The Second Edition includes expanded coverage of Laplace transforms and partial differential equations as well as a new chapter on numerical methods.

Preface to the Second Edition Preface to the First Edition Suggestions for the Instructor PART 1 THE NATURE OF DIFFERENTIAL EQUATIONS.

Fermat and the Bernoullis PART 2 FIRST ORDER EQUATIONS Chapter 7.

Simple Electric Circuits PART 3 SECOND ORDER LINEAR EQUATIONS Chapter 14.

The Homogeneous Equation with Constant Coefficients Chapter 18.

Newtons Law of Gravitation and the Motions of the Planets Chapter 22.

Operator Methods for Finding Particular Solutions Appendix A.

Euler Appendix B.

Newton PART 4 QUALITATIVE PROPERTIES OF SOLUTIONS Chapter 24.

The Sturm Comparison Theorem PART 5 POWER SERIES SOLUTIONS AND SPECIAL FUNCTIONS.

Chapter 26. Introduction.

A Review of Power Series Chapter 27.

Gauss Appendix D.

Chebyshev Polynomials and the Minimax Property Appendix E.

Riemanns Equation PART 6 FOURIER SERIES AND ORTHOGONAL FUNCTIONS Chapter 33.

A Pointwise Convergence Theorem PART 7 PARTIAL DIFFERENTIAL EQUATIONS AND BOUNDARY VALUE PROBLEMS Chapter 39.

Eigenvalues, Eigenfunctions, and the Vibrating String Chapter 41.

Additional Properties of Bessel Functions PART 9 LAPLACE TRANSFORMS Chapter 48.

Laplace Appendix B.

Abel PART 10 SYSTEMS OF FIRST ORDER EQUATIONS Chapter 54.

Homogeneous Linear Systems with Constant Coefficients Chapter 57.

Nonlinear Systems.

Volterras Prey-Predator Equations PART 11 NONLINEAR EQUATIONS Chapter 58.

Autonomous Systems.

The Phase Plane and Its Phenomena Chapter 59.

Periodic Solutions.

The Poincar-Bendixson Theorem Appendix A.

Proof of Lienards Theorem PART 12 THE CALCULUS OF VARIATIONS Chapter 65.

Introduction. Some Typical Problems of the Subject Chapter 66.

Hamiltons Principle and Its Implications PART 13 THE EXISTENCE AND UNIQUENESS OF SOLUTIONS Chapter 68.

Picards Theorem Chapter 70.

Systems. The Second Order Linear Equation PART 14 NUMERICAL METHODS Chapter 71.

George F Simmons Differential Equations Solutions Pdf