DifferentialEquations

Final Exam Review

Exam 5 Review

Series solutions, Taylor Series, Maclauren series, Convergence, Interval of convergence, Method of Frobenius

Linear Algebra for differential equations. Matrix exponential, eigenvalues and eigenvectors.

Exam 3 Review

Gamma function, convolution, Laplace transforms and linear systems.

Exam 4 Review

Undamped Pendulum, nonlinear system, equilibria, phase plane analysis, centers and saddles.

Linearization of nonlinear systems, classification of equilibria, stability, atable, asymptotically stable, unstable, asymptotically unstable, saddle points, Volterra-Lotka predator-prey equations, Euler's Method

Nonhomogeneous linear systems, method of undetermined coefficients, variation of parameters, fundamental matrix

Sources, sinks, spiral sources and sinks, saddle points, nodes, proper nodes, degenerate or improper nodes, trace and determinant in classifying equilibria, autonomous systems.

Abel's Lemma, linear systems and the complex eigenvalue case. Repeated eigenvalue case, generalized eigenvalues.

Abel's Lemma, Solution of linear systems in the distinct eigenvalue and complex eigenvalue cases.

Laplace transform, unit step function, dirac delta function

Laplace Transform, Definition, Theorems, properties, Inverse Laplace Transform

Exam 2 Review

Undetermined coefficients, variation of parameters, non-homogeneous, nonhomogeneous equations, resonance.

Cauchy-Euler Equidimensional Equations are discussed

Second-order linear constant coefficient homogeneous ordinary differential equations. Harmonic oscillators, underdamped, critically damped, overdamped, complex characteristic values

Second-order linear constant coefficient homogeneous ordinary differential equations. Real distinct characteristic values, complex characteristic values. Basic theory.

Exam 1 Review

Applications of differential equations. Natural growth law, Logistic growth law, ballistics with air resistance, electrical circuits, Kirchoff's Law, Ohm's Law, resistors, capacitors, inductors, integration by parts, tabular method.

Exact equations, integrating factors, Euler's Method, Friedman Equation, Big Bang Cosmology, Big Crunch, approximation scheme

Differential Equations, Lesson 2, Direction Slope Fields, Isocline, isoclines, separable function, separable differential equation, u-sub, substitution, partial fractions, trig subs, integration by parts, existence uniqueness theorem, Picard's Theorem, First-Order Linear equations, integrating factor,

Differential Equations, Malthusian/Natural Growth, Newton's Law of Cooling/Warming, identity, contradiction, conditional, order, linear, homogeneous, initial value problem, IVP, ordinary, ODE, partial, PDE, initial condition, data