# Calculus Differential Equations and Their Applications by Martin Braun

## For those who have used this book

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4. ### Strongly don't Recommend

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1. Jan 19, 2013

### Greg Bernhardt

Code (Text):

[LIST]
[*] First-order differential equations
[LIST]
[*] 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
[LIST]
[*] Newton's method
[/LIST]
[*] Difference equations, and how to compute the interest due on your student loans
[*] Numerical approximations; Euler's method
[LIST]
[*] Error analysis for Euler's method
[/LIST]
[*] The three term Taylor series method
[*] An improved Euler method
[*] The Runge-Kutta method
[*] What to do in practice
[/LIST]
[*] Second-order linear differential equations
[LIST]
[*] Algebraic properties of solutions
[*] Linear equations with constant coefficients
[LIST]
[*] Complex roots
[*] Equal roots; reduction of order
[/LIST]
[*] The nonhomogeneous equation
[*] The method of variation of parameters
[*] The method of judicious guessing
[*] Mechanical vibrations
[LIST]
[*] The Tacoma Bridge disaster
[*] Electrical networks
[/LIST]
[*] A model for the detection of diabetes
[*] Series solutions
[LIST]
[*] Singular points; Euler equations
[*] Regular singular points; the method of Frobenius
[*] Equal roots, and roots differing by an integer
[/LIST]
[*] 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
[/LIST]
[*] Systems of differential equations
[LIST]
[*] 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; $e^{At}$
[*] The nonhomogeneous equation; variation of parameters
[*] Solving systems by Laplace transforms
[/LIST]
[*] Qualitative theory of differential equations
[LIST]
[*] Introduction
[*] Stability of linear systems
[*] Stability of equilibrium solutions
[*] The phase-plane
[*] Mathematical theories of war
[LIST]
[*] L. F. Richardson's theory of conflict
[*] Lanchester's combat models and the battle of Iwo Jima
[/LIST]
[*] 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
[/LIST]
[*] Separation of variables and Fourier series
[LIST]
[*] Two point boundary-value problems
[*] Introduction to partial differential equations
[*] The heat equation; separation of variables
[*] Fourier series
[*] Even and odd functions
[*] The wave equation
[*] Laplace's equation
[/LIST]
[*] Appendix: Some simple facts concerning functions of several variables
[*] Appendix: Sequences and series
[*] Appendix: Introduction to APL