Scientific Computing

2.

Mathematical Foundations

2.1.

2.1.1.

Vector Spaces and Operations

2.1.2.

Matrix Operations and Properties

2.1.3.

Eigenvalues and Eigenvectors

2.1.4.

Matrix Decompositions

2.1.5.

Norms and Condition Numbers

2.2.

Calculus and Analysis

2.2.1.

Differential Calculus

2.2.2.

Integral Calculus

2.2.3.

Multivariable Calculus

2.2.4.

Vector Calculus

2.2.5.

Complex Analysis Basics

2.3.

Differential Equations

2.3.1.

Ordinary Differential Equations

2.3.2.

Partial Differential Equations

2.3.3.

Classification and Properties

2.3.4.

Analytical Solution Methods

2.4.

Probability and Statistics

2.4.1.

Probability Distributions

2.4.2.

Statistical Inference

2.4.3.

Hypothesis Testing

2.4.4.

Regression Analysis

2.4.5.

Bayesian Methods

2.5.

Discrete Mathematics

2.5.1.

2.5.2.

2.5.3.

Boolean Algebra

2.5.4.

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1. Introduction to Scientific Computing

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3. Foundational Computational Tools and Concepts