A first course in differential equations

Index annexed

1. INTRODUCTION TO DIFFERENTIAL EQUATIONSBasic Definitions and Terminology / Some Mathematical Models / Review / Exercises2. FIRST-ORDER DIFFERENTIAL EQUATIONSPreliminary Theory / Separable Variables / Homogeneous Equations / Exact Equations / Linear Equations / Equations of Bernoulli, Ricatti, and Clairaut / Substitutions / Picard''''s Method / Review / Exercises3. APPLICATIONS OF FIRST-ORDER DIFFERENTIAL EQUATIONSOrthogonal Trajectories / Applications of Linear Equations / Applications of Nonlinear Equations / Review / Exercises / Essay: Population Dynamics4. LINEAR DIFFERENTIAL EQUATIONS OF HIGHER-ORDERPreliminary Theory / Constructing a Second Solution from a Know Solution / Homogeneous Linear Equations with Constant Coefficients / Undetermined Coefficients: Superposition Approach / Differential Operators / Undetermined Coefficients: Annihilator Approach / Variation of Parameters / Review / Exercises / Essay: Chaos5. APPLICATIONS OF SECOND-ORDER DIFFERENTIAL EQUATIONS: VIBRATIONAL MODELSSimple Harmonic Motion / Damped Motion / Forced Motion / Electric Circuits and Other Analogous Systems / Review / Exercises / Essay: Tacoma Narrows Suspension Bridge Collapse6. DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTSCauchy-Euler Equation / Review of Power Series; Power Series Solutions / Solutions About Ordinary Points / Solutions About Singular Points / Two Special Equations / Review / Exercises7. LAPLACE TRANSFORMLaplace Transform / Inverse Transform / Translation Theorems and Derivatives of a Transform / Transforms of Derivatives, Integrals, and Periodic Functions / Applications / Dirac Delta Function / Review / Exercises8. SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONSOperator Method / Laplace Transform Method / Systems of Linear First-Order Equations / Introduction to Matrices / Matrices and Systems of Linear First-Order Equations / Homogeneous Linear Systems / Undetermined Coefficients / Variation of Parameters / Matrix Exponential / Review / Exercises9. NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONSDirection Fields / The Euler Methods / The Three-Term Taylor Method / The Runge-Kutta Methods / Multistep Methods / Errors and Stability / Higher-Order Equations and Systems / Second-Order Boundary-Value Problems / Review / Exercises / Essay: Nerve Impulse Models / APPENDIX I: GAMMA FUNCTION / APPENDIX II: LAPLACE TRANSFORMS / APPENDIX III: REVIEW OF DETERMINANTS / APPENDIX IV: COMPLEX NUMBERS / ANSWERS TO ODD-NUMBERED PROBLEMS

This work is intended for instructors who prefer not to emphasize technology, modelling, and applications but instead want to focus on fundamental theory and techniques.