University of Houston
Department of Mathematics
MATH 3321: Engineering Mathematics

Prerequisite: MATH 1432: Calculus II

Text: Text is in electronic form .

CourseWare

Exam Calendar
All exams will be departmental exams given at CASA .

1. Introduction to Differential Equations
   
   • 1.1 Basic Terminology
   • 1.2 n-Parameter Family of Solutions; General Solution; Particular Solution
   • 1.3 Initial-Value Conditions; Initial-Value Problems
2. First Order Differential Equations
   
   • 2.1 Linear Equations
   • 2.2 Separable Equations
   • 2.3 Some Applications
   • 2.4 Direction Fields; Existence and Uniqueness
   • 2.5 Some Numerical Methods*
3. Second Order Linear Differential Equations
   
   • 3.1 Introduction; Basic Terminology and Results
   • 3.2 Homogeneous Equations
   • 3.3 Homogeneous Equations with Constant Coefficients
   • 3.4 Nonhomogeneous Equations
   • 3.5 Nonhomogeneous Equations with Constant Coefficients; Undetermined Coefficients
   • 3.6 Vibrating Mechanical Systems
4. Laplace Transforms
   
   • 4.1 Introduction
   • 4.2 Basic Properties of Laplace Transforms
   • 4.3 Inverse Laplace Transforms and Initial-Value Problems
   • 4.4 Applications to Discontinuous Functions
   • 4.5 Initial-Value Problems with Piecewise Continuous Nonhomogeneous Terms
5. Linear Algebra
   
   • 5.1 Introduction
   • 5.2 Systems of Linear Equations; Some Geometry
   • 5.3 Solving Systems of Linear Equations
   • 5.4 Solving Systems of Linear Equations, Part 2
   • 5.5 Matrices and Vectors
   • 5.6 Square Matrices; Inverse of a Matrix and Determinants
   • 5.7 Vectors; Linear Dependence and Linear Independence
   • 5.8 Eigenvalues and Eigenvectors
6. Systems of First Order Linear Differential Equations
   
   • 6.1 Higher-Order Linear Differential Equations
   • 6.2 Systems of Linear Differential Equations
   • 6.3 Homogeneous Systems
   • 6.4 Homogeneous Systems with Constant Coefficients
   • 6.5 Nonhomogeneous Systems
   • 6.6 Some Applications

* Optional Section