- Chapter 1: Introduction to Differential Equations
- Chapter 1.1: Definitions and Terminology
- Chapter 1.1: Definitions and Terminology
- Chapter 1.2: Initial-Value Problems
- Chapter 1.2: Initial-Value Problems
- Chapter 1.3: Differential Equations as Mathematical Models
- Chapter 1.3: Differential Equations as Mathematical Models
- Chapter 1.R:
- Chapter 2: First-order Differential Equations
- Chapter 2.1: Solution Curves Without a Solution
- Chapter 2.1: Solution Curves Without a Solution
- Chapter 2.2: Separable Equations
- Chapter 2.2: Separable Equations
- Chapter 2.3: Linear Equations
- Chapter 2.3: Linear Equations
- Chapter 2.4: Exact Equations
- Chapter 2.4: Exact Equations
- Chapter 2.5: Solutions by Substitutions
- Chapter 2.5: Solutions by Substitutions
- Chapter 2.6: A Numerical Method
- Chapter 2.6: A Numerical Method
- Chapter 2.R:
- Chapter 3: Modeling with First-Order Differential Equations
- Chapter 3.1: Linear Models
- Chapter 3.1: Linear Models
- Chapter 3.2: Nonlinear Models
- Chapter 3.2: Nonlinear Models
- Chapter 3.3: Modeling with Systems of First-Order DEs
- Chapter 3.3: Modeling with Systems of First-Order DEs
- Chapter 3.R:
- Chapter 4: Higher-Order Differential Equations
- Chapter 4.1: Preliminary Theory—Linear Equations
- Chapter 4.1: Preliminary Theory—Linear Equations
- Chapter 4.10: Preliminary Theory—Linear Equations
- Chapter 4.2: Reduction of Order
- Chapter 4.2: Reduction of Order
- Chapter 4.3: Homogeneous Linear Equations with Constant Coefficient
- Chapter 4.3: Homogeneous Linear Equations with Constant Coefficient
- Chapter 4.4: Undetermined Coefficients—Superposition Approach
- Chapter 4.4: Undetermined Coefficients—Superposition Approach
- Chapter 4.5: Undetermined Coefficients—Annihilator Approach
- Chapter 4.5: Undetermined Coefficients—Annihilator Approach
- Chapter 4.6: Variation of Parameters
- Chapter 4.6: Variation of Parameters
- Chapter 4.7: Cauchy-Euler Equation
- Chapter 4.7: Cauchy-Euler Equation
- Chapter 4.8: Green’s Functions
- Chapter 4.8: Green’s Functions
- Chapter 4.9: Solving Systems of Linear DEs by Elimination
- Chapter 4.9: Solving Systems of Linear DEs by Elimination
- Chapter 4.R:
- Chapter 5: Modeling with Higher-Order Differential Equations
- Chapter 5.1: Linear Models: Initial-Value Problems
- Chapter 5.1: Linear Models: Initial-Value Problems
- Chapter 5.2: Linear Models: Boundary-Value Problems
- Chapter 5.2: Linear Models: Boundary-Value Problems
- Chapter 5.3: Nonlinear Models
- Chapter 5.3: Nonlinear Models
- Chapter 5.R:
- Chapter 6: Series Solution of Linear Equations
- Chapter 6.1: Review of Power Series
- Chapter 6.1: Review of Power Series
- Chapter 6.2: Solutions About Ordinary Points
- Chapter 6.2: Solutions About Ordinary Points
- Chapter 6.3: Solutions About Singular Points
- Chapter 6.3: Solutions About Singular Points
- Chapter 6.4: Special Functions
- Chapter 6.4: Special Functions
- Chapter 6.R:
- Chapter 7: The Laplace Transform
- Chapter 7.1: Definition of the Laplace Transform
- Chapter 7.1: Definition of the Laplace Transform
- Chapter 7.2: Inverse Transforms and Transforms of Derivatives
- Chapter 7.2: Inverse Transforms and Transforms of Derivatives
- Chapter 7.3: Operational Properties I
- Chapter 7.3: Operational Properties I
- Chapter 7.4: Operational Properties II
- Chapter 7.4: Operational Properties II
- Chapter 7.5: The Dirac Delta Function
- Chapter 7.5: The Dirac Delta Function
- Chapter 7.6: Systems of Linear Differential Equations
- Chapter 7.6: Systems of Linear Differential Equations
- Chapter 7.R:
- Chapter 8: Systems of Linear First-Order Differential Equations
- Chapter 8.1: Preliminary Theory—Linear Systems
- Chapter 8.1: Preliminary Theory—Linear Systems
- Chapter 8.2: Homogeneous Linear Systems
- Chapter 8.2: Homogeneous Linear Systems
- Chapter 8.3: Nonhomogeneous Linear Systems
- Chapter 8.3: Nonhomogeneous Linear Systems
- Chapter 8.4: Matrix Exponential
- Chapter 8.4: Matrix Exponential
- Chapter 8.R:
- Chapter 9: Numerical Solutions of Ordinary Differential Equations
- Chapter 9.1: Euler Methods and Error Analysis
- Chapter 9.1: Euler Methods and Error Analysis
- Chapter 9.2: Runge-Kutta Methods
- Chapter 9.2: Runge-Kutta Methods
- Chapter 9.3: Multistep Methods
- Chapter 9.3: Multistep Methods
- Chapter 9.4: Higher-Order Equations and Systems
- Chapter 9.4: Higher-Order Equations and Systems
- Chapter 9.5: Second-Order Boundary-Value Problems
- 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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Key Calculus Terms and definitions covered in this textbook
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Arccosine function
See Inverse cosine function.
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Closed interval
An interval that includes its endpoints
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Demand curve
p = g(x), where x represents demand and p represents price
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Eccentricity
A nonnegative number that specifies how off-center the focus of a conic is
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Identity function
The function ƒ(x) = x.
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Intercept
Point where a curve crosses the x-, y-, or z-axis in a graph.
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Leaf
The final digit of a number in a stemplot.
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Matrix, m x n
A rectangular array of m rows and n columns of real numbers
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Midpoint (in a coordinate plane)
For the line segment with endpoints (a,b) and (c,d), (aa + c2 ,b + d2)
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Observational study
A process for gathering data from a subset of a population through current or past observations. This differs from an experiment in that no treatment is imposed.
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Order of magnitude (of n)
log n.
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Outcomes
The various possible results of an experiment.
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Quadratic formula
The formula x = -b 2b2 - 4ac2a used to solve ax 2 + bx + c = 0.
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Row operations
See Elementary row operations.
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Sample space
Set of all possible outcomes of an experiment.
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Sum of an infinite series
See Convergence of a series
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Summation notation
The series a nk=1ak, where n is a natural number ( or ?) is in summation notation and is read "the sum of ak from k = 1 to n(or infinity).” k is the index of summation, and ak is the kth term of the series
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Symmetric difference quotient of ƒ at a
ƒ(x + h) - ƒ(x - h) 2h
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Time plot
A line graph in which time is measured on the horizontal axis.
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y-intercept
A point that lies on both the graph and the y-axis.