Differential Equations: Techniques, Theory, and Applications 1st edition

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Barbara D. MacCluer, Paul S. Bourdon, and Thomas L. Kriete
Publisher: Mathematical Association of America

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  • Chapter 1: Introduction
    • 1.1: What is a differential equation?
    • 1.2: What is a solution? (14)
    • 1.3: More on direction fields: Isoclines (1)

  • Chapter 2: First-Order Equations
    • 2.1: Linear equations (12)
    • 2.2: Separable equations (12)
    • 2.3: Applications: Time of death, time at depth, and ancient timekeeping (16)
    • 2.4: Existence and uniqueness theorems (15)
    • 2.5: Population and financial models (11)
    • 2.6: Qualitative solutions of autonomous equations (10)
    • 2.7: Change of variable (12)
    • 2.8: Exact equations (11)

  • Chapter 3: Numerical Methods
    • 3.1: Euler's method (6)
    • 3.2: Improving Euler's method: The Heun and Runge-Kutta Algorithms (6)
    • 3.3: Optical illusions and other applications (2)

  • Chapter 4: Higher-Order Linear Homogeneous Equations
    • 4.1: Introduction to second-order equations (11)
    • 4.2: Linear operators (18)
    • 4.3: Linear independence (6)
    • 4.4: Constant coefficient second-order equations (10)
    • 4.5: Repeated roots and reduction of order (18)
    • 4.6: Higher-order equations (7)
    • 4.7: Higher-order constant coefficient equations (8)
    • 4.8: Modeling with second-order equations (10)

  • Chapter 5: Higher-Order Linear Nonhomogeneous Equations
    • 5.1: Introduction to nonhomogeneous equations (7)
    • 5.2: Annihilating operators (15)
    • 5.3: Applications of nonhomogeneous equations (9)
    • 5.4: Electric circuits (4)

  • Chapter 6: Laplace Transforms
    • 6.1: Laplace transforms (13)
    • 6.2: The inverse Laplace transform (5)
    • 6.3: Solving initial value problems with Laplace transforms (19)
    • 6.4: Applications (4)
    • 6.5: Laplace transforms, simple systems, and Iwo Jima (3)
    • 6.6: Convolutions (4)
    • 6.7: The delta function (10)

  • Chapter 7: Power Series Solutions
    • 7.1: Motivation for the study of power series solutions
    • 7.2: Review of power series
    • 7.3: Series solutions
    • 7.4: Nonpolynomial coefficients
    • 7.5: Regular singular points
    • 7.6: Bessel's equation

  • Chapter 8: Linear Systems I
    • 8.1: Nelson at Trafalgar and phase portraits
    • 8.2: Vectors, vector fields, and matrices
    • 8.3: Eigenvalues and eigenvectors
    • 8.4: Solving linear systems
    • 8.5: Phase portraits via ray solutions
    • 8.6: More on phase portraits: Saddle points and nodes
    • 8.7: Complex and repeated eigenvalues
    • 8.8: Applications: Compartment models
    • 8.9: Classifying equilibrium points

  • Chapter 9: Linear Systems II
    • 9.1: The matrix exponential, Part I
    • 9.2: A return to the Existence and Uniqueness Theorem
    • 9.3: The matrix exponential, Part II
    • 9.4: Nonhomogeneous constant coefficient systems
    • 9.5: Periodic forcing and the steady-state solution

  • Chapter 10: Nonlinear Systems
    • 10.1: Introduction: Darwin's finches
    • 10.2: Linear approximation: The major cases
    • 10.3: Linear approximation: The borderline cases
    • 10.4: More on interacting populations
    • 10.5: Modeling the spread of disease
    • 10.6: Hamiltonians, gradient systems, and Lyapunov functions
    • 10.7: Pendulums
    • 10.8: Cycles and limit cycles

  • Chapter 11: Partial Differential Equations and Fourier Series
    • 11.1: Introduction: Three interesting partial differential equations
    • 11.2: Boundary value problems
    • 11.3: Partial differential equations: A first look
    • 11.4: Advection and diffusion
    • 11.5: Functions as vectors
    • 11.6: Fourier series
    • 11.7: The heat equation
    • 11.8: The wave equation: Separation of variables
    • 11.9: The wave equation: D'Alembert's method
    • 11.10: Laplace's equation


Differential Equations: Techniques, Theory, and Applications is designed for a modern first course in differential equations either one or two semesters in length. The organization of the book interweaves the three components in the subtitle, with each building on and supporting the others. Techniques include not just computational methods for producing solutions to differential equations, but also qualitative methods for extracting conceptual information about differential equations and the systems modeled by them. Theory is developed as a means of organizing, understanding, and codifying general principles. Applications show the usefulness of the subject as a whole and heighten interest in both solution techniques and theory. Formal proofs are included in cases where they enhance core understanding; otherwise, they are replaced by informal justifications containing key ideas of a proof in a more conversational format. Applications are drawn from a wide variety of fields: those in physical science and engineering are prominent, of course, but models from biology, medicine, ecology, economics, and sports are also featured.

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Group Quantity Questions
Chapter 1: Introduction
1.2 14 002 004 006 008 010 012 014 016 018 020 022 024 026 030
1.3 1 002
Chapter 2: First-Order Equations
2.1 12 002 004 006 008 010 012 014 016 018 020 022 024
2.2 12 002 004 006 008 010 012 014 016 018 020 024 026
2.3 16 002 004 006 008 010 012 014 016 018 020 022 024 026 028 030 032
2.4 15 002 004 006 008 010 012 014 016 018 020 022 024 026 028 032
2.5 11 002 004 006 008 010 012 016 020 022 024 026
2.6 10 002 004 006 008 010 012 014 016 018 020 022
2.7 12 002 004 006 008 010 012 014 016 018 020 022 024
2.8 11 002 004 006 008 010 012 014 018 022 024 026
Chapter 3: Numerical Methods
3.1 6 002 004 006 010 012 016
3.2 6 004 006 008 010 012 014
3.3 2 002 006 008
Chapter 4: Higher-Order Linear Homogeneous Equations
4.1 11 002 004 006 012 014 016 018 020 022 026 028
4.2 18 004 006 008 010 012 014 016 018 020 022 026 030 032 034 036 040 042 044
4.3 6 004 006 010 012 014 020
4.4 10 002 004 006 008 010 012 016 018 020 022
4.5 18 002 004 006 008 010 012 014 016 018 020 022 026 028 030 032 034 036 038
4.6 7 004 006 008 010 012 014 016
4.7 8 002 004 006 008 010 014 016 018
4.8 10 002 006 008 010 012 014 018 020 022 024
Chapter 5: Higher-Order Linear Nonhomogeneous Equations
5.1 7 002 004 006 008 010 016 018
5.2 15 002 004 006 008 010 012 014 016 020 022 024 026 028 030 032 034
5.3 9 002 004 006 008 010 012 014 016 018 020
5.4 4 002 004 006 008 010
Chapter 6: Laplace Transforms
6.1 13 002 004 006 008 010 012 014 016 018 024 026 036 038
6.2 5 002 004 006 008 010
6.3 19 002 004 006 010 012 014 016 018 020 022 024 028 030 032 034 036 038 040 042 044 046
6.4 4 002 004 006 008
6.5 3 002 004 010
6.6 4 002 006 008 010 014
6.7 10 002 004 006 008 010 012 014 020 022 024 028
Chapter 7: Power Series Solutions
7.2 002 004 006 008 010 012 014 016 018 020
7.3 002 004 006 008 010 012 014 016 018 020 022 024 026 028 030
7.4 002 004 006 008 010 012
7.5 002 004 006 008 010 012 014 016 018 020 022 024 026 028 030 032
7.6 002 004 006 008 010 012 014
Chapter 8: Linear Systems I
8.1 002 004 006 008 010 012 014 016 018 020 022 024
8.2 002 004 006 008 010 012 014
8.3 002 004 006 008 010 012 014 016 018 020 022 024
8.4 002 004 006 008 010 012 014 016 018 020 022 024 026 028
8.5 002 004 006 008 010
8.6 002 004 006 008 010 012 014
8.7 002 004 006 008 010 012 014 016 018 020
8.8 002 004 006 008 010 012 014 016 018 020 022
8.9 002 004 006 008 010 012 014 016 018 020
Chapter 9: Linear Systems II
9.1 002 004 006 008 010 012 014 016 018 020 022 024 026 028 030 032
9.2 002 004 006 008 010
9.3 002 004 006 008 010 012 014
9.4 002 004 006 008 010 012 014 016 018 020 022 024 026 028
9.5 002 004 006
Chapter 10: Nonlinear Systems
10.1 002 004 006 008 010 012 014 016 018
10.2 002 004 006 008 010 012 014 016 018 020 022 024 026 028 030
10.3 002 004 006 008
10.4 002 004 006 008 010 012 014 016 018
10.5 002 004 006 008 010 012 014
10.6 002 004 006 008 010 012 014 016 018 020 022 024 026
10.7 002 004 006 008 010
10.8 002 004 006 008
Chapter 11: Partial Differential Equations and Fourier Series
11.2 002 004 006 008 010 012 014
11.3 002 004 006 008 010 012 014 016 018
11.4 002 004 006 008 010 012 014 016
11.5 002 004 006 008 010 012 014 016
11.6 002 004 006 008 010 012 014 016 018 020 022 024
11.7 002 004 006 008 010 012 014 016
11.8 002 004 006 008 010 012 014 016 018 020
11.9 002 004 006 008 010 012
11.10 002 004 006 008 010 012 014 016 018 020 022
Total 309 (341)