Analysis

Description

The course covers the following topics:

·        Limits, continuity, limits involving infinity

·        Asymptotes of graphs, tangents to curves

·        Linearization

·        Derivative at a point, the derivative as a function, differentiation rules, derivatives of trigonometric functions, the chain rule

·        Implicit differentiation with examples on partial derivatives

·        Derivatives of inverse functions and logarithms

·        Extreme value of functions

·        Critical points, local and global extreme values

·        Fermat’s theorem

·        Intermediate value theorem

·        Rolle’s theorem and its applications

·        The mean value theorem and its applications

·        Monotonic functions

·        The first derivative test for local extreme values

·        Concavity, points of inflection and curve sketching

·        Indefinite integrals with examples of double and triple integrals

Compétences visées

By the end of this class, students should be able to :

·         Evaluate limits associated with a range of rational and transcendental functions, calculate limits and recognize common exceptions where limits do not exist

·         Use working knowledge of limits to evaluate basic derivatives

·         Calculate the derivatives of elementary functions using a variety of tools including the product rule, quotient rule, chain rule

·         Apply implicit and logarithmic differentiation

·         Characterize the graph of a function and its local and global extrema

·         Work with the concepts of continuity and differentiability and important ideas associated with fundamental theorems

Apply the basic concepts of integration to solving double and triple integrals.