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For one-semester sophomore- or junior-level courses in Differential Equations.

This package includes MyLab Math.

 

An introduction to the basic theory and applications of differential equations                                                                 

Fundamentals of Differential Equations presents the basic theory of differential equations and offers a variety of modern applications in science and engineering. This flexible text allows instructors to adapt to various course emphases (theory, methodology, applications, and numerical methods) and to use commercially available computer software. For the first time, MyLab™ Math is available for this text, providing online homework with immediate feedback, the complete eText, and more.

 

Note that a longer version of this text, entitled Fundamentals of Differential Equations and Boundary Value Problems, 7th Edition , contains enough material for a two-semester course. This longer text consists of the main text plus three additional chapters (Eigenvalue Problems and Sturm–Liouville Equations; Stability of Autonomous Systems; and Existence and Uniqueness Theory).

 

Personalize learning with MyLab Math

MyLab™ Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

 

0134665686 / 9780134665689   Fundamentals of Differential Equations Plus MyLab Math with Pearson eText -- Access Card Package


Package consists of:

  • 0321431308 / 9780321431301 MyLab Math -- Glue-in Access Card
  • 0321654064 / 9780321654069 MyLab Math Inside Star Sticker
  • 0321977068 / 9780321977069 Fundamentals of Differential Equations
Chapter 1 Introduction
1.1 Background
1(5)
1.2 Solutions and Initial Value Problems
6(9)
1.3 Direction Fields
15(8)
1.4 The Approximation Method of Euler
23(6)
Summary
29(1)
Review Problems
29(2)
Technical Writing Exercises
31(1)
Projects
32(6)
A Picard's Method
32(1)
B The Phase Line
33(2)
C Applications to Economics
35(1)
D Taylor Series Method
36(2)
Chapter 2 First-Order Differential Equations
2.1 Introduction: Motion of a Falling Body
38(3)
2.2 Separable Equations
41(7)
2.3 Linear Equations
48(9)
2.4 Exact Equations
57(9)
2.5 Special Integrating Factors
66(4)
2.6 Substitutions and Transformations
70(8)
Summary
78(1)
Review Problem
79(1)
Technical Writing Exercises
79(1)
Projects
80(10)
A Oil Spill in a Canal
80(1)
B Differential Equations in Clinical Medicine
81(2)
C Torricelli's Law of Fluid Flow
83(1)
D The Snowplow Problem
84(1)
E Two Snowplows
84(1)
F Clairaut Equations and Singular Solutions
85(1)
G Multiple Solutions of a First-Order Initial Value Problem
86(1)
H Utility Functions and Risk Aversion
86(1)
I Designing a Solar Collector
87(1)
J Asymptotic Behavior of Solutions to Linear Equations
88(2)
Chapter 3 Mathematical Models and Numerical Methods Involving First-Order Equations
3.1 Mathematical Modeling
90(2)
3.2 Compartmental Analysis
92(10)
3.3 Heating and Cooling of Buildings
102(7)
3.4 Newtonian Mechanics
109(9)
3.5 Electrical Circuits
118(3)
3.6 Numerical Methods: A Closer Look At Euler's Algorithm
121(11)
3.7 Higher-Order Numerical Methods: Taylor and Runge-Kutta
132(9)
Projects
141(11)
A Dynamics of HIV Infection
141(3)
B Aquaculture
144(1)
C Curve of Pursuit
145(1)
D Aircraft Guidance in a Crosswind
146(1)
E Market Equilibrium: Stability and Time Paths
147(1)
F Stability of Numerical Methods
148(2)
G Period Doubling and Chaos
150(2)
Chapter 4 Linear Second-Order Equations
4.1 Introduction: The Mass-Spring Oscillator
152(5)
4.2 Homogeneous Linear Equations: The General Solution
157(8)
4.3 Auxiliary Equations with Complex Roots
165(9)
4.4 Nonhomogeneous Equations: the Method of Undetermined Coefficients
174(6)
4.5 The Superposition Principle and Undetermined Coefficients Revisited
180(7)
4.6 Variation of Parameters
187(5)
4.7 Variable-Coefficient Equations
192(9)
4.8 Qualitative Considerations for Variable-Coefficient and Nonlinear Equations
201(11)
4.9 A Closer Look at Free Mechanical Vibrations
212(9)
4.10 A Closer Look at Forced Mechanical Vibrations
221(8)
Summary
229(2)
Review Problems
231(1)
Technical Writing Exercises
232(1)
Projects
233(8)
A Nonlinear Equations Solvable by First-Order Techniques
233(1)
B Apollo Reentry
234(1)
C Simple Pendulum
235(1)
D Linearization of Nonlinear Problems
236(1)
E Convolution Method
237(1)
F Undetermined Coefficients Using Complex Arithmetic
237(2)
G Asymptotic Behavior of Solutions
239(1)
H Gravity Train
240(1)
Chapter 5 Introduction to Systems and Phase Plane Analysis
5.1 Interconnected Fluid Tanks
241(2)
5.2 Differential Operators and the Elimination Method for Systems
243(9)
5.3 Solving Systems and Higher-Order Equations Numerically
252(9)
5.4 Introduction to the Phase Plane
261(13)
5.5 Applications to Biomathematics: Epidemic and Tumor Growth Models
274(9)
5.6 Coupled Mass-Spring Systems
283(6)
5.7 Electrical Systems
289(6)
5.8 Dynamical Systems, Poincare Maps, and Chaos
295(9)
Summary
304(2)
Review Problems
306(1)
Projects
307(12)
A Designing a Landing System for Interplanetary Travel
307(1)
B Spread of Staph Infections in Hospitals-Part I
308(2)
C Things That Bob
310(1)
D Hamiltonian Systems
311(2)
E Cleaning Up the Great Lakes
313(1)
F The 2014-2015 Ebola Epidemic
314(3)
G Phase-Locked Loops
317(2)
Chapter 6 Theory of Higher-Order Linear Differential Equations
6.1 Basic Theory of Linear Differential Equations
319(8)
6.2 Homogeneous Linear Equations with Constant Coefficients
327(7)
6.3 Undetermined Coefficients and the Annihilator Method
334(4)
6.4 Method Of Variation of Parameters
338(4)
Summary
342(1)
Review Problems
343(1)
Technical Writing Exercises
344(1)
Projects
345(5)
A Computer Algebra Systems and Exponential Shift
345(1)
B Justifying the Method of Undetermined Coefficients
346(1)
C Transverse Vibrations of a Beam
347(1)
D Higher-Order Difference Equations
347(3)
Chapter 7 Laplace Transforms
7.1 Introduction: A Mixing Problem
350(3)
7.2 Definition of the Laplace Transform
353(8)
7.3 Properties of the Laplace Transform
361(5)
7.4 Inverse Laplace Transform
366(10)
7.5 Solving Initial Value Problems
376(7)
7.6 Transforms of Discontinuous Functions
383(9)
7.7 Transforms of Periodic and Power Functions
392(5)
7.8 Convolution
397(8)
7.9 Impulses and the Dirac Delta Function
405(7)
7.10 Solving Linear Systems with Laplace Transforms
412(2)
Summary
414(1)
Review Problems
415(1)
Technical Writing Exercises
416(1)
Projects
417(4)
A Duhamel's Formulas
417(1)
B Frequency Response Modeling
418(2)
C Determining System Parameters
420(1)
Chapter 8 Series Solutions of Differential Equations
8.1 Introduction: The Taylor Polynomial Approximation
421(5)
8.2 Power Series and Analytic Functions
426(9)
8.3 Power Series Solutions to Linear Differential Equations
435(10)
8.4 Equations with Analytic Coefficients
445(5)
8.5 Cauchy-Euler (Equidimensional) Equations
450(4)
8.6 Method of Frobenius
454(11)
8.7 Finding a Second Linearly Independent Solution
465(9)
8.8 Special Functions
474(13)
Summary
487(2)
Review Problems
489(1)
Technical Writing Exercises
490(1)
Projects
491(5)
A Alphabetization Algorithms
491(1)
B Spherically Symmetric Solutions to Schrodinger's Equation for the Hydrogen Atom
492(1)
C Airy's Equation
493(1)
D Buckling of a Tower
493(2)
E Aging Spring and Bessel Functions
495(1)
Chapter 9 Matrix Methods for Linear Systems
9.1 Introduction
496(4)
9.2 Review 1: Linear Algebraic Equations
500(4)
9.3 Review 2: Matrices and Vectors
504(11)
9.4 Linear Systems in Normal Form
515(8)
9.5 Homogeneous Linear Systems with Constant Coefficients
523(11)
9.6 Complex Eigenvalues
534(4)
9.7 Nonhomogeneous Linear Systems
538(7)
9.8 The Matrix Exponential Function
545(8)
Summary
553(3)
Review Problems Technical Writing Exercises
556(1)
Projects
557(3)
A Uncoupling Normal Systems
557(1)
B Matrix Laplace Transform Method
558(1)
C Undamped Second-Order Systems
559(1)
Chapter 10 Partial Differential Equations
10.1 Introduction: A Model for Heat Flow
560(3)
10.2 Method of Separation of Variables
563(8)
10.3 Fourier Series
571(16)
10.4 Fourier Cosine and Sine Series
587(5)
10.5 The Heat Equation
592(12)
10.6 The Wave Equation
604(12)
10.7 Laplace' s Equation
616(12)
Summary
628(2)
Technical Writing Exercises
630(1)
Projects
631
A Steady-State Temperature Distribution in a Circular Cylinder
631(2)
B Laplace Transform Solution of the Wave Equation
633(1)
C Green's Function
634(1)
D Numerical Method for Au = f on a Rectangle
635(2)
E The Telegrapher's Equation and the Cable Equation
637
Appendices
A Review of Integration Techniques
A-1
B Newton's Method
A-9
C Simpson's Rule
A-11
D Cramer's Rule
A-13
E Method of Least Squares
A-14
F Runge-Kutta Procedure for n Equations
A-16
G Software for Analyzing Differential Equations
A-17
Answers to Odd-Numbered Problems B-1
Index I-1