Online tutoring for Linear Algebra, Multivariable Calculus and Differential Equations – by a PhD Mathematician.

Specialized & flexible online tutoring for students & professionals in STEM fields.

Structured maths courses designed for Engineering, Data science (including AI), Economics, Biology and more.

High-quality LaTeX notes, study guides and problem sets with well structured math explanations.

Certification upon completion, verifying your mastery of advanced mathematics.
Welcome to UniMaths Academy
At UniMaths Academy, we believe that advanced mathematics is the foundation of innovation, technology, and scientific breakthroughs. Our goal is to equip engineers, scientists, and innovators with the mathematical tools they need to tackle complex challenges, optimize solutions, and drive progress across industries.
About UniMaths Academy
Led by Dr. Hannelie Brooks, a PhD mathematician, UniMaths Academy offers expert-led tutoring in Linear Algebra, Multivariable Calculus, Differential Equations, and other advanced mathematics topics.
Whether you’re a university student preparing for rigorous exams, a data scientist mastering optimization, or an engineer applying mathematical models in real-world applications, our structured learning programs provide clarity, depth, and practical insights.
Learn, Apply, Innovate
Mathematics for the future of technology and discovery.
Our Courses


Advanced Linear Algebra for Data Science, Machine Learning, and Engineering
- Matrix operations and vector spaces
- Eigenvalues, eigenvectors, and diagonalization
- Singular Value Decomposition (SVD) and Principal Component Analysis (PCA)
- Linear transformations and real-world applications
For students in engineering, computer science, data science, and physics who want to build a rock-solid foundation in vector spaces, matrices, and linear transformations.
Learn the language of modern science, machine learning, and quantum theory.
Your learning, your pace – choose what works best for you!
At Advanced UniMath Academy, flexibility is key. Our structured courses are designed to fit your schedule while maximizing mastery of complex mathematical concepts.
Choose Your Ideal Learning Format:
- 60-minute express sessions – Perfect for focused learning on specific topics.
- 90-minute deep-dive lessons – Ideal for tackling complex theories and problem-solving strategies.
- 120-minute intensive masterclasses – Designed for advanced learners who need in-depth coaching.
Convenient Scheduling: Choose from weekday, evening, and weekend sessions to fit your routine.
What’s Included in Every Session?
- Expert-Led Teaching – Learn directly from an experienced mathematician.
- LaTeX-Based Study Notes – Professionally formatted materials for deep
comprehension. - Interactive Problem-Solving – Engage in live discussions, exercises, and
applications. - Certification Upon Completion – Validate your mastery with an official
UniMath Academy certificate.
Flexible bookings-structured for your success! Ready to start? Choose your session and book today!
Module 1: Foundations of Linear Algebra
- Vector Spaces & Subspaces
• Basis, dimension, and linear independence.
• Applications in computational mathematics. - Matrix Operations
• Matrix addition, multiplication, and inversion.
• Special matrices: symmetric, diagonalizable, and orthogonal matrices. - Linear Transformations
• Geometric interpretations and real-world applications.
Module 2: Eigenvalues, Eigenvectors, and Diagonalization
- Eigenvalue Decomposition
• Definition and importance in stability analysis.
• Diagonalizing a matrix step-by-step. - Applications
• Markov chains, physics simulations, and quantum mechanics.
Module 3: Singular Value Decomposition (SVD)
- Understanding SVD
• Matrix decomposition.
• Interpreting singular values in feature reduction. - Applications
• Principal Component Analysis (PCA).
• Noise reduction in images and data compression.
Module 4: Inner Products and Norms
- Inner Product Spaces
• Gram-Schmidt Orthogonalization. - Vector Norms & Distance Metrics
• Frobenius and spectral norms. - Applications
• Optimization and machine learning loss functions.
Module 5: Advanced Matrix Factorization
- LU, QR, and Cholesky Factorization
• Direct methods for solving linear systems. - Applications
• Scientific computing and numerical stability.
Advanced Multivariable Calculus for Optimization & Applied Sciences
- Partial derivatives and gradients
- Vector calculus and integral theorems (Stokes, Gauss)
- Constrained optimization (Lagrange multipliers)
- Applications in finance, optimization, and engineering
Perfect for STEM learners tackling problems in physics, engineering, and economics, where functions depend on more than one variable.
Gain the tools to explore 3D space, gradients, optimization, and vector fields.
Your learning, your pace – choose what works best for you!
At Advanced UniMath Academy, flexibility is key. Our structured courses are designed to fit your schedule while maximizing mastery of complex mathematical concepts.
Choose Your Ideal Learning Format:
- 60-minute express sessions – Perfect for focused learning on specific topics.
- 90-minute deep-dive lessons – Ideal for tackling complex theories and problem-solving strategies.
- 120-minute intensive masterclasses – Designed for advanced learners who need in-depth coaching.
Convenient Scheduling: Choose from weekday, evening, and weekend sessions to fit your routine.
What’s Included in Every Session?
- Expert-Led Teaching – Learn directly from an experienced mathematician.
- LaTeX-Based Study Notes – Professionally formatted materials for deep
comprehension. - Interactive Problem-Solving – Engage in live discussions, exercises, and
applications. - Certification Upon Completion – Validate your mastery with an official
UniMath Academy certificate.
Flexible bookings-structured for your success! Ready to start? Choose your session and book today!
Module 1: Fundamentals of Multivariable Calculus
- Partial Derivatives and the Gradient
• Definition of partial derivatives.
• The gradient vector and directional derivatives.
• Applications in machine learning and optimization. - Tangent Planes and Linear Approximations
• Multivariable Taylor series expansion.
• Application in error estimation and predictive modeling. - Linear Transformations
• Geometric interpretations and real-world applications.
Module 2: Vector Calculus and Integral Theorems
- Divergence, Curl, and Vector Fields
• Physical interpretation of divergence and curl.
• Applications in fluid dynamics and electromagnetism. - Line and Surface Integrals
• Green’s Theorem, Stokes’ Theorem, and Gauss’ Divergence Theorem.
• Case studies in engineering and economic modeling.
Module 3: Constrained Optimization and Lagrange Multipliers
- Optimization in Higher Dimensions
• Finding local extrema for multivariable functions.
• Hessian matrix and convexity analysis. - Lagrange Multipliers for Constrained Optimization
• Applications in finance, economics, and Al model optimization.
• Solving resource allocation problems.




Advanced Differential Equations for Scientific and Computational Applications
Topics Covered:- Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs)
- Fourier and Laplace transforms
- Numerical methods (Finite Difference, Finite Element)
Designed for learners in applied math, engineering, biology, and finance who need to model change and real-world dynamics over time.
Bring life to equations-whether you’re studying circuits, epidemics, or motion.
Your learning, your pace – choose what works best for you!
At Advanced UniMath Academy, flexibility is key. Our structured courses are designed to fit your schedule while maximizing mastery of complex mathematical concepts.
Choose Your Ideal Learning Format:
- 60-minute express sessions – Perfect for focused learning on specific topics.
- 90-minute deep-dive lessons – Ideal for tackling complex theories and problem-solving strategies.
- 120-minute intensive masterclasses – Designed for advanced learners who need in-depth coaching.
Convenient Scheduling: Choose from weekday, evening, and weekend sessions to fit your routine.
What’s Included in Every Session?
- Expert-Led Teaching – Learn directly from an experienced mathematician.
- LaTeX-Based Study Notes – Professionally formatted materials for deep
comprehension. - Interactive Problem-Solving – Engage in live discussions, exercises, and
applications. - Certification Upon Completion – Validate your mastery with an official
UniMath Academy certificate.
Flexible bookings-structured for your success! Ready to start? Choose your session and book today!
Module 1: Fundamentals of Differential Equations
- Classification of Differential Equations
• ODES vs. PDES
• Linear vs. Nonlinear equations - First-Order Differential Equations
• Separable equations
• Exact and integrating factor methods
• Applications in population dynamics - Second-Order Differential Equations
• Homogeneous and non-homogeneous cases
• Method of undetermined coefficients
• Real-world uses: mechanical vibrations, electrical circuits
Module 2: Partial Differential Equations (PDEs)
- Wave, Heat, and Laplace Equations
• Boundary value problems
• Fourier series solutions
• Applications in signal processing and thermodynamics - Numerical Methods for PDEs
• Finite Difference and Finite Element Methods
Module 3: Fourier and Laplace Transforms in Differential Equations
- Transform Methods for Solving ODEs & PDEs
At UniMaths Academy, we don’t just teach math – we unlock its power for real-world applications in data science, engineering, economics, and more.
Pricing Table in ZAR
Invest in world-class instruction, structured materials, and a transformative learning experience.
Individual Lessons
(per session)
R600
Perfect for quick concept reviews or focused guidance.
R750
Perfect for deep topic exploration with guided practice
R900
Perfect for comprehensive sessions with extended support
Course Packages
(Lessons + Materials)
R6,400
8 × 90-min sessions (4 wks)
R8,000
10 x 90-min sessions (5 wks)
R9,600
12 × 90-min sessions (6 wks)
Full Course Bundle
Get all 3 courses (30 sessions) as a bundle: R21,000
(Save R3,000!)
Premium Coaching
Packages
R3,800
4 x 2-hour private sessions
R2,700
3 x 2-hour intensive prep sessions in 1 week
From R850/hour
Hourly coaching for thesis/academic projects
All sessions include LaTeX-based notes & personalized study insights.
Please contact us if you require training in any alternative maths module other than the courses listed above.
We can tailor a program to suit your needs.
Join UniMaths in 3 Simple Steps
1
Choose a Course
Choose between a course in Linear Algebra, Calculus, Differential Equations or request a bespoke course based on your requirements.
2
Schedule a Free Consultation
Lets discuss your learning goals and create a structured plan tailored to your needs.
3
Start Learning
Begin your journey to mastering Linear Algebra, Calculus and beyond with expert guidance.
Ready to elevate your Mathematical skills?
Lets discuss your goals in a free consultation.
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