General Mathematics I

Introductory material: Straight lines, functions and plots, exponential fubctions, inverse functions and logarithms, trigonometric functions and their inverses, parametric equations (0.5 weeks)

Limits and Continuity: Rates of change and limits, computing limits and side limits, infinite limits, continuity, tangent lines (1.5 weeks).

Derivatives: The derivative as a function, the derivative as a rate of change, derivative of a fraction and a negative power, derivatives of trigonometric functions, derivation chain rule, derivative of an implicit function (1 week).

Applications of derivatives: Extrema of functions, mean value theorem,rules for plotting functions, construction of optimization models, differentials, Newton's algorithm, introduction of taylor's formula (2 weeks).

Integration: Indefinite integrals, integration rules, integration by substitution, intergral estimates from finite sums, Riemann sums and definite integrals, mean value theorem, fundamental theorem of integration, evaluation of definite integrals by substitution, numerical integration, main types of integration, integration by parts, partial fractions, trigonometric substitutions, computational algebra systems, Monte Carlo integration, generalized integrals (3 weeks).

Applications of integrals:Calculation of volumes by slicing and rotation around an axis, by using cylindrical shells, calculation of lengths of curves in the plane, springs, pumps, elevators, fluid forces, center of mass and torques. (2 weeks).

Non-algebraic functions: Logarithms, exponentials, derivatives of inverse trigonometric functions, integrals of hyperbolic functions.(1 week)

Infinite Series: Limits of sequences, subsequences, bounded sequences, Picard's method, infinite series, non-negative series, alternating series, absolute convergence, conditiuonal convergence, power series, Taylor and McLaurin series, applications of power series. (2 weeks).