Calculus I

Functions and their graphs, review of some common functions. Limit and continuity, Properties of continuous functions; limits involving infinity, asymptotes. Derivative at a point, derivative as a function. Differentiation rules; the Chain Rule; implicit differentiation. Derivatives of inverse functions and logarithms. Related rates problems. Linearization and differentials. Extreme values and critical points of a function; the Mean Value Theorem. Monotonic functions; concavity and curve sketching. Indeterminate forms; L’Hôpital’s rule. Applications of derivatives: optimization problems. The definite integral; Riemann sum. The Fundamental Theorem of Calculus. Indefinite integrals and the substitution method. Applications of definite integrals: area between curves.

To gain basic engineering math skills.