COURSE NAME: Mathematics for Biological Sciences
COURSE CODE: BIF403
PROGRAM: MSc Bioinformatics
Quantities and units, Numbers and equations, basic calculus, Limits of a function; Derivative of a function at a point, geometrical significance of derivative, rules for differentiation, differentiation of trigonometric, exponential and logarithmic functions, differentiation of inverse algebraic and inverse trigonometric functions, chain rule, differentiation of implicit functions and logarithmic differentiation; Physical aspects of derivatives; Higher order derivatives - maxima and minima; Applications of derivative - example from energy minimization, Integration: Anti-derivatives, finding function from its derivative; Definite integral as the limit of the Sum, properties of definite integrals; Fundamental theorem of integral calculus; Integration of Elementary Functions - standard integrals; Methods of integration - integration by substitution, integration by parts; Integration of trigonometric functions; Applications – Area under a curve, volume of bounded region; linear systems, differentiation, integration, differential equations, Continuity and Derivability, Concept of continuity (continuous and discontinuous functions), trigonometry, continuous and discrete models, ordinary differential equations, linear algebra – matrices and determinants, matrix operations, Matrices – why matrices needed; Linear equations & Matrices - row/column operations, Gauss elimination, decomposition, inverse; Determinant - properties of determinants, Cramer’s rule, determinant to transpose and inverse; Matrices and sequence matching in bioinformatics (substitution matrices). Gauss-Jordan elimination, solutions of linear systems, description of orthogonality, basic optimization theory, linear programming, simplex method, basics of nonlinear programming. - Properties of Determinants, Minors and Cofactors, Multiplication of Determinants, Adjoint, Reciprocal, Symmetric Determinants, Cramer’s rule, Different types of matrices, Matrix Operations, Transpose of a matrix, Adjoint of a square matrix, Inverse of a matrix, Eigen values and eigen vector The concept of a Vector, Vector addition and subtraction, Products of two vectors. Dot product and Cross product, Products of three vectors- scalar triple product and vector triple product, Gradient, Divergence and Curl.