Introduction to Differential Equations with Dynamical Systems

Stephen L. Campbell, Richard Haberman

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Princeton University Press img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Mathematik

Beschreibung

Many textbooks on differential equations are written to be interesting to the teacher rather than the student. Introduction to Differential Equations with Dynamical Systems is directed toward students. This concise and up-to-date textbook addresses the challenges that undergraduate mathematics, engineering, and science students experience during a first course on differential equations. And, while covering all the standard parts of the subject, the book emphasizes linear constant coefficient equations and applications, including the topics essential to engineering students. Stephen Campbell and Richard Haberman--using carefully worded derivations, elementary explanations, and examples, exercises, and figures rather than theorems and proofs--have written a book that makes learning and teaching differential equations easier and more relevant. The book also presents elementary dynamical systems in a unique and flexible way that is suitable for all courses, regardless of length.

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Schlagwörter

Numerical analysis, Amplitude, Phase plane, Uniqueness theorem, Linear stability, Euler's formula, Trigonometric functions, Differential equation, Vector field, Voltage source, Logistic function, Summation, Chain rule, Theorem, Special case, Saddle point, Linear differential equation, Ordinary differential equation, Diagram (category theory), Partial fraction decomposition, Derivative, Equation, Polynomial, Dimension, Method of undetermined coefficients, Complex number, Lyapunov stability, Convolution theorem, Quadratic function, Phase line (mathematics), Periodic function, Inverse Laplace transform, Eigenvalues and eigenvectors, Linear combination, Algebraic equation, Variable (mathematics), Division by zero, Quantity, Initial condition, Asymptote, Upper half-plane, Integrating factor, Wronskian, Linear equation, Nonlinear system, Characteristic equation, Initial value problem, Scientific notation, Coefficient, Numerical integration, Calculation, Addition, Equilibrium point, Exponential growth, System of linear equations, Capacitor, Maxima and minima, Proportionality (mathematics), Forcing function (differential equations), Homogeneous differential equation, Newton's laws of motion, Parameter, Characteristic polynomial, Approximation, Matrix theory (physics), Dynamical system, Laplace transform, Hooke's law, Taylor series, Linearization