What you are trying to learn/understand falls under the rubric of Scientific Computing/Numerical Methods/Numerical Analysis/Numerical Algorithms. The mathematics underpinning them is quite wide but mostly Linear Algebra and Calculus. You might find the following useful for your study;

1) Scientific Computing by Michael Heath - Classic text covering a broad swath of domains and tries to build motivation/intuition before the mathematics (affordable Indian edition available).

2) Mathematical Principles for Scientific Computing and Visualization by Gerald Farin and Dianne Hansford - Nice overview of needed background. The authors also have a book named Practical Linear Algebra: A Geometry Toolbox which you might find a ideal companion.

3) Numerical Methods: Fundamentals and Applications by Rajesh Kumar Gupta - A relatively recent book with a really broad coverage of subjects and detailed mathematical expositions (affordable Indian edition available).

4) Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics by Justin Solomon - Good explanations (affordable Indian edition available). Free ebook available at https://people.csail.mit.edu/jsolomon/

5) Finally, Mathematics for Physicists: Introductory Concepts and Methods by Alexander Altland and Jan Von Delft is an excellent book to have as a reference. It has three sections viz. Linear Algebra, Calculus and Vector Calculus. The presentation is very precise, does not focus on proofs/lemmas but on concepts and covers a wide swath of important mathematics.