In this course we had an overview of Non-Newtonian Fluid Dynamics, and discussed two approaches for building constitutive models for complex fluids: continuum modeling and kinetic-microstructural modeling. We also learned about “multiphase complex fluids” and “numerical models and algorithms for computing complex fluid flows”. Through this course, I got a deep understanding of the fact that how we can apply different mathematical models for certain types of physical problems.
Deriving a theorem in Fluid Dynamics which explains how boundary conditions would affect behavior of Newtonian fluids and obtaining numerical results using accurate numerical schemes.
Numerical Schemes Used in Thesis:
Spectral Methods, Compact finite differences (The most accurate scheme applicable to the problem)
Advanced Mathematical Techniques Used for Modeling the Problem:
Dynamical Systems, Linear Algebra, Complex and Real Analysis, Inversion Theory and Conformal Mapping, Topology.
Math Thesis Link
My Tutoring Style
The Organized, Patient Tutor: What I’ve heard multiple times from my students is “you are so organized and patient” and I believe those are the most important and necessary factors for any teacher. During my tutoring sessions, I listen carefully to my students to understand the parts that they are struggling with and after that we carefully go through those concepts and I’ll teach them their weaknesses until we make sure that they are no longer strange with those concepts.
Teaching Through Examples: I usually ask my students which way they prefer to study and most of my students prefer to study through problems of their assignments, specially online webwork assignments. So what we’ll do is we would go over their webwork assignments to see which problems they haven’t solved properly or even the problems that they have tried to solve it a couple of times and see which part they are struggling in it. After finding their weaknesses in those examples, we would solve a couple of similar problems either from their webwork problems or from the suggested problems of their textbook or old UBC exams to make sure they are pretty comfortable with the concepts that they were struggling with.
Conceptual Teaching: Some of my students prefer to learn through their textbook. This particularly happen for the conceptual courses where they are struggling with learning concepts of the course with themselves. Linear algebra and more advanced math courses and physics course are among them. In that case, we start reviewing the sections of the course where my students need helps in it and after teaching them the concepts, we solve a couple of examples from their textbooks, webwork problems, old UBC exams or other sources.
Crash Course Tutoring: Usually close to midterms or finals, some students ask me to review the entire course in a few sessions. What I’ll do for those students is I would prepare a summary of the important points of the course and we quickly go over all the materials of the course and at the end, in the areas that they feel they need more help in it, we would solve a couple of more examples to make sure they are totally ready for their exam.
Solving Old UBC Exams: Finally when it’s pretty close to the exam date, my students ask me to have a session to solve old UBC exams and in that case we solve some sample examples from old UBC mid/final exams.
My UBC Tutoring Experience
Tutoring of the following first year UBC Math courses:
- Math 001 Pre-Calculus
- Math 100 Differential Calculus
- Math 101 Integral Calculus
- Math 102 Differential Calculus
- Math 103 Integral Calculus
- Math 104 Differential Calculus
- Math 105 Integral Calculus
- Math 110 Differential Calculus
- Math 121 Integral Calculus
- Math 152 Linear Systems
- Math 180 Differential Calculus
- Math 184 Differential Calculus
Tutoring of the following first year UBC Physics courses:
- Physics 101 Energy and Waves
- Physics 118 Electricity, Light and Radiation
- Physics 158 Introductory Physics for Engineers II
- Physics 170 Mechanics I
Tutoring of the following second year UBC Math courses:
- Math 215 Elementary Differential Equations
- Math 220 Mathematical Proof
- Math 221 Matrix Algebra
- Math 255 Ordinary Differential Equations
- Math 256 Differential Equation
- Math 257 Partial Differential Equation
- FRST 231 Introduction to Biometrics and Business Statistics
Tutoring of the following third year UBC Math courses:
- Math 300 Complex Analysis
- Math 312 Introduction to Number Theory
- Math 316 Elementary Differential Equation II
- Math 340 Introduction to Linear Programming
My Teaching Experiences at UBC
- Teaching Assistant of Math 358 Engineering Analysis
- Teaching Assistant of Math 317 Calculus IV
- Teaching Assistant of Math 215 Elementary Differential Equation
- Teaching Assistant of Math 102 Differential Calculus
- Teaching Assistant of Pre-Calculus Math (Supervisor of Labs)
- Instructor at Math Learning Center of UBC Mathematics Department
I started my undergraduate studies in Mechanical Engineering. My thesis there was about “Vibration Analysis Of Functionally Graded Material (FGM) Beams Using The Third Order Shear Deformation Theory”, which was a problem in Elasticity and Shear Deformation Theory . You can find a summary of my thesis here.
After that due to my old passion in mathematics, I started another bachelor in Mathematics with a focus on Pure Mathematics. In my thesis, I was working on Banach Spaces and properties of a sub-space of it called “Infinite Dimensional Banach Spaces” which is a branch of Functional Analysis.
I started my grad studies in the Harmonic Analysis Group of the Mathematics Department Of UBC where I could find answer of many of my questions related to my research in Banach Space Theory. After working there for 9 months, I continued my study in the Fluid Mechanics Lab of the Institute Of Applied Mathematics. My thesis was about “Effect of Geometry On The Behavior Of Steady Newtonian Fluid In a Multiply Connected Domain” which was a problem in Chaotic Advection. You can find a copy of my thesis here.