 Chapter 1: INTRODUCTION TO DIFFERENTIAL EQUATIONS
 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: FIRSTORDER DIFFERENTIAL EQUATIONS
 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: MODELING WITH FIRSTORDER DIFFERENTIAL EQUATIONS
 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: HIGHERORDER DIFFERENTIAL EQUATIONS
 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: MODELING WITH HIGHERORDER DIFFERENTIAL EQUATIONS
 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: SERIES SOLUTIONS OF LINEAR EQUATIONS
 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: SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS
 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: SYSTEMS OF LINEAR FIRSTORDER DIFFERENTIAL EQUATIONS
 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: NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS
 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
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: 10. This expansive textbook survival guide covers the following chapters: 109. A First Course in Differential Equations with Modeling Applications was written by 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 , our top Calculus 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 74868 students have viewed full stepbystep answer.

Average rate of change of ƒ over [a, b]
The number ƒ(b)  ƒ(a) b  a, provided a ? b.

Compounded continuously
Interest compounded using the formula A = Pert

Distance (in a coordinate plane)
The distance d(P, Q) between P(x, y) and Q(x, y) d(P, Q) = 2(x 1  x 2)2 + (y1  y2)2

Distance (on a number line)
The distance between real numbers a and b, or a  b

Focus, foci
See Ellipse, Hyperbola, Parabola.

Interquartile range
The difference between the third quartile and the first quartile.

Interval
Connected subset of the real number line with at least two points, p. 4.

Natural logarithmic regression
A procedure for fitting a logarithmic curve to a set of data.

Numerical model
A model determined by analyzing numbers or data in order to gain insight into a phenomenon, p. 64.

Parameter
See Parametric equations.

Periodic function
A function ƒ for which there is a positive number c such that for every value t in the domain of ƒ. The smallest such number c is the period of the function.

Quadratic formula
The formula x = b 2b2  4ac2a used to solve ax 2 + bx + c = 0.

Quotient polynomial
See Division algorithm for polynomials.

Real axis
See Complex plane.

Sinusoidal regression
A procedure for fitting a curve y = a sin (bx + c) + d to a set of data

Solve by elimination or substitution
Methods for solving systems of linear equations.

Unit vector in the direction of a vector
A unit vector that has the same direction as the given vector.

Upper bound test for real zeros
A test for finding an upper bound for the real zeros of a polynomial.

Vertex form for a quadratic function
ƒ(x) = a(x  h)2 + k

Vertex of a parabola
The point of intersection of a parabola and its line of symmetry.