Unlike older textbooks that treat coding as an afterthought or rely on legacy languages like MATLAB or Fortran, this edition is built explicitly around Julia.
This is where Julia shines brightest.
Numerical optimization involves finding the minimum or maximum of a function. Julia provides:
The backbone of regression.
Julia's DifferentialEquations package provides a comprehensive set of numerical methods for solving ordinary and partial differential equations.
# Differential equation example
using DifferentialEquations
function lotka_volterra!(du, u, p, t)
du[1] = p[1] * u[1] - p[2] * u[1] * u[2]
du[2] = p[3] * u[1] * u[2] - p[4] * u[2]
end
u0 = [1.0, 1.0]
p = [1.5, 1.0, 3.0, 2.0]
tspan = (0.0, 10.0)
sol = solve(lotka_volterra!, u0, p, tspan)
println(sol) # Output: solution
Conclusion
In this article, we have explored the fundamentals of numerical computation using the Julia programming language. Julia's high-performance capabilities, dynamism, and extensive package ecosystem make it an ideal language for numerical and scientific computing. By mastering the basics of numerical computation in Julia, researchers and practitioners can tackle complex problems in a wide range of fields.
References
Further Reading
The definitive resource for modern scientific computing is Fundamentals of Numerical Computation: Julia Edition, authored by Tobin A. Driscoll and Richard J. Braun. This textbook bridges the gap between mathematical theory and practical implementation, utilizing the high-performance Julia programming language to solve complex numerical problems. Accessing the Textbook
While many users search for a "PDF" version, it is important to note the available formats:
Online Interactive Version: The book is primarily an online-first resource available for free digital viewing.
Official E-book: A formal e-book is available through the SIAM Bookstore, though it often requires a purchase for full offline access or PDF-like functionality.
Hardcover Edition: For those who prefer physical copies, the print version was released in August 2022. Core Content and Curriculum
The textbook is designed for advanced undergraduate students in math, science, and engineering. It covers a comprehensive range of numerical methods, including:
Linear Algebra: Square linear systems, LU factorization, and eigenvalues. fundamentals of numerical computation julia edition pdf
Rootfinding: Solving nonlinear equations using Newton's method and quasi-Newton methods.
Data Approximation: Polynomial interpolation, least squares, and cubic splines.
Differential Equations: Initial-value problems (IVPs) and Runge-Kutta methods. Key Features of the Julia Edition Home — Fundamentals of Numerical Computation
Fundamentals of Numerical Computation: Julia Edition is a textbook authored by Tobin A. Driscoll Richard J. Braun , published by the Society for Industrial and Applied Mathematics (SIAM)
in 2022. Originally written for MATLAB, this revised edition adapts the core principles of numerical analysis specifically for the Julia programming language Core Content & Structure
The book is designed for advanced undergraduate students in math, science, and engineering. It emphasizes linear algebra as the primary framework for solving computational problems. Amazon.com Topics Covered Linear Algebra : Square and overdetermined linear systems. Root-finding : Techniques for nonlinear equations. Approximation
: Global function approximation and piecewise interpolation. Differential Equations
: Initial-value problems (ODEs) and boundary-value problems. Advanced Methods
: Krylov subspace methods, diffusion, and advection equations. Organization
: The 13 chapters are structured for a one-semester introduction (Chapters 1–6) or a full two-semester sequence (Chapters 7–13). SIAM Publications Library Key Features Code-Rich Learning : Includes over 40 functions 160 examples fully coded in Julia. Exercise Bank : Contains over 600 exercises
, split between mathematical theory and computational practice. Supplementary Resources : An online companion website (fncbook.com) provides source code, student projects, and in-class labs. Modern Accessibility tri-language version
was updated in early 2025 to include examples for Julia, MATLAB, and Python (NumPy/SciPy). SIAM Publications Library Accessibility and Formats Fundamentals of Numerical Computation: Julia Edition
Fundamentals of Numerical Computation: Julia Edition is a comprehensive textbook by Tobin A. Driscoll and Richard J. Braun designed for advanced undergraduates in mathematics, engineering, and computer science. Originally written for MATLAB, this 2022 edition provides a complete transition to the
programming language, leveraging its speed and clarity for scientific computing. SIAM Publications Library Core Content & Educational Approach
The book introduces the mathematics and algorithmic use for fundamental problems in numerical analysis: SIAM Publications Library Linear Algebra: Unlike older textbooks that treat coding as an
Systems of equations, LU factorization, least squares, and eigenvalues. Root-Finding: Algorithms for finding roots of nonlinear equations. Approximation:
Interpolation (polynomial and splines), finite differences, and numerical integration. Differential Equations:
Solving initial-value problems (ODEs) and boundary-value problems. Floating-Point Arithmetic:
A critical focus on how finite-precision arithmetic (rounding errors and condition numbers) impacts results. Amazon.com Key Features of the Julia Edition Home — Fundamentals of Numerical Computation
The Julia Edition of Fundamentals of Numerical Computation (2022) by Tobin A. Driscoll and Richard J. Braun is a major update to the 2017 MATLAB original, designed to leverage Julia's performance and clarity for scientific computing. Core Concept: "Unlearn What You Have Learned"
The book emphasizes that numerical computation is not just mathematics on a computer; it begins with discretization—replacing real numbers with a finite "surrogate set". This fundamental shift introduces:
Floating-point Arithmetic: Understanding how small roundoff errors accumulate.
Conditioning: Quantifying how sensitive a problem is to small perturbations.
Stability: Identifying algorithms that prevent errors from growing out of control. Key Julia-Specific Features
Unlike its MATLAB predecessor, this edition utilizes modern Julia syntax to clarify numerical concepts:
Broadcasting: Using the . syntax for elementwise operations, which clarifies how functions apply to arrays.
Comprehensions: Offering concise ways to construct vectors and matrices.
Multiple Dispatch: Leveraging Julia's core design to allow specialized treatment of different data types. Structured Learning Path
The book is divided into a survey course (Chapters 1–6) and advanced topics:
Foundations: Floating-point numbers, linear systems of equations, and LU factorization. Conclusion In this article, we have explored the
Linear & Nonlinear Problems: Overdetermined systems (least squares), rootfinding, and nonlinear optimization.
Approximation & Calculus: Piecewise interpolation, numerical differentiation, and integration.
Differential Equations: Initial-value problems (ODEs) and eventually boundary-value problems and PDEs.
Advanced Matrix Analysis: Eigenvalues (EVD), Singular Value Decomposition (SVD), and Krylov subspace methods. Home — Fundamentals of Numerical Computation
The textbook Fundamentals of Numerical Computation: Julia Edition
by Tobin A. Driscoll and Richard J. Braun serves as a comprehensive guide for undergraduates in math, computer science, and engineering to learn numerical methods through the Julia programming language
. It emphasizes a "linear algebra first" approach, using Julia's performance and mathematical syntax to implement fundamental algorithms. SIAM Publications Library Core Topics Covered
The book is structured into sections that transition from simple numerical foundations to advanced applications: SIAM Publications Library Introduction to Numerical Computing : Focuses on discretization of real numbers, floating-point arithmetic
, and the concepts of condition numbers and algorithm stability. Root-finding
: Covers techniques like the bisection method, secant method, and Newton's method to solve Linear Algebra & Simultaneous Equations : Explores LU factorization
, QR factorization, and iterative solvers like GMRES and MINRES. Approximation & Interpolation
: Includes polynomial collocation, piecewise linear interpolants, and cubic splines Calculus & Differential Equations
: Features numerical integration (trapezoid and adaptive rules), finite differences, and Initial Value Problems (IVPs) SIAM Publications Library Why Use Julia for Numerical Computation? Julia Edition
highlights several language-specific advantages for students: Toby Driscoll Fundamentals of Numerical Computation: Julia Edition
This overview is designed to highlight why this specific text is a critical resource for students and practitioners moving from mathematical theory to practical software implementation.