This unique volume covers two fundamental elements of computational methods — numbers and functions. It provides an in-depth discussion of the behaviors of numbers, including both real and complex numbers. The discussion leads to the important closure properties of numbers, ensuring solution consistence and existence, and also possible failure in numerical computations in science and engineering.This text then introduces types of functions that take numbers as independent variables and produce a single number. Approaches for constructing inverse functions are also provided. Frequently used basis functions are introduced, with detailed studies on their properties and behaviors. Techniques are presented for constructing basis functions and their use in function approximation in computational methods.

This unique compendium covers the fundamental principles of mechanics of materials, focusing on the mechanical behaviour of structural members under various types of loads, including axial loading, bending, shearing, and torsion. The members can have various shape and constrained in different ways. Concepts of energy and failure criteria are also included.The useful text/reference book is written in Jupyter notebook format, so that description of theory, formulation, and coding can all be done in a unified document. This provides an environment for easy reading, exercise, practicing, and further exploration.

This comprehensive volume explores differentiation and integration, detailing their theories, concepts, and formulations. The book introduces various techniques for computing these mathematical elements for different types of functions and presents their applications.Python code is extensively used throughout the book, allowing readers to practice and interact with the concepts in real-time. This hands-on approach helps in comprehending the theory, techniques, and results of computational operations in differentiation and integration. Real-world engineering problems are connected to the theoretical discussions through numerous examples.Written in Jupyter notebook format, the useful reference text offers a unified environment for theory description, code execution, and real-time interaction, making it ideal for reading, practicing, and further exploration.

This unique compendium deals with the differentiation and integration of vector functions. It examines critical effects and extracts important features using powerful tools of differentiation and integration. Techniques and codes for computing the divergence, curl, and gradients of a given field function, which reveal the mathematical behavior of the vector field, are discussed. Green's theorem, Stokes's theorem, and Gauss's formula, along with their novel extensions, are presented in detail with applications such as the smoothed gradient method.Written in Jupyter notebook format, the book offers a unified environment for theory description, code execution, and real-time interaction, making it ideal for reading, practicing, and further exploration.

This book covers the fundamental principles of solid mechanics, focusing on the mechanical behavior of solids in two and three dimensions under various types of loads. The solids are defined in the Cartesian coordinate system and may have specific shapes and constraints.Techniques, including stress methods and displacement methods, for solving solid mechanics problems are explained in detail, formulated, and demonstrated with numerous examples and illustrations. Python is used to derive formulations, find solutions symbolically or numerically, and plot the results graphically.Written in Jupyter notebook format, this useful reference text offers a unified environment for theory description, code execution, and formulation, for easy reading and practicing.

This unique volume covers two fundamental elements of computational methods — numbers and functions. It provides an in-depth discussion of the behaviors of numbers, including both real and complex numbers. The discussion leads to the important closure properties of numbers, ensuring solution consistence and existence, and also possible failure in numerical computations in science and engineering.This text then introduces types of functions that take numbers as independent variables and produce a single number. Approaches for constructing inverse functions are also provided. Frequently used basis functions are introduced, with detailed studies on their properties and behaviors. Techniques are presented for constructing basis functions and their use in function approximation in computational methods.

This unique compendium covers the fundamental principles of mechanics of materials, focusing on the mechanical behaviour of structural members under various types of loads, including axial loading, bending, shearing, and torsion. The members can have various shape and constrained in different ways. Concepts of energy and failure criteria are also included.The useful text/reference book is written in Jupyter notebook format, so that description of theory, formulation, and coding can all be done in a unified document. This provides an environment for easy reading, exercise, practicing, and further exploration.

This comprehensive volume explores differentiation and integration, detailing their theories, concepts, and formulations. The book introduces various techniques for computing these mathematical elements for different types of functions and presents their applications.Python code is extensively used throughout the book, allowing readers to practice and interact with the concepts in real-time. This hands-on approach helps in comprehending the theory, techniques, and results of computational operations in differentiation and integration. Real-world engineering problems are connected to the theoretical discussions through numerous examples.Written in Jupyter notebook format, the useful reference text offers a unified environment for theory description, code execution, and real-time interaction, making it ideal for reading, practicing, and further exploration.

This unique compendium deals with the differentiation and integration of vector functions. It examines critical effects and extracts important features using powerful tools of differentiation and integration. Techniques and codes for computing the divergence, curl, and gradients of a given field function, which reveal the mathematical behavior of the vector field, are discussed. Green's theorem, Stokes's theorem, and Gauss's formula, along with their novel extensions, are presented in detail with applications such as the smoothed gradient method.Written in Jupyter notebook format, the book offers a unified environment for theory description, code execution, and real-time interaction, making it ideal for reading, practicing, and further exploration.

This book covers the fundamental principles of solid mechanics, focusing on the mechanical behavior of solids in two and three dimensions under various types of loads. The solids are defined in the Cartesian coordinate system and may have specific shapes and constraints.Techniques, including stress methods and displacement methods, for solving solid mechanics problems are explained in detail, formulated, and demonstrated with numerous examples and illustrations. Python is used to derive formulations, find solutions symbolically or numerically, and plot the results graphically.Written in Jupyter notebook format, this useful reference text offers a unified environment for theory description, code execution, and formulation, for easy reading and practicing.