1. The continuity of chapter 7 from the first semester: exponential growth and decay, inverse of trigonometric functions, Hyperbolic functions, indeterminate forms and L’Hospital’s Rule
2. Techniques of Integration: integration by parts, trigonometric integrals, trigonometric substitution, integration of rational functions by partial fractions, approximate integration. improper integrals,
3. Further applications of integration: arc length, area of surface of revolution, application to Physics, Engineering, application to Economics and Biology, Probability.
4. Differential Equation: Modeling with differential equations, direction fields and Euler’s Method, separable equations, linear equations, Predator-Prey Systems.
5. Parametric equations and polar coordinates: curves defined by parametric equations, polar coordinates, areas and lengths in polar coordinates, conic sections, conic sections in polar coordinates.
6. Infinite sequences and series: sequences, series, the integral test and estimate of sums, comparison tests, alternating series, absolute convergence, the ratio and root test, power series, representations of functions as power series, Taylor and Maclaurin series, application of Taylor polynomials
7. Vectors and the geometry of space: dot product, cross product, equations of lines and planes, cylinders and quadric surfaces
8. Vector functions: vector functions and space curves, arc length and curvature, derivatives and integral of vector functions
9. Partial derivatives: Functions of several variables, limits and continuity, partial derivatives, tangent planes and linear approximations, the chain rule, directional derivatives and the gradient vector, maximum and minimum values, Lagrange Multipliers