Mathematics of Biological Systems

Doelstellingen van dit vak

Calculus Students should be able to: ● Appreciate the difference between functions using discrete and continuous time and be able to suggest when each is appropriate. ● Be able to calculate limits ● Be able to integrate and differentiate a wide range of functions ● Solve basic differential equations ● Understand the use of calculus and be able to select the correct method for solving a problem framed solely in a biological context Basic skills and statistics Students should be able to: ● Distinguish between the forms of linear, polynomial, rational, exponential and logarithmic functions and know their properties. ● Work with real and complex numbers, understand their properties and graphical representations. ● Sketch graphs, using function, its first derivative, and the second derivative. ● Apply different types of curve fitting in the biological context. ● Understand the basic principles of probability including Bayes theorem. ● Understand the definitions of discrete and continuous variables, probability and cumulative distribution functions. ● Calculate expectation, variance, covariance and correlation. ● Appreciate the basic components of hypothesis testing. Linear algebra Students should be able to: ● Solve systems of linear equations, understand different types of possible solutions, and use the ideas in applied problems. ● Perform the common operations of matrix algebra and use them to solve applied problems. ● Compute determinant of a square matrix and understand its properties. ● Understands the concepts of linear independence, spanning set, basis, rank of matrix, vector space and subspace, and linear transformation. ● Understand eigenvectors and eigenvalues, how they characterize the action of some linear transformations and how to used them to solve applied problems. ● Use the ideas of inner products, orthogonality, and projections to determine least square solutions to a linear systems. Matlab Students should be able to: ● Use Matlab to import/export data and produce figures based on this data ● Understand and run code provided to them, and interpret the output ● Computationally check results from any of the other strands of the course ● Adapt code provided to them to improve or alter its functionality