Differential Equations and Linear Algeb...4th EditionStephen W. Goode, Scott A. Annin Publisher: PEARSONISBN: 9780321964670
Differential Equations and Linear Algeb...
Solutions for Differential Equations and Linear Algebra (4th Edition)
Problem 1TFR:
True-False review For items a-n, decide if the given statement is true or false, and give a brief...Problem 5P:
Verify that, for t0, y(t)=lnt is a solution to the differential equation 2(dydx)3=d3ydt3.Problem 6P:
Verify that y(x)=x/(x+1) is a solution to the differential equation y+d2ydx2=dydx+x3+2x23(1+x)3.Problem 8P:
By writing Equation 1.1.7 in the form 1TTmdTdt=k and using u1dudt=ddt(lnu), derive 1.1.8.Problem 9P:
A glass of water whose temperature is 50F is taken outside at noon on a day whose temperature is...Problem 10P:
On a cold winter day (10F), an object is brought outside from a 70F room. If it takes 40 minutes for...Problem 11P:
For Problems 11-16, find the equation of the orthogonal trajectories to the given family of curves....Problem 12P:
For Problems 11-16, find the equation of the orthogonal trajectories to the given family of curves....Problem 13P:
For Problems 11-16, find the equation of the orthogonal trajectories to the given family of curves....Problem 14P:
For Problems 11-16, find the equation of the orthogonal trajectories to the given family of curves....Problem 15P:
For Problems 11-16, find the equation of the orthogonal trajectories to the given family of curves....Problem 16P:
For Problems 11-16, find the equation of the orthogonal trajectories to the given family of curves....Problem 17P:
For problems 17-20, m denotes a fixed nonzero constant, and c is the constant distinguishing the...Problem 18P:
For problems 17-20, m denotes a fixed nonzero constant, and c is the constant distinguishing the...Problem 19P:
For problems 17-20, m denotes a fixed nonzero constant, and c is the constant distinguishing the...Problem 20P:
For problems 17-20, m denotes a fixed nonzero constant, and c is the constant distinguishing the...Problem 21P:
Consider the family of circles x2+y2=2cx. Show that the differential equation for determining the...Problem 22P:
We call a coordinate system (u,v) orthogonal if its coordinate curves the two family of curves...Problem 23P:
Any curve with the property that whenever it intersects a curve of a given family it does so at an...Problem 24P:
An object is released from rest at a height of 100 meters above the ground. Neglecting frictional...Problem 25P:
A five-foot-tall boy tosses a tennis ball straight up from the level of the top of his head....Problem 26P:
A pyrotechnic rocket is to be launched vertically upwards from the ground. For optimal viewing, the...Problem 27P:
Repeat Problem 26 under the assumption that the rocket is launched from a platform five meters above...Problem 29P:
An object that is released from a height h meters above the ground with a vertical velocity of v0...Problem 30P:
Verify that y(t)=Acos(t) is a solution to the differential equation 1.1.21, where A and are nonzero...Problem 31P:
Verify that y(t)=c1cost+c2sint is a solution to the differential equation 1.1.21. Show that the...Browse All Chapters of This Textbook
Chapter 1.1 - Differential Equations EverywhereChapter 1.2 - Basic Ideas And TerminologyChapter 1.3 - The Geometry Of First-order Differential EquationsChapter 1.4 - Separable Differential EquationsChapter 1.5 - Some Simple Population ModelsChapter 1.6 - First-order Linear Differential EquationsChapter 1.7 - Modeling Problems Using First-order Linear Differential EquationsChapter 1.8 - Change Of VariablesChapter 1.9 - Exact Differential EquationsChapter 1.10 - Numerical Solution To First-order Differential Equations
Chapter 1.11 - Some Higher-order Differential EquationsChapter 1.12 - Chapter ReviewChapter 2.1 - Matrices: Definitions And NotationChapter 2.2 - Matrix AlgebraChapter 2.3 - Terminology For Systems Of Linear EquationsChapter 2.4 - Row-echelon Matrices And Elementary Row OperationsChapter 2.5 - Gaussian EliminationChapter 2.6 - The Inverse Of A Square MatrixChapter 2.7 - Elementary Matrices And The Lu FactorizationChapter 2.8 - The Invertible Matrix Theorem IChapter 2.9 - Chapter ReviewChapter 3.1 - The Definition Of The DeterminantChapter 3.2 - Properties Of DeterminantsChapter 3.3 - Cofactor ExpansionsChapter 3.4 - Summary Of DeterminantsChapter 3.5 - Chapter ReviewChapter 4.1 - Vectors In R.nChapter 4.2 - Definition Of A Vector SpaceChapter 4.3 - SubspacesChapter 4.4 - Spanning SetsChapter 4.5 - Linear Dependence And Linear IndependenceChapter 4.6 - Bases And DimensionChapter 4.7 - Change Of BasisChapter 4.8 - Row Space And Column SpaceChapter 4.9 - The Rank-nullity TheoremChapter 4.11 - Chapter ReviewChapter 5.1 - Definition Of An Inner Product SpaceChapter 5.2 - Orthogonal Sets Of Vectors And Orthogonal ProjectionsChapter 5.3 - The Gram-schmidt ProcessChapter 5.4 - Least Squares ApproximationChapter 5.5 - Chapter ReviewChapter 6.1 - Definition Of A Linear TransformationChapter 6.2 - Transformations Of R.2Chapter 6.3 - The Kernel And Range Of A Linear TransformationChapter 6.4 - Additional Properties Of Linear TransformationsChapter 6.5 - The Matrix Of A Linear TransformationChapter 6.6 - Chapter ReviewChapter 7.1 - The Eigenvalue/eigenvector ProblemChapter 7.2 - General Results For Eigenvalues And EigenvectorsChapter 7.3 - DiagonalizationChapter 7.4 - An Introduction To The Matrix Exponential FunctionChapter 7.5 - Orthogonal Diagonalization And Quadratic FormsChapter 7.6 - Jordan Canonical FormsChapter 7.7 - Chapter ReviewChapter 8.1 - General Theory For Linear Differential EquationsChapter 8.2 - Constant Coefficient Homogeneous Linear Differential EquationsChapter 8.3 - The Method Of Undetermined Coefficients: AnnihilatorsChapter 8.5 - Oscillations Of A Mechanical SystemChapter 8.6 - Rlc CircuitsChapter 8.7 - The Variation Of Parameters MethodChapter 8.8 - A Differential Equation With Nonconstant CoefficientsChapter 8.9 - Reduction Of OrderChapter 8.10 - Chapter ReviewChapter 9.1 - First-order Linear SystemsChapter 9.2 - Vector FormulationChapter 9.3 - General Results For First-order Linear Differential SystemsChapter 9.4 - Vector Differential Equations: Nondefective Coefficient MatrixChapter 9.5 - Vector Differential Equations: Defective Coefficient MatrixChapter 9.6 - Variation-of-parameters For Linear SystemsChapter 9.7 - Some Applications Of Linear Systems Of Differential EquationsChapter 9.8 - Matrix Exponential Function And Systems Of Differential EquationsChapter 9.9 - The Phase Plane For Linear Autonomous SystemsChapter 9.10 - Nonlinear SystemsChapter 9.11 - Chapter ReviewChapter 10.1 - Definition Of The Laplace TransformChapter 10.2 - The Existence Of The Laplace Transform And The Inverse TransformChapter 10.3 - Periodic Functions And The Laplace TransformChapter 10.4 - The Transform Of Derivatives And Solution Of Initial-value ProblemsChapter 10.5 - The First Shifting TheoremChapter 10.6 - The Unit Step FunctionChapter 10.7 - The Second Shifting TheoremChapter 10.8 - Impulsive Driving Terms: The Dirac Delta FunctionChapter 10.9 - The Convolution IntegralChapter 10.10 - Chapter ReviewChapter 11.1 - A Review Of Power SeriesChapter 11.2 - Series Solutions About An Ordinary PointChapter 11.3 - The Legendre EquationChapter 11.4 - Series Solutions About A Regular Singular PointChapter 11.5 - Frobenius TheoryChapter 11.6 - Bessel's Equation Of Order PChapter 11.7 - Chapter ReviewChapter A - Review Of Complex NumbersChapter B - Review Of Partial FractionsChapter C - Review Of Integration Techniques
Book Details
Differential Equations and Linear Algebra is designed for use in combined differential equations and linear algebra courses. It is best suited for students who have successfully completed three semesters of calculus. Differential Equations and Linear Algebra presents a carefully balanced and sound integration of both differential equations and linear algebra. It promotes in-depth understanding rather than rote memorization, enabling readers to fully comprehend abstract concepts and leave the course with a solid foundation in key areas. Flexible in format, it explains concepts clearly and logically with an abundance of examples and illustrations, without sacrificing level or rigor. The Fourth Edition includes many updated problems to support the material, with varying difficulty levels from which students/instructors can choose.
Sample Solutions for this Textbook
We offer sample solutions for Differential Equations and Linear Algebra (4th Edition) homework problems. See examples below:
Chapter 1.12, Problem 1APChapter 2.9, Problem 1APChapter 3.5, Problem 1APChapter 4.11, Problem 1APChapter 5.5, Problem 1APGiven: The given mapping is, T:ℝ2→ℝ4 defined by T(x,y)=(x+y,0,x−y,xy). Approach: The following...Given: The given matrix A is, A=[3016−1] Approach: An n×n matrix that is similar to a diagonal...Chapter 8.10, Problem 1APChapter 9.11, Problem 1AP
Given: A function f is defined on an interval [0,∞) as, f(t)=3t−4 Approach: The function F(s) is...Chapter 11.7, Problem 1APGiven: The given complex number is, z=2+5i Approach: The definition of complex conjugate states...Given: The given rational function is, 2x−1(x+1)(x+2). Approach: The standard way to find the...The given integral is, ∫xcosxdx Approach: Integration by parts: the basic formula for integration by...
More Editions of This Book
Corresponding editions of this textbook are also available below:
Differential Equations & Linear Algebra 3e
3rd Edition
ISBN: 9781292025131
Differential Equations And Linear Algebra
3rd Edition
ISBN: 9780130457943
EBK DIFFERENTIAL EQUATIONS AND LINEAR A
4th Edition
ISBN: 9780321990167
Differential Equations And Linear Algebra, Books A La Carte Edition (4th Edition)
4th Edition
ISBN: 9780321985811
EBK DIFFERENTIAL EQUATIONS AND LINEAR A
4th Edition
ISBN: 8220102019799
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