Part IV: Plotting and Solving Equations

In this part we start to use SageMath for plotting and to solve problems. We model a mathematical problem, apply advanced solvers, and visualize the setup and the computational results. This part of the course ends with the second midterm exam.

• Lecture 25: Two Dimensional Plots
  • Plotting Formulas and Functions
  • Curves in the Plane
  • Assignments
• Lecture 26: Plotting in Three Dimensions and Beyond
  • Surface Plots
  • Space Curves
  • Four Dimensional Plots with Colormaps
  • Assignments
• Lecture 27: Animations
  • Animating Plots
  • Designing an Animation
  • Animating Surfaces
  • Animating Space Curves
  • Assignments
• Lecture 28: Solving Equations
  • Polynomials in One Variable
  • Solving Systems of Polynomial Equations
  • Groebner Bases
  • Assignments
• Lecture 29: Linear Algebra
  • Matrices and Linear Systems
  • Matrices over Fields
  • Matrices over Rings
  • Resultants
  • Plotting Matrices
  • Assignments
• Lecture 30: Solving Differential Equations
  • The Pendulum Problem
  • Plotting the Slope Field
  • Laplace Transforms
  • Numerically Solving a First Order System
  • Heat Diffusion
  • Assignments
• Lecture 31: Polyhedral and Unconstrained Optimization
  • Polyhedra
  • Linear Programming
  • Unconstrained Minimization
  • Assignments
• Lecture 32: Review of Lectures 18 to 31
• Lecture 33: the Second Midterm Exam
  • Questions on the Spring 2017 Second Midterm Exam
  • Questions on the Fall 2018 Second Midterm Exam
  • Questions on the Spring 2019 Second Midterm Exam
  • Questions on the Summer 2022 Second Midterm Exam