MATH 3321 - Engineering Mathematics - University of Houston

# MATH 3321 - Engineering Mathematics

***This is a course guideline.  Students should contact instructor for the updated information on current course syllabus, textbooks, and course content***

Prerequisite: Calculus II

Course Description: First order ordinary differential equations and initial value problems; higher order differential equations; vector spaces, matrices, determinants, eigenvectors and eigenvalues; applications to systems of first order equations; Laplace transforms. *Note: Students may not receive credit for both MATH 3321 and MATH 3331.

(Some sections) Textbook & Access Code: The textbook,online quizzes, and additional help materials will be made available by logging into CASA Campus Services (CCS) at https://ccs.casa.uh.edu/ . Students pay for access to CCS as part of their fee bill via CTAP. If one opts out of the CTAP, they can purchase an access code for this course at UH Bookstore. In this case, if the code is not entered by the deadline specified on CASA, students will lose access to CASA. No make ups will be given for assignments missed during the no-access period.

*Note: Some sections of this course are enrolled in CTAP; others are not. Please contact your instructor or view your instructor's syllabus to determine if your method of purchase is available through CTAP or not.

Note: Additional important information is contained at your instructor’s personal webpage. You are responsible for knowing all of this information.

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