Course Description
This course provides the student the mathematical skills and necessary background to undertake scientific, engineering, economy or business careers. Topics include finite and infinite limits, concept of continuity, concept of derivative, differentiation rules, product and quotient rules, the chain rule, the power rule, second derivative, applications of differentiation, Rolle’s theorem, the mean value theorem, critical points, extrema points, first derivative test, second derivative test, points of inflection, concavity, transcendental functions (trigonometric, logarithmic, exponential), concept of anti-derivative, upper and lower sums, Riemann’s sums and definite integrals, numerical integration, first and second fundamental theorems of calculus, the mean value theorem for integrals, indefinite integration, integration techniques, integration by parts, applications of integration, areas between curves, volumes of solids with constant or varying cross section, solids of revolution, disc method, shell method. At the same time the student develops skills, to model a physical situation, to use technology, to communicate mathematics verbally and by writing, to determine the reasonableness of solutions and to “appreciate calculus as a coherent body of knowledge and as a human accomplishment”.