Kurssi

Julkaistu

(Päivitetty )

Helsingin yliopisto

Quantitative methods for pharmaceutical research

5 op

Paikan päällä
Aineopinnot

Part I: Probability and calculus

1. Review of math from statistics course and introduction to DESMOS:

  • Math language introduced: sums, sets, subscripts, functions, inversion,
  • Important functions: Exponentials, logarithms, gaussian functions
  • Function visualization with DESMOS
  • Discrete and continuous probability distribution
  • Central limits theorem and normal distribution

2. Continuing the probability distribution story:

  • Some basic concepts of information theory
  • demonstrating the hole that needs calculus to fill: random walks, diffusion, newtons laws of motion, area under normal distribution...

3. Basic calculus:

  • Motivating calculus, intuitive description
  • Fundamental theorem of calculus and what it means
  • How derivatives are solved: a completely mechanical process
  • How integrals are solved: some tricks, not always possible...

4. Integral calculus put to work: ordinary differential equations (ODEs)

  • Definition of ODEs
  • Technique of separation of variables
  • APPLICATION: rate equations (pharmacokinetics)

Part II: Many dimensions: how do we handle this

1. Spaces in many dimensions

  • introduction to concept in linear algebra and topology
  • coordinate system transformations
  • Introduction to symmetry: quantified by group theory
  • APPLICATION: group theory in spectroscopy and crystallography

2. Calculus in many dimensions

  • Gradient and Laplacian
  • APPLICATION: the REAL Fick's laws of diffusion
  • multidimensional integrals
  • integral coordinate transformations and gaussian integrals

Part III: Advanced topics

  1. Taylor series, complex numbers and Eulers formula
  2. Fourier transformation: MANY APPLICATIONS

Part IV. Topics that might be covered if time allows and class has interest:

  • Numerical integration: Trapezoidal and Simpsons rule
  • Newton-Raphson method
  • Lagrange multipliers: optimization with constraints
  • More information theory: principle of maximum entropy and how this leads to the Maxwell-Boltzmann distribution
  • Coupled differential equations solved through numerical analysis: real pharmacokinetics
  • Qualitative description of partial differential equations
  • Multi-criterion optimization, machine learning, artificial intelligence and emergence

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