M 427K. Advanced Calculus for Applications I-Engineering Honors.
Unique #54285, QR Flag, Spring 2015
Prof. Todd Arbogast
Office: RLM 11.162, Phone: 512-471-0166
Office hours: MTWTh 8:30-9:30 a.m.
Mr. Roman Fayvisovich
Office: RLM 11.152, Phone: 512-471-1684
Office hours: T 2:00-4:00 p.m.
M 408D, M 408L, or M 408S with a grade of at least C-.
TTh 11:00-12:30 p.m. in
CPE 2.214 (lecture)
and MW 11:00-12:00 noon in
BEL 328 (discussion).
Attendance is required at all class meetings.
Differential Equations and their Applications, 4th ed., by M. Braun, Springer, 1993.
Class Web Site
We will use the University's CLIPS and
Canvas web sites. Please check that your scores are recorded
correctly in Canvas.
We plan to cover the following textbook chapters and sections.
Chapter 1. First-order differential equations (supplement with direction fields) [4 hours]
1.2 First-order linear differential equations
1.4 Separable equations
1.9 Exact equations, and why we cannot solve very many differential equations
1.10 The existence-uniqueness theorem; Picard iteration
Chapter 2. Second-order linear differential equations [12 hours]
2.1 Algebraic properties of solutions
2.2 Linear equations with constant coefficients
2.2.1 Complex roots
2.2.2 Equal roots; reduction of order
2.3 The nonhomogeneous equation
2.4 The method of variation of parameters
2.5 The method of judicious guessing
2.6 Mechanical vibrations
2.8 Series solutions
2.8.1 Singular points, Euler equations
2.8.2 Regular singular points, the method of Frobenius
Chapter 3. Systems of differential equations (with supplementary material added) [14 hours]
3.1 Algebraic properties of solutions of linear systems
3.A Matrix multiplication as linear combinations of columns
3.2 Vector spaces
3.B Vectors as arrows in Rn and a geometric meaning of operations
3.C Complete solution system of linear equations (RREF)
3.D Null and column spaces of a matrix
3.3 Dimension of a vector space
3.4 Applications of linear algebra to differential equations
3.5 The theory of determinants
3.6 Solutions of simultaneous linear equations
3.7 Linear transformations
3.8 The eigenvalue-eigenvector method of finding solutions
3.9 Complex roots
3.10 Equal roots
3.11 Fundamental matrix solutions; eAt
Chapter 4. Qualitative theory of differential equations [3 hours]
4.2 Stability of linear systems
4.4 The phase-plane
4.7 Phase portraits of linear systems
Chapter 5. Separation of variables and Fourier series [8 hours]
5.1 Two point boundary-value problems
5.2 Introduction to partial differential equations
5.3 The heat equation; separation of variables
5.4 Fourier series
5.5 Even and odd functions
5.6 Return to the heat equation
Chapter 6. Sturm-Liouville boundary value problems [optional 3 hours, if time permits]
6.2 Inner product spaces
6.3 Orthogonal bases, Hermitian operators
6.4 Sturm-Liouville theory
A computer account on the Mathematics Department network can be obtained in the Undergraduate
Computer Lab, RLM 7.122.
Homework and Quizzes
Homework will be assigned weekly, with only a portion to be fully graded, and due generally on
Wednesdays. It is acceptable for groups of students to help each other with the homework exercises;
however, each student must write up his or her own work. Late homework will not be accepted for
credit (unless there is a valid health issue), and homework must be turned in during class. The
textbook has answers to the odd numbered exercises. Quizzes will be given periodically on Mondays
or Wednesdays in the discussion sessions.
Three exams will be given on Wednesdays, February 11, March 11, and April 15. A comprehensive final
exam will be given during finals week on Friday, May 15, 2:00-5:00 p.m.
Grades on the three midterm exams will be scaled to count 20 points each. For the homework and
quizzes, the two lowest scores will be dropped, and the result will count as 20 points. The final
exam will count 40 points. The final grade on the letter plus/minus scale will be determined out of
100 points by dropping the lowest midterm test grade, or by weighting the final test grade by 1/2
(i.e., count it as 20 points). The homework and quiz score will count in the final grade.
Student Honor Code
"As a student of The University of Texas at Austin, I shall abide by the core values of the
University and uphold academic integrity."
Code of Conduct
The core values of The University of Texas at Austin are learning, discovery, freedom, leadership,
individual opportunity, and responsibility. Each member of the university is expected to uphold
these values through integrity, honesty, trust, fairness, and respect toward peers and community.
Students with Disabilities
The University provides upon request appropriate academic accommodations for qualified students with
disabilities. Contact the Office of the Dean of Students at 512-471-6259, 512-471-4641 TTY, and
notify your instructor early in the semester.
Appropriate academic accommodation for major religious holidays is provided upon request.
Emergency Classroom Evacuation
Occupants of University of Texas buildings are required to evacuate when a fire alarm is activated.
Alarm activation or announcement requires exiting and assembling outside. Familiarize yourself with
all exit doors of each classroom and building you may occupy. Remember that the nearest exit door
may not be the one you used when entering the building. Do not re-enter a building unless given
instructions by the Austin Fire Department, the University Police Department, or the Fire Prevention