MATH 3321 - Engineering Mathematics - University of Houston
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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 . 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.

More information on the Cougar Textbook Access Program (CTAP) & Canvas/CCS:

 *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

Grading: Please consult your instructor's syllabus regarding any and all grading guidelines.

Justin Dart Jr. Center Accommodations:

Academic Adjustments/Auxiliary Aids: The University of Houston System complies with Section 504 of the Rehabilitation Act of 1973 and the Americans with Disabilities Act of 1990, pertaining to the provision of reasonable academic adjustments/auxiliary aids for students who have a disability. In accordance with Section 504 and ADA guidelines, University of Houston strives to provide reasonable academic adjustments/auxiliary aids to students who request and require them. If you believe that you have a disability requiring an academic adjustments/auxiliary aid, please visit Justin Dart Jr. Student Accessibility Center website at for more information.


Counseling and Psychological Services (CAPS) can help students who are having difficulties managing stress, adjusting to college, or feeling sad and hopeless. You can reach (CAPS) by calling 713-743-5454 during and after business hours for routine appointments or if you or someone you know is in crisis. No appointment is necessary for the "Let's Talk" program, a drop-in consultation service at convenient locations and hours around campus.