Aktosun, Fall 2026, Math 3319

Instructor: Tuncay Aktosun, PKH 461, (817) 272-1545, aktosun@uta.edu

Course: Differential Equations and Linear Algebra, Math 3319, Section 003, Course number 94077

Office Hours: 4:30-5:20 pm, Tuesday and Thursday, and by appointment

Classroom: PKH 111 (Pickard Hall 111)

Classtime: 5:30-6:50 pm Tuesday and Thursday

Textbook: Stephen Goode and Scott Annin, Differential Equations and Linear Algebra, 4th ed., Pearson, 2017.

Coverage: The following sections in the textbook:

1.1: Differential equations everywhere

1.2: Basic ideas and terminology

1.4: Separable differential equations

1.6: First-order linear differential equations

1.8: Change of variables

1.9: Exact differential equations

2.1: Matrices: definitions and notations

2.2: Matrix algebra

2.3: Terminology for systems of linear equations

2.4: Elementary row operations

2.5: Gaussian elimination

2.6: Inverse of a square matrix

3.1: Definition of the determinant

3.2: Properties of determinants

3.3: Cofactor expansions

4.1: Vectors in Rⁿ

4.2: Definition of a vector space

4.3: Subspaces

4.4: Spanning sets

4.5: Linear dependence and linear independence

4.6: Bases and dimensions

6.1: Definition of a linear transformation

7.1: Eigenvalue/eigenvector problem

8.1: General theory of linear differential equations

8.2: Constant-coefficient homogeneous linear differential equations

8.3: Method of undetermined coefficients

Grading: Letter grades will be assigned based on the three exam grades (the final exam is considered to be the third exam), with the lowest exam score contributing 20% and the other two exam scores each contributing 40% to the course grade. All grades out of 100 will correspond to the following scale: 0 < F< 60, 60 < D < 70, 70 < C < 80, 80 < B < 90, 90 < A < 100.

Exams: Exam 1: Thursday, September 24, 2026; Exam 2: Thursday, November 5; Exam 3: December 8, 2026 (5:30-6:50 pm in the classroom).

Information on Exams: Each exam will contain 30 questions (the first 15 are true/false questions and the remaining are multiple-choice questions with 4 options to choose from). No materials are allowed during the exam besides a pencil or a pen; blank sheets are provided; the answer sheet is provided and will be collected at the end of the exam. The coverage for each exam will be announced in class and will be posted here.

Sample Exam 1

Sample Exam 2

Sample Exam 3

Prerequisites: A grade of C or better in Math 2425 or concurrent enrollment.

Practice problems: (the solutions will not be collected for grading)

1.1: 3, 5, 11, 13, 15

1.2: 1, 3, 5, 7, 9, 11, 13, 17, 19, 21, 25, 27, 31, 35, 37, 39

1.4: 1, 3, 5, 7, 15

1.6: 1, 3, 5, 7, 9, 15, 17

1.8: 1, 3, 5, 7, 9, 11, 13, 15

1.9: 1, 3, 5, 7, 11, 13, 15

2.1: 1, 3, 5, 9, 11, 13, 15, 17, 19, 23, 27

2.2: 1, 3, 7, 9, 11, 13, 15, 17, 19, 27, 31, 33, 37, 39, 43

2.3: 1, 3, 7, 9, 11, 13, 15, 17

2.4: 1, 3, 5, 9, 11, 15, 19, 21, 25

2.5: 1, 3, 5, 7, 13, 17, 21, 33, 37

2.6: 1, 3, 7, 9, 11, 15

3.1: 9, 11, 13, 17, 19, 21

3.2: 1, 3, 9, 15, 19, 21, 23, 25, 27, 29, 37, 39

3.3: 1, 3, 5, 7, 9, 11, 15, 41

4.1: 1, 3

4.2: 1, 3, 5, 7, 9, 11

4.3: 3, 5, 7, 9, 11, 13, 17, 19, 21

4.4: 1, 3, 5, 7, 11, 13, 17, 21, 23, 25

4.5: 1, 3, 5, 7, 13, 15, 19, 21, 29, 31

4.6: 3, 5, 7, 13, 15, 17, 21, 23

6.1: 1, 3, 5, 7, 9, 11, 13

7.1: 1, 3, 9, 11, 13, 15, 17, 21, 23, 25

8.1: 1, 3, 5, 7, 9

8.2: 1, 3, 17, 21, 23, 27, 31, 33, 35, 37

8.3: 5, 7, 9, 13, 17, 19, 21, 23, 29, 31, 33

Information on Exam 1: The first exam will be given in class during the class period on Thursday, September 24, 2026. The exam will contain 30 questions (the first 15 are true/false questions and the remaining are multiple-choice questions with 4 options to choose from). No materials are allowed during the exam besides a pencil or a pen; blank sheets are provided; the answer sheet is provided and will be collected at the end of the exam. The coverage will contain Sections 1.1, 1.2, 1.4, 1.6, 1.8, and 1.9 in the textbook, and the following topics are emphasized:

ODE: general solution, particular solution, explicit solution, implicit solution; arbitrary constants, initial conditions
First-order ODEs: linear, separable, exact, homogeneous, Bernoulli; methods to solve such ODEs
First-order linear ODEs: standard form, an integrating factor
Differential, exact differential, total differential; criteria for exactness
Substitution for Bernoulli equations, substitution for homogeneous equations
Linear ODEs: nonhomogeneous term, homogeneous linear ODE, superposition principle, general solution, particular solution
Linear nth-order ODEs: with constant coefficients, Cauchy-Euler equations; functions satisfying such homogeneous linear ODEs
Applications: LRC circuits, mass-spring systems

Exam 1 Answers (corrected Answer B to Question 30)

Information on Exam 2: The exam will contain 30 questions (the first 15 are true/false questions and the remaining are multiple-choice questions with 4 options to choose from). No materials are allowed during the exam besides a pencil or a pen; blank sheets are provided; the answer sheet is provided and will be collected at the end of the exam. The coverage will contain Sections 2.1-2.6, 3.1-3.3, and 4.1-4.6 in the textbook, and the following topics are emphasized:

solving linear systems, Cramer's rule
reduced row echelon form, elementary row operations
matrices, rows and columns, matrix size
matrix algebra (adding matrices, multiplying matrices, multiplying a matrix with a scalar)
square matrix, identity matrix, diagonal matrix, upper and lower triangular matrices
square of a matrix, cube of a matrix
trace of a matrix, transpose of a matrix, inverse of a matrix, null space of a matrix
permutation tensor
determinant, properties of determinants
vectors, vector space, subspace
basis for a vector space, dimension of a vector space
linear dependence/independence of a set of vectors
linear combination of vectors
vector space of m×n matrices
vector space of polynomials of degree n or less

solving linear systems, Cramer's rule
reduced row echelon form, elementary row operations
matrices, rows and columns, matrix size
matrix algebra (adding matrices, multiplying matrices, multiplying a matrix with a scalar)
square matrix, identity matrix, diagonal matrix, upper and lower triangular matrices
square of a matrix, cube of a matrix
trace of a matrix, transpose of a matrix, inverse of a matrix, null space of a matrix
permutation tensor
determinant, properties of determinants
vectors, vector space, subspace
basis for a vector space, dimension of a vector space
linear dependence/independence of a set of vectors
linear combination of vectors
vector space of m×n matrices
vector space of polynomials of degree n or less

Tuncay Aktosun aktosun@uta.edu
Last modified: September 30, 2026