Calculus 2

What you will learn

• •Determine whether a sequence of real numbers is monotonic, and evaluate the limit to determine the convergence of a sequence.
• •Numerical Series: evaluate the sum of a convergent geometric series and telescoping sum; determine the convergence of series using kth-term test, integral test, direct and limit comparison tests, ratio and root tests; classify alternating series into absolutely convergent, conditionally convergent, or divergent, and approximate the sum of a convergent alternating series; apply the ratio or root test to determine the radius and interval of convergence of power series; construct Maclaurin or Taylor series using the definition, substitution, differentiation and integration. Applications.
• •Real functions with several real variables: finding limits and concluding about continuity; evaluate partial derivatives; apply the Chain Rule; find the Tangent Planes at a given point; evaluate Directional Derivatives and the Gradient Vector.
• •Solving optimisation problems involving real functions with several real variables: find absolute extrema in a closed bounded set; find relative extrema in the domain of the function.
• •Use parametric equations to define curves.

How it is graded

Week by week