MATH 3321

Engineering Mathematics

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