Numerical Analysis in Modern Scientific Computing

This introductory book directs the reader to a selection of useful elementary numerical algorithms based on a sound theoretical foundation developed within the text. The primary aim is to foster algorithmic thinking, emphasizing enduring computational concepts over rapidly changing software issues. The guiding principle is to explain modern numerical analysis concepts applicable in complex scientific computing through simpler model problems. For example, the two adaptive techniques in numerical quadrature discussed here lay the groundwork for exploration methods or multigrid methods in differential equations, which are not covered in this text. The presentation utilizes geometrical intuition where appropriate, supported by a large number of illustrations. Numerous exercises are included for further practice and enhanced understanding. This text will appeal to undergraduate and graduate students.