 4.8: GREENS FUNCTIONS
 Chapter 4.9:
 Chapter 4.9: SOLVING SYSTEMS OF LINEAR DES BY ELIMINATION
 Chapter 4.R:
 Chapter 5.1:
 Chapter 5.1: LINEAR MODELS: INITIALVALUE PROBLEMS
 Chapter 5.2:
 Chapter 5.2: LINEAR MODELS: BOUNDARYVALUE PROBLEMS
 Chapter 5.3:
 Chapter 5.3: NONLINEAR MODEL
 Chapter 5.R:
 Chapter 6.1:
 Chapter 6.1: REVIEW OF POWER SERIES
 Chapter 6.2:
 Chapter 6.2: SOLUTIONS ABOUT ORDINARY POINTS
 Chapter 6.3:
 Chapter 6.3: SOLUTIONS ABOUT SINGULAR POINTS
 Chapter 6.4:
 Chapter 6.4: SPECIAL FUNCTIONS
 Chapter 6.R:
 Chapter 7.1:
 Chapter 7.1: DEFINITION OF THE LAPLACE TRANSFORM
 Chapter 7.2:
 Chapter 7.2: INVERSE TRANSFORMS AND TRANSFORMS OF DERIVATIVES
 Chapter 7.3:
 Chapter 7.3: OPERATIONAL PROPERTIES
 Chapter 7.4:
 Chapter 7.4: OPERATIONAL PROPERTIES II
 Chapter 7.5:
 Chapter 7.5: THE DIRAC DELTA FUNCTION
 Chapter 7.6:
 Chapter 7.6: SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS
 Chapter 7.R:
 Chapter 8.1:
 Chapter 8.1: PRELIMINARY THEORYLINEAR SYSTEMS
 Chapter 8.2:
 Chapter 8.2: HOMOGENEOUS LINEAR SYSTEMS
 Chapter 8.3:
 Chapter 8.3: NONHOMOGENEOUS LINEAR SYSTEMS
 Chapter 8.4:
 Chapter 8.4: MATRIX EXPONENTIAL
 Chapter 8.R:
 Chapter 9.1:
 Chapter 9.1: EULER METHODS AND ERROR ANALYSIS
 Chapter 9.2:
 Chapter 9.2: RUNGEKUTTA METHODS
 Chapter 9.3:
 Chapter 9.3: MULTISTEP METHODS
 Chapter 9.4:
 Chapter 9.4: HIGHERORDER EQUATIONS AND SYSTEMS
 Chapter 9.5:
 Chapter 9.5: SECONDORDER BOUNDARYVALUE PROBLEMS
 Chapter 9.R:
 Chapter A.I:
 Chapter A.II:
 Chapter APPENDIX I: GAMMA FUNCTION
 Chapter APPENDIX II: MATRICES
 Chapter Chapter 1: INTRODUCTION TO DIFFERENTIAL EQUATIONS
 Chapter Chapter 2: FIRSTORDER DIFFERENTIAL EQUATIONS
 Chapter Chapter 3: MODELING WITH FIRSTORDER DIFFERENTIAL EQUATIONS
 Chapter Chapter 4: HIGHERORDER DIFFERENTIAL EQUATIONS
 Chapter Chapter 5: MODELING WITH HIGHERORDER DIFFERENTIAL EQUATIONS
 Chapter Chapter 6: SERIES SOLUTIONS OF LINEAR EQUATIONS
 Chapter Chapter 7: SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS
 Chapter Chapter 8: SYSTEMS OF LINEAR FIRSTORDER DIFFERENTIAL EQUATIONS
 Chapter Chapter 9: NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS
A First Course in Differential Equations with Modeling Applications 10th Edition  Solutions by Chapter
Full solutions for A First Course in Differential Equations with Modeling Applications  10th Edition
ISBN: 9781111827052
A First Course in Differential Equations with Modeling Applications  10th Edition  Solutions by Chapter
Get Full SolutionsThis textbook survival guide was created for the textbook: A First Course in Differential Equations with Modeling Applications, edition: 10th. This expansive textbook survival guide covers the following chapters: 109. A First Course in Differential Equations with Modeling Applications was written by Sieva Kozinsky and is associated to the ISBN: 9781111827052. The full stepbystep solution to problem in A First Course in Differential Equations with Modeling Applications were answered by Sieva Kozinsky, our top Math solution expert on 07/17/17, 09:41AM. Since problems from 109 chapters in A First Course in Differential Equations with Modeling Applications have been answered, more than 15913 students have viewed full stepbystep answer.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib IIĀ· Condition numbers measure the sensitivity of the output to change in the input.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.
I don't want to reset my password
Need help? Contact support
Having trouble accessing your account? Let us help you, contact support at +1(510) 9441054 or support@studysoup.com
Forgot password? Reset it here