University of Arizona | Department of Mathematics | Ildar Gabitov | MATH 322 | Syllabus

MATH 322
Mathematical Analysis for Engineers

Classroom:  PAS 314, TR, 9:30–10:45am
Instructor:  Ildar Gabitov
office: MATH 722
e-mail: gabitov[at]math.arizona.edu
phone: ☎ (520) 626-8853
Office Hours:  Tuesday 4:00–5:00pm, Wednesday 2:00–3:00pm, Thursday 4:00–5:00pm (subject to change) and by appointment
Text: Erwin Kreyszig,
Advanced Engineering Mathematics
10th ed.

Course description: Complex variables, linear algebra, Fourier series, partial differential equations. Examples will have a strong emphasis on optics, photonics, and engineering.

Course Objectives and Expected Learning Outcomes: This course is designed to prepare students for the study of a wide class of linear systems arising in engineering applications. The mathematical methods covered by this course are the basis for the analysis of a broad range of engineering problems including stability, dynamics and thermodynamics of systems, signal processing, etc. The proposed material develops the ability to understand, critically evaluate and use mathematical models and methods of modern engineering. Students who successfully complete the course should


Homework: Will be assigned regularly. Homeworks will be posted on WileyPlus® course ID is 749882, graded by computer. Homework is an essential component of the course, whether it is assigned for grading or not. Written homework could be turned in in 1) class; 2) MATH 108 room (before 4:30pm); 3) MATH 722 office (slide it under the door if I'm not there). All penalties for late homeworks are at the discretion of your instructor. They could depend on how late it is, whether solutions are discussed in class before or not, etc. It is allowed to work together on homework problems, but the work you turn in must be your own. Will be assigned regularly.


Grading: The total number of points available on tests, homework and quizes is 700 = 200(homeworks (90%) + quizes (10%)) + 3×100(midterms) + 200(final exam). Three in-class midterms are scheduled for Tu, Feb 18, for Th, Mar 19, and Th, Apr 23. The final exam is on Thu, May 12, 8:00am–10:00am (Sec 003) in the same room where the class met all semester. The University's Exam regulations for final exam week will be strictly followed, in particular those regarding students with multiple exams on a single day. Grades will be no lower than set forth in the following table:

630 ≤ points ≤ 700 90% to 100%A
560 ≤ points ≤ 629 80% to 90%B
490 ≤ points ≤ 559 70% to 80%C
420 ≤ points ≤ 489 60% to 70%D
0 ≤ points ≤ 419   0% to 60%E

Withdrawing from the course: You can drop the course without W grade by Tue, Feb 5. If can withdraw from the course by Tue, Mar 26. The University allows withdraws after Tue, Mar 26, but only with the Dean's signature. Late withdraws will be dealt with on a case-by-case basis, and requests for late withdraw with a W without a valid reason may or may not be honored.

Incompletes: The grade of I will be awarded if all of the following conditions are met:
  1. The student has completed all but a small portion of the required work.
  2. The student has scored at least 50% on the work completed.
  3. The student has a valid reason for not completing the course on time.
  4. The student agrees to make up the material in a short period of time.
  5. The student asks for the incomplete before grades are due, 48 hours after the final exam.

Grade Policies of the University of Arizona.


Scheduled Topics/Activities by Week

Th Jan 16Complex Numbers, Polar Form, Powers and Roots,13.1, 13.2;
Tu Jan 21Powers and Roots, Derivative, Analytic Function13.2, 13.3;
Th Jan 23Cauchy–Riemann Equations, Exponential Function13.4, 13.5;
Tu Jan 28Trig./Hyperb. Functions, Logarithm13.6, 13.7; WHW1
Th Jan 30Matrices, Vectors: operations7.1, 7.2;
Tu Feb 04Linear Systems, Linear Independ., Rank, Vector Space7.3, 7.4; HW2
Th Feb 06Solutions, Existence, Uniqueness,7.4, 7.5;
Tu Feb 11Determinants, inverse matrix7.6, 7.8; HW3
Th Feb 13Vector Spaces, Linear Transformations,7.8, 7.9;
Tu Feb 18 Matrix Eigenvalues and Eigenvectors8.1, 8.2; HW4
Th Feb 20Midterm 1
Tu Feb 25Review, Eigenbasis similarity transformation8.4; HW5
Th Feb 27Diagonalization, 2-nd order Homogen. Lin. ODEs (HLODEs),8.4,2.2;
Tu Mar 03HLODEs with const. coef., Nonhomogen. ODEs2.2, 2.7; HW6
Th Mar 05Higher order HLODEs with const. coef, systems of ODEs3.2, 4.1;
Tu Mar 10Spring recess - no classes
Th Mar 12Spring recess - no classes
Tu Mar 17Theory of Systems of ODEs,4.1, 4.2; HW7
Th Mar 19Midterm 2
Tu Mar 24Review, Constant-Coefficient Systems,4.2, 4.3;
Th Mar 26Discussion of WHW6, Nonhomogen. Lin. Syst. of ODEs4.6;
Tu Mar 31Fourier Series, properties11.1, 11.2; QZ5
Th Apr 02Approximation by Trigonometric Polynomials, ζ(2)=π2/6,11.4;
Tu Apr 07Fourier Integral and Fourier transform11.7, 11.9; HW8
Th Apr 09PDEs, Vibrating String, Wave Equation,12.1, 12.2; QZ6
Tu Apr 14Solution by Separating Variables,12.2, 12.3; WHW9
Th Apr 16Solution by Separating Variables 12.3, 12.5; QZ7
Tu Apr 21Solution by Separating Variables, examples12.5, 12.6; HW10
Th Apr 23 Solution by Fourier Integrals and Transforms, 12.6, 12.7;
Tu Apr 28Review of class materialsHW11
Th Apr 30 Midterm 3
Tu May 05Review of class materials
Tu May 12Final Exam 08:00&bdash;10:00am (Sec 003)


Accessibility and accommodations: It is the University's goal that learning experiences be as accessible as possible. If you anticipate or experience physical or academic barriers based on disability, please let me know immediately so that we can discuss options. You are also welcome to contact Disability Resources,  (520) 621-3268, to establish reasonable accommodations.

Please be aware that the accessible table and chairs in this room should remain available for students who find that standard classroom seating is not usable.


Attendance and Protocol: You are expected to be familiar with the University Class Attendance policy. It is your responsibility to stay informed of any announcements, syllabus adjustments, or policy changes.

The UA policy regarding absences for any sincerely held religious belief, observance or practice will be accommodated where reasonable. Absences pre-approved by the UA Dean of Students (or Dean's designee) will be honored.

You are expected to behave in accordance with the Student Code of Conduct and the Code of Academic Integrity. The University is committed to creating and maintaining an environment free of discrimination.


The information contained in this syllabus, other than the grade and absence policies, may be subject to change with reasonable advance notice, as deemed appropriate by the instructor.