Catalogue Description and Prerequisites

MA 221 Differential Equations and Matrix Algebra I 4R-0L-4C F,W Pre: MA 113 or permission of mathematics department head
Basic matrix algebra with emphasis on understanding systems of linear equations from algebraic and geometric viewpoints, including the least squares process and eigenvalues and eigenvectors. First order differential equations including basic solution techniques and numerical methods. Second order linear, constant coefficient differential equations, including both the homogeneous and non-homogeneous cases. Introduction to complex arithmetic, as needed. Applications to problems in science and engineering.

Prerequisite: All of the topics in MA112, in addition to some topics in MA113, will be assumed. In addition, familiarity with some Maple commands form Calculus is assumed. The Maple files  MapleIntRGL.mws (introduction) and calcrev.mws (review for DE) may be helpful. These files are available on Angel in the (Rose-Only) Mathematics Course Information Repository.

Course Goals

1. Develop a deeper understanding of equations and their solutions, especially linear algebraic and differential equations.
2. Improve mathematical modeling and analytical problem solving skills.
3. Develop ability to communicate mathematically.
4. Improve skill using the computer as a tool for mathematical analysis and problem solving.
5. Introduce applications of mathematics, especially to science and engineering.

Textbook and other required materials

Course Topics

Here the course topics are separated  into differential equation topics and matrix algebra topics, though the development will parallel that in the book.

1. First order differential equations
• Review basic notions (e.g., separation of variables, initial value problems)
• Review dx/dt = ax and dx/dt = ax + b and show structure of solution as particular solution plus homogeneous solution
• Numerical methods (e.g., Euler, RK4)
• Applications as appropriate
2. Second order linear differential equations
   • Constant coefficient, homogeneous case (solving the characteristic equation requires basics of complex arithmetic through Euler's formula)
   • Method of undetermined coefficients for non-homogeneous case
   • Resonance
   • Applications as appropriate
     
3. Matrix Algebra
   • Matrix Arithmetic (e.g., addition, scalar multiplication, matrix multiplication, inverses --emphasis on the 2 x 2 case for "by-hand" inverting)
   • Understanding a matrix A as a transformation (avoiding general vector space ideas) ; Ax = b
   • Representation of systems of linear equations as matrix equations
   • Gaussian Elimination for solving Ax = b.
   • Structure of general solution for Ax = b: algebraic point of view (particular solution plus homogeneous solution);
   • Understanding the Least Squares Process: algebraic point of view (solve the normal equations); geometric point of view (project b onto the range of A and solve)
   • Eigenvalues and Eigenvectors: algebraic point of view (solve Ax = lx for x and l ), and  geometric point of view (Ax is parallel to x)
   • Applications as appropriate.

Course Requirements and Policies

Computer Policy

Performance Standards

Paper and pencil

1. Demonstrate skill with matrix arithmetic including
• 2x2 inverses
• eigenvalues and eigenvectors for 2x2 matrices
2. Demonstrate skill using complex numbers
• basic arithmetic and geometric interpretation
3. Solve linear systems of equations
• at most 3x4
4. Solve linear differential equations including
• direct integration
• separate and integrate involving simple integrations
• integrating factors with simple integration
• graphing and interpreting the solutions
• constant coefficient, second order equations with simple driving functions

Maple

1. Use Maple to solve linear systems of equations, including obtaining least squares solutions
• students may be required to develop normal equations in matrix form
• Use Maple to compute eigenvalues and eigenvectors
  
2. Use Maple to solve differential equations symbolically and numerically
• using dsolve
• numerically by using the method=numeric
• using Maple to assist in separate and integrate, undetermined coefficients, and variation of paremters solution methods
• graphing and interpreting the solutions

Final Exam Policy

Individual Instructor Policies

• the grading scheme, based on the various course components.
• the number and format of hour exams, quizzes, homework assignments, in class assignments, and projects,
• the policies governing the work items above, e.g., whether the computer will be used, what collaboration is allowed, and the format of assignments.
• all policies for classroom procedure, including group work, class participation, laptop use and attendance*.

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Go to

• Online materials specific to the course section and instructor.
• The Mathematics Department Course Information Page
• The Mathematics Department Syllabus page
• The Mathematics Department Home Page.
• The Rose-Hulman Home Page