Introduction to Differential Equations and Dynamical Systems

A Elementary Solution Formulas B Initial Values 2 Direction Fields A Definition and Examples B Isoclines C Continuity, Existence and Uniqueness 3 Integration A y'=f(x) B Variables Separable C Transformations (Optional) 4 LinearEquations A Exponential Integrating Factors B Linear Models C From nonlinear to linear (Optional) 5 Exact Equations (Optional) A Solutions by Integration B Exactness Test C Integrating Factors Chapter Review and Supplement Chapter 2 Applications: Dynamics & Equilibrium 1 Population Dynamics 2 Velocity in a Resisting Medium 3 Equilibrium Solutions (Optional) Computing Supplement A Euler Method B Modified Euler Method C Newton's Method Chapter 3 Equations of Order Two or More 1 Introduction A Exponential Solutions B Factoring Operators 2 Oscillatory Solutions A Complex Exponentials B Complex Characteristic Roots C Sinusoidal Oscillations D Order More Than Two 3 Nonhomogeneous Equations A General Solution B Undetermined Coefficient Method C Integration Method (Optional) 4 Nonlinear Equations (Optional) A Independence of Position: y=f(t,y) B Independence of Time: y=f(y,y) Chapter 4 Applications: Dynamics and Phase-Space 1 Mechanical Oscillators 2 Electric Circuits 3 Phase-Space and Periodicity A Phase Space B Equilibrium C Periodic Solutions (Optional) Computing Supplement A Euler Method B Stiffness C Functions Defined Piecewise D Poincare Sections (Optional) Chapter 5 Introduction to Systems 1 Vector Equations A Geometric Setting B Vector Fields C Order Reduction and Normal Form D Equilibrium Solutions E Existence, Uniqueness, and Flow (Optional) 2 Linear Systems A Definition B Elimintion Method C General Form of Solutions 3 Matrix Operators A Eigenvalues and Eigenvectors B Generalized Eigenvectors (Optional) Chapter Review and Supplement Chapter 6 Applications: Dynamics & Stability 1 Multicompartment Mixing 2 Interacting Populations 3 Mechanical Oscillations A Masses in Linear Motion B Nonlinear Motion in Space. (Part Contents)