This book was written as a textbook on applied mathematics for engineers and scientist, with the expressed goal of merging both analytical and numerical methods more tightly than other textbooks. The role of appliedmathematics has continued to grow increasingly important with advancement of science and technology, ranging from modeling and analysis of natural phenomenon to simulation and optimization of man-made systems. With the huge and rapid advances of computing technology, larger and more complex problems can now be tackled and analyzed in a very timely fashion. In several cases, what used to require supercomputers can now be solved using personal computers. Nonetheless, as the technological tools continue to progress, it has become even more imperative that the results can be understood and interpreted clearly and correctly, as well as the need for a deeper knowledge behind the strengths and limitations of the numerical methods used. This means that we cannot forgo the analytical techniques because they continue to provide indispensable insights on the veracity and meaning of the results. The analytical tools remain to be of prime importance for basic understanding for buildingmathematical models and data analysis. Still, when it comes to solving large and complex problems, numerical methods are needed.