Numerical Mathematics presents the innovative approach of using numerical methods as a practical laboratory for all undergraduate mathematics courses in science and engineering streams. The authors bridge the gap between numerical methods and undergraduate mathematics and emphasize the graphical visualization of mathematical properties, numerical verification of formal statements, and illustrations of the mathematical ideas. Students using Numerical Mathematics as a supplementary reference for basic mathematical courses will be encouraged to develop their mathematical intuition with an effective component of technology, while students using it as the primary text for numerical courses will have a broader, reinforced understanding of the subject.

• Numerical examples and inline MATLAB codes provide convenient tools for classroom use. Detailed descriptions highlight the mathematical ideas behind the theorems and algorithms, providing students with a clearer understanding of the material at hand. The text provides a self-contained introduction and overview of undergraduate numerical analysis, including error analysis, computer arithmetic, and detailed algorithms for standard numerical techniques. Includes discussions on key theoretical concepts in all major areas of undergraduate mathematics for science and engineering (scalar and vector calculus, linear algebra, and differential equations) followed by step-by-step numerical implementation of milestone examples. Includes detailed explanations of selected examples from applied mathematics, providing students with hands-on experience in modeling, including the choice of appropriate methods, programming, and analysis of results.

Preface / Elements of the Laboratory / Linear Systems / Orthogonality / Eigenvalues and Eigenvectors / Polynomial Functions / Differential and Integral Calculus / Vector Calculus / Zeros and Extrema of Functions / Initial-Value Problems for ODEs / Boundary-Value Problems for ODEs and PDEs / Spectral Methods / Splines and Finite Elements / Bibliography / Subject Index / MATLAB Index / New MATLAB Scripts and Functions.

Undergraduate Students in Mathematics, Science and Engineering Programs