Unlock the power of numerical methods for engineering and data science with this comprehensive textbook. Designed for students, this book provides a practical guide to implementing and understanding the accuracy of numerical algorithms, including those from machine learning. Explore fundamental engineering mathematics and delve into classical techniques for solving equations, integrals, and differential equations. With a strong emphasis on theoretical foundations, error analysis, and hands-on Octave implementation, this resource ensures a solid grasp of concepts. The latter half bridges to machine learning, covering essential algorithms like linear regression and classification, while meticulously detailing bias, variance, and noise. Ideal for engineering students, mathematicians, and data scientists seeking to enhance their skills.