Chapter 4: Advanced Features of Sage

4.1. Using Sage with Multivariable Functions and Equations

• 4.1

4.2. Working with Large Formulas in Sage

• 4.2.2. Physics: Gravitation and Satellites
• 4.2.2

4.4. Matrices and Sage, Part 2

• 4.4.3. Right and Left System Solving
• 4.4.3
• 4.4.4. Matrix Inverses
• 4.4.4
• 4.4.5. Computing the Kernel of a Matrix
• 4.4.5 (left)
• 4.4.5 (right)
• 4.4.5 (Figure 4.1 left_kernel)
• 4.4.5 (Figure 4.1 right_kernel)

4.5. Vector Operations

• 4.5

4.6. Working with the Integers and Number Theory

• 4.6.2. More about Prime Numbers
• 4.6.2

4.12. Can Sage Do Sudoku?

• 4.12

4.15. Using Sage and LATEX, Part One

• 4.15

4.16. Matrices and Sage, Part 3

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

4.17. Computing Taylor or MacLaurin Polynomials

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

4.18. Minimizations and Lagrange Multipliers

• 4.18.3. A Lagrange Multipliers Example in Sage
• 4.18.3

4.21. Systems of Inequalities and Linear Programming

• 4.21.1. A Simple Example
• 4.21.1

4.22. Differential Equations

• 4.22.1. Some Easy Examples
• 4.22.1
• 4.22.2. An Initial-Value Problem
• 4.22.2
• 4.22.3. Graphing a Slope Field
• 4.22.3.a
• 4.22.3.b (Figure 4.4)
• 4.22.3.c (Figure 4.4)
• 4.22.3.d (Figure 4.4)
• 4.22.3.e (Figure 4.4)
• 4.22.4. The Torpedo Problem: Working with Parameters
• 4.22.4

4.24. Vector Calculus in Sage

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

4.26. Complex Numbers and Sage

• 4.26.1. Working with Complex Numbers
• 4.26.1.a
• 4.26.1.b
• 4.26.5. Cube Roots and Higher-Order Roots
• 4.26.5
• 4.26.8. Polar Coordinates and Complex Numbers
• 4.26.8.a
• 4.26.5.b
• 4.26.10. Graphs of a Complex Function
• 4.26.10 (Figure 4.4)