### Chapter 4: Advanced Features of Sage

#### 4.2. Working with Large Formulas in Sage

• 4.2.2. Physics: Gravitation and Satellites

#### 4.4. Matrices and Sage, Part 2

• 4.4.3. Right and Left System Solving
• 4.4.4. Matrix Inverses
• 4.4.5. Computing the Kernel of a Matrix

#### 4.6. Working with the Integers and Number Theory

• 4.6.2. More about Prime Numbers

#### 4.16. Matrices and Sage, Part 3

• 4.16.1. Introduction to Eigenvectors
• 4.16.2. Finding Eigenvalues Efficiently in Sage
• 4.16.4. Matrix Factorizations
• 4.16.5. Solving Linear Systems Approximately with Least Squares

#### 4.17. Computing Taylor or MacLaurin Polynomials

• 4.17.1. Examples of Taylor Polynomials
• 4.17.2. An Application: Understanding How g Changes

#### 4.18. Minimizations and Lagrange Multipliers

• 4.18.3. A Lagrange Multipliers Example in Sage

#### 4.21. Systems of Inequalities and Linear Programming

• 4.21.1. A Simple Example

#### 4.22. Differential Equations

• 4.22.1. Some Easy Examples
• 4.22.2. An Initial-Value Problem
• 4.22.3. Graphing a Slope Field
• 4.22.4. The Torpedo Problem: Working with Parameters

#### 4.24. Vector Calculus in Sage

• 4.24.2. Computing the Hessian Matrix
• 4.24.3. Computing the Laplacian
• 4.24.4. The Jacobian Matrix
• 4.24.5. The Divergence
• 4.24.6. Verifying an Old Identity
• 4.24.7. The Curl of a Vector-Valued Function

#### 4.26. Complex Numbers and Sage

• 4.26.1. Working with Complex Numbers
• 4.26.5. Cube Roots and Higher-Order Roots
• 4.26.8. Polar Coordinates and Complex Numbers
• 4.26.10. Graphs of a Complex Function