Syllabus of Jawaharlal Nehru University MSc Biotechnology - BT511 - Mathematics for Biologists

Credits: 2

Preliminaries: Coordinates, lines and increments, function, shifting graphs, trigonometric functions.

Limits and Continuity: Rates of change and limits, rules for finding limits, target values and formal definitions of limits, extensions of the limit concept, continuity, tangent lines.

Derivatives: The derivative of a function, differentiation rules, rates of change, derivatives of trigonometric functions, the chain rule, implicit differentiation and rational exponents, related rates of change.

Applications of derivatives: Extreme values of functions, the mean value theorem, the first derivative test for local extreme values, graphing with y' and y",, limits as x→ ±∞ , Asymptotes, and dominant terms, optimization, linearization and differentials, Newton's method.

Integration: Indefinite integrals, differential equations, initial value problems and mathematical modeling, integration by substitution-running the chain rule backward, estimating with finite sums, Riemann sums and definite integrals, properties, area and the mean value theorem, the fundamental theorem, substitution in definite integrals, numerical integration.

Applications of integrals: Areas between curves, finding volumes by slicing, volumes of solids of revolution disks and washers, cylindrical shells, lengths of plane curves, areas of surfaces of revolution, moments and centres of mass, work, fluid pressures and forces, the basic pattern and other modeling applications.