Differential EquationsUsing the same innovative and proven approach that made the authors' Engineering Mathematics a worldwide bestseller, this book can be used in the classroom or as an indepth selfstudy guide. Its unique programmed approach patiently presents the mathematics in a stepbystep fashion together with a wealth of worked examples and exercises. It also contains Quizzes, Learning Outcomes, and Can You? checklists that guide readers through each topic and reinforce learning and comprehension. Both students and professionals alike will find this book a very effective learning tool and reference.

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Contents
Solution of differential equations  6 
Review summary  36 
Inhomogenous equations  51 
Further problems 2  64 
Series 2  95 
Standard series  103 
Limiting values indeterminate forms  109 
Can You? Checklist 4  119 
Table of Z transforms  259 
Sampling  274 
Can You? Checklist 9  279 
Elementary operations and equivalent matrices  286 
Solution of sets of equations  295 
CayleyHamilton theorem  319 
Diagonalization of a matrix  325 
Matrix transformation  337 
Power series solutions  130 
Bessels equation  157 
Review summary  171 
Can You? Checklist 6  196 
Review summary  217 
The Dirac delta function the unit impulse  232 
Forced harmonic motion with damping  245 
Common terms and phrases
ar(c arbitrary constants auxiliary equation binomial series CayleyHamilton theorem cell D2 checklist column convergent copied into cells corresponding eigenvector cosh cosh ax cosx d2y dy Determine divergent dx2 dx eigenvalues eigenvectors enter the formula equation gives Euler EulerCauchy method Euler's method Example expression firstorder differential equations function f(t Further problems given equation highlight in cell indeterminate form indicial equation initial conditions integrating factor inverse Laplace transform inverse transform l'Hopital's rule Legendre polynomials Leibnitz theorem limiting value Maclaurin's series move to Frame multiply obtain ordinary differential equations partial fractions periodic functions Program rank recurrence relation result Review summary righthand side RungeKutta method secondorder differential equations sequence xk series solution sinhx sinx sketch the graph Solve the equation spreadsheet substitution Table of Laplace Taking Laplace transforms Taylor's series Test exercise unit step function xy plane Z{xk zero