- Chapter 1: INTRODUCTION TO DIFFERENTIAL EQUATIONS
- Chapter 1.1:
- Chapter 1.1: DEFINITIONS AND TERMINOLOGY
- Chapter 1.2:
- Chapter 1.2: INITIAL-VALUE PROBLEMS
- Chapter 1.3:
- Chapter 1.3: DIFFERENTIAL EQUATIONS AS MATHEMATICAL MODEL
- Chapter 1.R:
- Chapter 2: FIRST-ORDER 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 FIRST-ORDER 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 FIRST-ORDER DEs
- Chapter 3.R:
- Chapter 4: HIGHER-ORDER 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: CAUCHY-EULER 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 HIGHER-ORDER DIFFERENTIAL EQUATIONS
- Chapter 5.1:
- Chapter 5.1: LINEAR MODELS: INITIAL-VALUE PROBLEMS
- Chapter 5.2:
- Chapter 5.2: LINEAR MODELS: BOUNDARY-VALUE 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 FIRST-ORDER 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: RUNGE-KUTTA METHODS
- Chapter 9.3:
- Chapter 9.3: MULTISTEP METHODS
- Chapter 9.4:
- Chapter 9.4: HIGHER-ORDER EQUATIONS AND SYSTEMS
- Chapter 9.5:
- Chapter 9.5: SECOND-ORDER BOUNDARY-VALUE 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
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This 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 step-by-step 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 step-by-step answer.
Key Calculus Terms and definitions covered in this textbook
-
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
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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.
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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.