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  • Abstracts
    • Nonlinear Dynamics of Microbubbles in Tissue
    • Integrability, localisation and bifurcation of an elastic conducting rod in a uniform magnetic field
    • Artificial Intelligence in Therapeutic Ultrasound
    • Patient-Specific Modelling of Microwave Ablation
    • Factors for validation of measurement-based simulation
    • Assessing generalized multi-pool exchange tissue model MRI simulations for the modelling of an ultra-low field scanner
    • Transcostal High-Intensity Focused Ultrasound: Planning Treatment Delivery for Phased Arrays
    • A comparison between theory and experiment in thermal ablation of perfused livers
  • Experience
  • Talks
    • Nonlinear Dynamics of Microbubbles in Tissue
    • Mathematical Modelling and Numerical Simulation in Medicine
    • Integrability, localisation and bifurcation of an elastic conducting rod in a magnetic field
    • Artificial Intelligence in Therapeutic Ultrasound
    • Patient-Specific Modelling of Microwave Ablation
    • Factors for Validation of Measurement-Based Simulation
  • Projects
    • QuaLiPerF
    • EHMA
    • MAIBAI: Metrology for Image-Based AI
    • CUBDL: Challenge on Ultrasound Beamforming with Deep Learning
    • AEGEUS
    • Cosserat Theory
  • Opensources
    • k-wave-python
  • Blogs
    • Awesome List of Scientific Computing Resources
    • Annual Meeting of the Society for Thermal Medicine 2022
  • Slides
  • Courses
    • CTMS-MAT-13: Numerical Methods
      • Course Details
      • Taylor Series
      • Number Representations
      • Linear Equations
      • Nonlinear Equations
      • Interpolation
      • Integration
      • Finite Differences
      • Notebooks
        • Taylor Series
        • Number Representations
        • Linear Systems
        • Iterative Solvers
        • Nonlinear Solvers
        • Secant Method
        • Lagrange Polynomials
        • Least Squares
        • Numerical Integration
        • Runge Phenomena
        • ODE Solvers
      • Assignments
      • Exams
      • Slides
        • Slides
      • Course Notes
    • MDE-MET-01; Calculus and Linear Algebra for Graduate Students
      • Course Details
      • Vectors
      • Matrices
      • Linear Equations
      • Vector Spaces
      • Eigenvalues and PCA
      • Single Variable Calculus
      • Taylor Series
      • Multivariate Calculus
      • Notebooks
        • Gram-Schmidt Algorithm
        • Principal Component Analysis
        • Taylor Series
      • Assignments
      • Course Notes
    • CA-MATH-804: Numerical Analysis
      • Course Details
      • Principles
      • Iterative Methods
      • Interpolation
      • Integration
      • Finite Difference Methods
      • Finite Element Methods
      • Notebooks
        • Lagrange Interpolation
        • Lagrange Polynomials
        • Numerical Integration
        • One-Dimensional Finite Element Simulations
        • Two-Dimensional Finite Element Simulations
      • Assignments
      • Exam
      • Course Notes
    • MECH1010: Modelling and Analysis in Engineering I
    • Math6502: Mathematics for Engineers II
  • Courses
  • Experience
  • Homes
  • Papers in which I have been acknowledged
    • Numerical analysis of a wave equation for lossy media obeying a frequency power law
  • Publications
    • Visual ensemble analysis with deep learning prediction for studying the effect of tissue properties on radiofrequency ablation
    • Optimizing microwave ablation planning with the ablation success ratio
    • Numerical Modelling for Simulation and Planning of Focused Ultrasound Treatments
    • A novel concept of transperineal focused ultrasound transducer for prostate cancer local deep hyperthermia treatments
    • Three-dimensional assessment of vascular cooling effects on hepatic microwave ablation in a standardized ex vivo model
    • Studying the effect of tissue properties on radiofrequency ablation by visual simulation ensemble analysis
    • Pyroelectric ultrasound sensor model: directional response
    • Deep learning for ultrasound image formation: CUBDL evaluation framework and open datasets
    • Improving image quality of single plane wave ultrasound via deep learning based channel compounding
    • Building confidence in digital health through metrology
    • Numerical and experimental study of mechanisms involved in boiling histotripsy
    • Reducing uncertainties for spatial averaging at high frequencies
    • Dosimetry implications for correct ultrasound dose deposition: uncertainties in descriptors, planning and treatment delivery
    • Approximations for acoustically excited bubble cluster dynamics
    • The buckling of magneto-strictive Cosserat rods
    • Localisation of a twisted conducting rod in a uniform magnetic field: the Hamiltonian-Hopf-Hopf bifurcation
    • The effects of nonlinear wave propagation on the stability of inertial cavitation
    • Integrability, Localisation and Bifurcation of an Elastic Conducting Rod in a Uniform Magnetic Field
    • Spatial chaos of an extensible conducting rod in a uniform magnetic field
    • Integrability of a conducting elastic rod in a magnetic field
  • Software
    • Languages
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  • CTMS-MAT-13: Numerical Methods
    • Course Details
    • Taylor Series
    • Number Representations
    • Linear Equations
    • Nonlinear Equations
    • Interpolation
    • Integration
    • Finite Differences
    • Notebooks
      • Taylor Series
      • Number Representations
      • Linear Systems
      • Iterative Solvers
      • Nonlinear Solvers
      • Secant Method
      • Lagrange Polynomials
      • Least Squares
      • Numerical Integration
      • Runge Phenomena
      • ODE Solvers
    • Assignments
    • Exams
    • Slides
    • Course Notes
  • MDE-MET-01; Calculus and Linear Algebra for Graduate Students
    • Course Details
    • Vectors
    • Matrices
    • Linear Equations
    • Vector Spaces
    • Eigenvalues and PCA
    • Single Variable Calculus
    • Taylor Series
    • Multivariate Calculus
    • Notebooks
      • Gram-Schmidt Algorithm
      • Principal Component Analysis
      • Taylor Series
    • Assignments
    • Course Notes
  • CA-MATH-804: Numerical Analysis
    • Course Details
    • Principles
    • Iterative Methods
    • Interpolation
    • Integration
    • Finite Difference Methods
    • Finite Element Methods
    • Notebooks
      • Lagrange Interpolation
      • Lagrange Polynomials
      • Numerical Integration
      • One-Dimensional Finite Element Simulations
      • Two-Dimensional Finite Element Simulations
    • Assignments
    • Exam
    • Course Notes
  • MECH1010: Modelling and Analysis in Engineering I
  • Math6502: Mathematics for Engineers II
Courses
CTMS-MAT-13: Numerical Methods
Slides

Numerical Methods: Slides

Slides

Slides for the lectures, as pdfs, can be found on this page.

Note

Currently a work in progress.

  • Taylor Series
  • Number Representations
  • Linear Equations
  • Nonlinear Equations
  • Interpolation
  • Integration
  • Ordinary Differential Equations

Changelog

All changes to the notes will be documented here.

[0.1.0] : 10.09.2026

Added
  • Uploaded slides.
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Last updated on Sep 10, 2026

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