205math. Differential and Integral Calculus

Students are introduced to the following Infinite Series (4 weeks): Sequences, infinite series, Convergent and divergent series, Positive-term series, The Integral, ratio and root tests, Alternating series and absolute convergence, Power Series (radius and interval of convergence), Power series representation of functions, Maclaurin and Taylor Series.

Vectors and Vector-Valued Functions (2 weeks): Vectors, vector algebra, Dot and cross products, Lines and planes, surfaces, Vector-valued functions and applications.
Partial Differentiation (3 weeks): Functions of several variables, Limits
and continuity, Partial derivatives, Chain Rule; Gradients, Local extrema of functions of two variables, Lagrange multipliers.

Multiple Integrals (2 weeks): Double Integrals, Double Integrals in polar coordinates, Applications of double integrals (surface area and volumes).