1st lesson free
Sarah
- Rate $70
- Response 1h
$70/hr
Contact
1st lesson free
- Maths
- Trigonometry
- Arithmetic
- Geometry
- Statistics
Mathematics with 13 years of experience, covering partial differential equations, fluid dynamics, wave propagation, and applied analysis for research and engineering.
- Maths
- Trigonometry
- Arithmetic
- Geometry
- Statistics
Lesson location
About Sarah
Mathematics tutor with 13 years of experience teaching advanced high school and college students. Have taught around 350 students, helping many prepare for competitive exams, research projects, and graduate-level applied mathematics. My teaching philosophy is built on applied analysis and physical modeling. I focus on building deep understanding of PDEs and fluid dynamics while developing research and computational skills. Notable achievements include helping over 50 students secure top ranks in national mathematics competitions and guiding several to publish research papers. I create a supportive, intellectually challenging environment where questions are celebrated. I keep detailed records of each session to track progress and adjust methods as needed. Whether you are preparing for competitive exams or pursuing research, I tailor every lesson to your specific goals.
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About the lesson
- Primary
- High School
- NCEA Level 1
- +5
levels :
Primary
High School
NCEA Level 1
NCEA Level 2
NCEA Level 3
Adult education
Masters
Doctorate
- English
All languages in which the lesson is available :
English
My teaching approach for Mathematics and related subjects is built on applied analysis, partial differential equations, and physical modelling. I connect PDEs to fluid dynamics, acoustics, and electromagnetism, so you understand how mathematics describes continuous systems. We break down topics like elliptic, parabolic, and hyperbolic PDEs, potential flow, shock waves, and boundary layers into clear, methodical frameworks. I encourage creative thinking by asking you to derive models and solve real-world problems. Motivation comes from setting research-style goals and celebrating each applied solution. Integrity means I give honest feedback, never accept hand-waving, and always adapt to your learning style. For Mathematics, we cover partial differential equations (classification, characteristics, separation of variables, transforms, Green's functions), fluid dynamics (Navier-Stokes, Euler equations, potential theory, vorticity, turbulence), wave propagation (acoustics, elastic waves, electromagnetic waves), and applied analysis (asymptotic methods, perturbation theory, variational methods). We also work on numerical solutions (FDM, FEM), data analysis, and scientific writing. I also teach related subjects that support your math mastery: Physics for Math – continuum mechanics, thermodynamics, and electrodynamics. Engineering – fluid mechanics, aerodynamics, and structural mechanics. Computer Science – scientific computing and simulations. In every lesson, I use case studies from engineering and geophysics and my own students. For example, I show how one student mastered potential flow using a simple stream function approach, then we apply that to your current problems. I share stories of students who improved by solving PDE problems daily. My sessions are interactive and research-driven. We derive equations, solve problems, run numerical simulations, and discuss current research. I assign homework like solving a PDE analytically, deriving a model, or writing a mini-research report. I adapt my pace to your goals, whether for exams, research, or intellectual growth. I never compare you to others, only to your previous self. I keep detailed notes of each lesson so we always build on what we did before. My goal is to make you a confident, applied, and research-ready mathematician.
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Rates
Rate
- $70
Pack prices
- 5h: $350
- 10h: $700
online
- $70/h
free lessons
The first lesson with Sarah will allow you to get to know each other and discuss your needs for future lessons.
- 1hr
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