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Calculus Differential Equations and Their Applications by Martin Braun

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  1. Jan 19, 2013 #1

    Table of Contents:
    Code (Text):

    [*] First-order differential equations
    [*] Introduction
    [*] First-order linear differential equations
    [*] The Van Meegeren art forgeries
    [*] Separable equations
    [*] Population models
    [*] The spread of technological innovations
    [*] An atomic waste disposal problem
    [*] The dynamics of tumor growth, mixing problems, and orthogonal trajectories
    [*] Exact equations, and why we cannot solve very many differential equations
    [*] The existence-uniqueness theorem; Picard iteration
    [*] Finding roots of equations by iteration
    [*] Newton's method
    [*] Difference equations, and how to compute the interest due on your student loans
    [*] Numerical approximations; Euler's method
    [*] Error analysis for Euler's method
    [*] The three term Taylor series method
    [*] An improved Euler method
    [*] The Runge-Kutta method
    [*] What to do in practice
    [*] Second-order linear differential equations
    [*] Algebraic properties of solutions
    [*] Linear equations with constant coefficients
    [*] Complex roots
    [*] Equal roots; reduction of order
    [*] The nonhomogeneous equation
    [*] The method of variation of parameters
    [*] The method of judicious guessing
    [*] Mechanical vibrations
    [*] The Tacoma Bridge disaster
    [*] Electrical networks
    [*] A model for the detection of diabetes
    [*] Series solutions
    [*] Singular points; Euler equations
    [*] Regular singular points; the method of Frobenius
    [*] Equal roots, and roots differing by an integer
    [*] The method of Laplace transforms
    [*] Some useful properties of Laplace transforms
    [*] Differential equations with discontinuous right-hand sides
    [*] The Dirac delta function
    [*] The convolution integral
    [*] The method of elimination for systems
    [*] Higher-order equations
    [*] Systems of differential equations
    [*] Algebraic properties of solutions of linear systems
    [*] Vector spaces
    [*] Dimension of a vector space
    [*] Applications of linear algebra to differential equations
    [*] The theory of determinants
    [*] Solutions of simultaneous linear equations
    [*] Linear transformations
    [*] The eigenvalue-eigenvector method of finding solutions
    [*] Complex roots
    [*] Equal roots
    [*] Fundamental matrix solutions; [itex]e^{At}[/itex]
    [*] The nonhomogeneous equation; variation of parameters
    [*] Solving systems by Laplace transforms
    [*] Qualitative theory of differential equations
    [*] Introduction
    [*] Stability of linear systems
    [*] Stability of equilibrium solutions
    [*] The phase-plane
    [*] Mathematical theories of war
    [*] L. F. Richardson's theory of conflict
    [*] Lanchester's combat models and the battle of Iwo Jima
    [*] Qualitative properties of orbits
    [*] Phase portraits of linear systems
    [*] Long time behavior of solutions; the Poincare-Bendixson Theorem
    [*] Introduction to bifurcation theory
    [*] Predator-prey problems; or why the percentage of sharks caught in the Mediterranean Sea rose dramatically during World War I
    [*] The principle of competitive exclusion in population biology
    [*] The Threshold Theorem of epidemiology
    [*] A model for the spread of gonorrhea
    [*] Separation of variables and Fourier series
    [*] Two point boundary-value problems
    [*] Introduction to partial differential equations
    [*] The heat equation; separation of variables
    [*] Fourier series
    [*] Even and odd functions
    [*] Return to the heat equation
    [*] The wave equation
    [*] Laplace's equation
    [*] Appendix: Some simple facts concerning functions of several variables
    [*] Appendix: Sequences and series
    [*] Appendix: Introduction to APL
    [*] Answers to odd-numbered exercises
    [*] Index
    Last edited: May 6, 2017
  2. jcsd
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