MATH 2552

MATH 2552 covers ordinary differential equations and Laplace transforms.

Topic List

• Introduction
  • Mathematical Models
  • Direction Fields
  • Classification of Differential Equations
• First Order Equations
  • Separable Equations
  • Linear Equations
  • Modeling
  • Solution Structures
    • Intervals of Existence
  • Autonomous Equations
    • Population Dynamics
    • Phase Portraits
    • Stability of Solutions
• Linear Systems of First Order Equations
  • Two-Dimensional Systems
  • n-Dimensional Systems
  • Homogenous Systems with Constant Coefficients
    • Distinct Real Nonzero Eigenvalues
    • Zero Eigenvalues
    • Complex Eigenvalues
    • Repeated Real Eigenvalues
    • Phase Portraits
  • Shifted Systems
    • Salt in Several Tanks
    • Electric Circuits
• Second Order Linear Equations
  • Homogenous Equations
  • Homogenous Equations with Constant Coefficients
    • Distinct Real Nonzero Eigenvalues
    • Complex Eigenvalues
    • Repeated Eigenvalues
    • Zero Eigenvalues
  • Free Vibrations
  • Nonhomogeneous Equations
    • Method of Undetermined Coefficients
    • Variation of Parameters
  • Forced Vibrations
• The Laplace Transform
  • The Inverse Laplace Transform
  • Solving Differential Equations
  • Discontinuous Functions
  • Periodic Functions
  • Impulse Functions
  • Convolution
• Nonlinear Systems
  • Stability
  • Almost Linear Systems
  • Competing Species
  • Predator-Prey Systems
  • Lorenz Attractor
• Numerical Methods
  • Euler's Method
  • Improved Euler's Method
  • Runge-Kutta Method

Class Structure

MATH 2552 is a core math class focused more on computation than pure theory.

Chen

At the beginning of the course, Chen posts a comprehensive course schedule that contains all topics, lecture notes, and textbook exercises. In addition, Chen makes lectures and studios optional, allowing the course to be easily self-studied. Chen's quizzes and exams tend to be straightforward, containing problems very similar to the textbook examples, if not easier.

Prerequisite Knowledge

Single Variable Calculus

Single variable calculus is used extensively throughout MATH 2552. Differential equations is often considered to be another calculus course, and uses differentiation and/or integration in almost every topic. Partial fraction decomposition is used frequently when working with Laplace transforms.

Linear Algebra

Linear algebra is also used extensively throughout MATH 2552. Eigenvalues and eigenvectors are used to analyze systems of differential equations and second order linear differential equations. Other linear algebra topics, such as row reduction, linear combinations, and linear independence are also used in the analysis of these types of differential equations.

Scheduling

MATH 2552 is required by most engineering and science majors, and it is also required for the modsim thread in cs. It is a prerequisite itself for many classes required by engineering and science majors. Due to its prerequisites, MATH 2552 is generally taken sometime between late freshmen year and early sophomore year.

Equivalent Courses

• MATH 2562 is the honors equivalent, which includes additional topics and goes into more depth in general.

Resources

• https://www.youtube.com/user/msebastiznf/playlists is a set of youtube videos created by Sebastian Fernandez, a former MATH 2552 TA. These videos cover the entire course and are very popular.