pcazeaux@ku.edu
Office: 509 Snow Hall
(785) 864-7116

Paul Cazeaux
405 Snow Hall
1460 Jayhawk Blvd.
University of Kansas
Lawrence, KS 66045, USA

pcazeaux@ku.edu
Office: 509 Snow Hall
(785) 864-7116

Paul Cazeaux
405 Snow Hall
1460 Jayhawk Blvd.
University of Kansas
Lawrence, KS 66045, USA

Teaching



Spring 2019: KU MATH 320, Elementary Differential Equations

This is an introductory course in ordinary differential equations. These are equations linking functions and their derivatives in various ways.

Differential equations are of tremendous importance in many applications, as they model a wide range of phenomena happening around us every day: from fluid dynamics (water waves, aerodynamics) to the motion of atoms (protein folding), from population dynamics to economics or finance (option pricing), differential equations are everywhere in science and engineering.

Syllabus
Tentative schedule
Student Conduct Code


Fall 2018: KU MATH 220, Applied Differential Equations

This was a third semester course of calculus concerning applied differential equations.

Course notes:

Week I: Introduction (Definitions, Classification, Direction Fields)
Week II: First-Order ODEs (Integrating Factors, Separable Equations)
Week III: First-Order ODEs (Salt Tank Problems, Newton's Law of Cooling)
Week IV: First-Order ODEs (Autonomous equations, Existence and Uniqueness Theorem)
Week V: First-Order ODEs (Exact Equations, Conclusion) and Second-Order ODEs (Introduction, Constant Coefficients)
Week VI: Second-Order ODEs (Linear Homogeneous Equations, Wronskian)
Week VII: Second-Order ODEs (Complex Roots of the Characteristic Equation)
Week VIII: Second-Order ODEs (Repeated Roots, Reduction of Order, Undetermined Coefficients)
Week IX: Second-Order ODEs (Mechanical and Electrical Vibrations, Forced Vibrations)
Week X-XI: Systems of First-Order ODEs (Introduction, Vectors and Matrices, Basic Theory)

Student Conduct Code

Spring 2018: KU MATH 647, Applied Partial Differential Equations

This was an advanced undergraduate course of calculus concerning applied partial differential equations.
Syllabus
Student Conduct Code

Fall 2017: KU MATH 220, Applied Differential Equations

This was a third semester course of calculus concerning applied differential equations.

Course notes:

Week I: Introduction (Definitions, Classification, Direction Fields)

Student Conduct Code

Fall 2016: MATH 2373 CSE, Linear Algebra and Differential Equations at the University of Minnesota

This was a third semester of calculus concerning linear algebra and differential equations, pitched to budding engineers.

Course notes:

Week I-II: Matrices (Definition, Gaussian elimination, Determinants, Inverse)
Week III-: ODEs (First order, tangents)
Week VI: ODEs and Linear Algebra, A. Binder (Characteristic polynomial, linear independence and combinations)
Week VII-VIII: Eigenvalues, eigenvectors, diagonalization (Definition, characteristic polynomial, practical method to compute the eigenvalues and eigenvectors, diagonalization)
Week VIII: Note on Matrix Powers by Prof. Mori

Student Conduct Code
General Policy Statements for Syllabi

2014: Supervision of semester projects at EPFL

  • S. Amraoui, an exchange student from Polytech Nice studying at the EPF Lausanne (4th year, Master's level), a mathematics major. During the spring of 2014, she conducted a semester project under my supervision on the subject Topological Optimization for Conductive Problems, using gradient descent and Newton methods as well as the Solid Isotropic Material with Penalization (SIMP) method.

  • J. Droxler, a Master's student, mathematics major at EPF Lausanne. During the spring of 2014, he conducted a semester project under my supervision on the subject Topological Optimization for Conductive Problems, using global optimization methods such as simulated annealing and genetic algorithms. He is currently continuing as a MSc student in the MCSS Chair at EPFL.