Applied Partial Differential Equations

Partial differential equations are a central concept in mathematics. They arise in mathematical models whose dependent variables vary continuously as functions of several independent variables (usually space and time). Their power lies in their universality: there is a huge and ever-growing range of real-world problems to which they can be applied, from fluid mechanics and electromagnetism to probability and finance. This is an enthusiastic and clear guide to the theory and applications of PDEs. It deals with questions such as the well-posedness of a PDE problem: when is there a unique solution that changes only slightly when the input data is slightly changed? This is connected to the problem of establishing the accuracy of a numerical solution to a PDE, a problem that becomes increasingly important as the power of computer software to produce numerical solutions grows. This book is intended for final year undergraduates and graduate students in applied mathematics and engineering.