Table of contents

Mathematical and Scientific Computing in C++

From programming fundamentals to reliable numerical simulation

Read each section in order. Every title can be opened as a TheoryTrace document.

• Cover
• Copyright
• How to read this book
• Introduction
• Chapter 1: Computing as a Mathematical Tool
• Chapter 2: C++ Essentials for Numerical Work
• Chapter 3: Types, Precision, and Floating-Point Arithmetic
• Chapter 4: Functions, Modularity, and Mathematical Code Design
• Chapter 5: Arrays, Vectors, and Data Representation
• Chapter 6: Error, Stability, and Conditioning
• Chapter 7: Mathematical Algorithms and Complexity
• Chapter 8: Numerical Differentiation and Integration
• Chapter 9: Roots and Nonlinear Equations
• Chapter 10: Linear Algebra Foundations in C++
• Chapter 11: Solving Linear Systems
• Chapter 12: Eigenvalues, Least Squares, and Data Fitting
• Chapter 13: Interpolation and Approximation
• Chapter 14: Ordinary Differential Equations
• Chapter 15: Scientific Modeling and Simulation
• Chapter 16: Random Numbers and Monte Carlo Methods
• Chapter 17: Optimization and Parameter Estimation
• Chapter 18: Working with Scientific Data
• Chapter 19: Using Modern C++ Libraries
• Chapter 20: Performance, Memory, and Profiling
• Chapter 21: Testing, Verification, and Reproducibility
• Chapter 22: Capstone Projects in Mathematical and Scientific Computing
• Conclusion