For centuries, physical models have been used to investigate complex hydraulic problems. Leonardo da Vinci (1452-1519) stated, "I will treat of such a subject. But first of all, 1 shall make a few experiments and then demonstrate why bodies are forced to act in this matter. " Even with the current advancements of mathematical numerical models, certain complex three-dimensional flow phenomena must still rely on physical model studies. Mathematical models cannot provide adequate solutions if physical processes involved are not completely known. Physical models are particularly attractive to investigate phenomena-involved sediment movements because many three-dimensional sediment processes are still unclear at this stage. Theoretically, there are numerous factors governing movable bed processes and it is nearly impossible to design model studies to obey all the model criteria. Sometimes, appropriate lightweight materials are difficult or too costly to obtain. Often, distorted models are used due to the limitation of available space and the requirement for greater vertical flow depth to investigate vertical differences of various parameters. The turbulence level in the model may also be maintained at a sufficient level to reproduce a similar flow pattern in the prototype. Frequently, engineers are forced to employ distorted models that cannot be designed to satisfy all governing criteria correctly. Thus each hydraulic laboratory has developed its own rules for model testing and a great deal of experience is needed to interpret model results.

Developed during ten years of teaching experience, this book serves as a set of lecture notes for an introductory course on numerical computation, at the senior undergraduate level. These notes contain the material that can be covered in a semester, together with a few optional sections for additional reading. Rather than surveying a large number of algorithms, the book presents the most important computational methods and emphasizes the underlying mathematical ideas. In most chapters, graphs and drawings are relied on, to build up intuition. The notes are written in a rather colloquial style, presenting the subject matter in the same form as it can be explained in a classroom. For instructors, this will minimize the amount of effort required to prepare their blackboard presentations.As prerequisites, the book only relies on standard calculus, an introductory course on matrices, and some basic computer programming skills. As a new feature, these notes are supplemented by two sets of videos from the author's Youtube channel. These videos contain a complete set of live lectures given in Spring 2015, together with a complete set of short tutorials, from 5 to 15 minutes each.A set of homework problems is included at the end of each chapter. Homework projects cover a variety of applications, in connection with population dynamics, engineering, mechanics, image reconstruction, etc. A complete set of solutions is available for instructors, upon request.

For centuries, physical models have been used to investigate complex hydraulic problems. Leonardo da Vinci (1452-1519) stated, "I will treat of such a subject. But first of all, 1 shall make a few experiments and then demonstrate why bodies are forced to act in this matter. " Even with the current advancements of mathematical numerical models, certain complex three-dimensional flow phenomena must still rely on physical model studies. Mathematical models cannot provide adequate solutions if physical processes involved are not completely known. Physical models are particularly attractive to investigate phenomena-involved sediment movements because many three-dimensional sediment processes are still unclear at this stage. Theoretically, there are numerous factors governing movable bed processes and it is nearly impossible to design model studies to obey all the model criteria. Sometimes, appropriate lightweight materials are difficult or too costly to obtain. Often, distorted models are used due to the limitation of available space and the requirement for greater vertical flow depth to investigate vertical differences of various parameters. The turbulence level in the model may also be maintained at a sufficient level to reproduce a similar flow pattern in the prototype. Frequently, engineers are forced to employ distorted models that cannot be designed to satisfy all governing criteria correctly. Thus each hydraulic laboratory has developed its own rules for model testing and a great deal of experience is needed to interpret model results.

This book serves as a set of lecture notes for a senior undergraduate level course on the introduction to numerical computation, which was developed through 4 semesters of teaching the course over 10 years. The book requires minimum background knowledge from the students, including only a three-semester of calculus, and a bit on matrices.The book covers many of the introductory topics for a first course in numerical computation, which fits in the short time frame of a semester course. Topics range from polynomial approximations and interpolation, to numerical methods for ODEs and PDEs. Emphasis was made more on algorithm development, basic mathematical ideas behind the algorithms, and the implementation in Matlab.The book is supplemented by two sets of videos, available through the author's YouTube channel. Homework problem sets are provided for each chapter, and complete answer sets are available for instructors upon request.The second edition contains a set of selected advanced topics, written in a self-contained manner, suitable for self-learning or as additional material for an honored version of the course. Videos are also available for these added topics.

This book serves as a set of lecture notes for a senior undergraduate level course on the introduction to numerical computation, which was developed through 4 semesters of teaching the course over 10 years. The book requires minimum background knowledge from the students, including only a three-semester of calculus, and a bit on matrices.The book covers many of the introductory topics for a first course in numerical computation, which fits in the short time frame of a semester course. Topics range from polynomial approximations and interpolation, to numerical methods for ODEs and PDEs. Emphasis was made more on algorithm development, basic mathematical ideas behind the algorithms, and the implementation in Matlab.The book is supplemented by two sets of videos, available through the author's YouTube channel. Homework problem sets are provided for each chapter, and complete answer sets are available for instructors upon request.The second edition contains a set of selected advanced topics, written in a self-contained manner, suitable for self-learning or as additional material for an honored version of the course. Videos are also available for these added topics.