Course Detail

Students who take this course will acquire much of the mathematical background required throughout the rest of KGI's MBS curriculum. Lectures and assignments will cover topics in differential equations and linear algebra, with applications to life sciences.. Both analytical and numerical methods will be described, with the numerical aspects and assignments being based on MATLAB. Calculus is considered a prerequisite for this material, i.e., it is assumed that the students are comfortable with derivatives and integrals.

Reference Books

S. C. Chapra, Applied Numerical Methods with MATLAB for Engineers and Scientists, McGraw-Hill, New York (2005). ISBN 0-07-297677-2

E. Kreyszig, Advanced Engineering Mathematics, 8th Edition, Wiley (1999). ISBN 0-471-15496-2

Ordinary Differential Equations

• First order equations: separable equations, exact differential equations, integrating factors, linear first order differential equations, relaxation phenomena.
• Second order differential equations: homogenous equations, general solution, linear oscillations (overdamped, underdamped and critically damped solutions).
• Second order differential equations: inhomogeneous linear equations, general solution, resonance in forced oscillations.

Linear Algebra

• Scalars, vectors, linear combinations, basis vectors, dot and cross products.
• Matrices and matrix operations (addition, transpose, multiplication), rank of a matrix.
• Determinant, matrix inverse, solution of a system of linear equations.
• Eigenvalues and eigenvectors.
• Combination of techniques from linear algebra and ordinary differential equations: systems of ordinary differential equations with biological applications; stability analysis of such systems.

Students will be able to use mathematical methods to solve problems in bioengineering, computational biology and other areas of the applied life sciences.

Weekly Assignments 70%
Final Exam 30%