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: MATH 1432

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.

Text: Available in electronic form (PDF) through CASA for all enrolled students via an Access Code*Note: If you misplace/lose your code, you will need to purchase another. There is no exception to this.

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

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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


CSD 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 The Center for Students with DisABILITIES (CSD) website at for more information.

Accommodation Forms: Students seeking academic adjustments/auxiliary aids must, in a timely manner (usually at the beginning of the semester), provide their instructor with a current Student Accommodation Form (SAF) (paper copy or online version, as appropriate) from the CSD office before an approved accommodation can be implemented.

Details of this policy, and the corresponding responsibilities of the student are outlined in The Student Academic Adjustments/Auxiliary Aids Policy (01.D.09) document under [STEP 4: Student Submission (5.4.1 & 5.4.2), Page 6]. For more information please visit the Center for Students with Disabilities Student Resources page.

Additionally, if a student is requesting a (CSD approved) testing accommodation, then the student will also complete a Request for Individualized Testing Accommodations (RITA) paper form to arrange for tests to be administered at the CSD office. CSD suggests that the student meet with their instructor during office hours and/or make an appointment to complete the RITA form to ensure confidentiality.

*Note: RITA forms must be completed at least 48 hours in advance of the original test date. Please consult your counselor ahead of time to ensure that your tests are scheduled in a timely manner. Please keep in mind that if you run over the agreed upon time limit for your exam, you will be penalized in proportion to the amount of extra time taken.



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.