The new material since test 2 includes more series tests (see the series theorems sheet), radius or interval of convergence of a power series or Taylor series, Taylor polynomials and series, finding new series from known ones, the error bound formula, whether a function solves a differential equation, finding a particular solution with an initial condition, slope fields and equilibrium points, Euler's method, separation of variables, and setting up differential equations related to real-life applications.

- Material from previous classes includes slope directions, the tangent line, above or below the x-axis via the sign of the function value, increasing or decreasing via the sign of the first derivative, concave up or down via the sign of the second derivative, graphs of functions, left and right sums, limits, L'Hopitals rule, divide by the highest term in limits, and earlier sequences and series from middle or high school.
**series convergence**convergence tests slides and clickers, review slides and clickers, Group Work Target Practice, 9.4 Group Work solutions**power series**slides and clickers, 9.5 group sols**Taylor polynomials and series, calculations and convergence**slides and clickers, Animation, practice, 10.1 and 10.2 Maple worksheet solutions, and 10.1 and 10.2 group work solutions**new Taylor series from old, error bounds**slides and clickers, finding and using Taylor series practice, 10.3 group work sols, 10.4 sols**testing a DE, slope fields, equilibrium, stability, Euler's method, separation of variables**slides and clickers, 11.1 sols, slope field practice, (solutions are in the slides), Maple worksheet solutions.**applications of des, setting up from real-life scenarios**slides, group work target practice, solutions

**Overall review slides from class**- We have continued to use integration techniques (or set up and note what would be useful) including expand by multiplying out a quadratic and then power rule, w-subs, trig sub, improper integral followed by parts to integrate ln(x), and the conceptual ideas of numerical integration (for both 8.1 and 9.3), for example.
- Material from previous classes includes graphs of functions, Riemann sums, limits, L'Hopitals rule, divide by the highest term in limits, Pythagorean theorem, similarity of triangles, area of a circle, area of a rectangle, volume of a box and cylinder, and earlier sequences and series from middle or high school.
**areas and volumes by slicing 8.1**slides and clicker, practice sheet for area, practice sheet for volume, and group work solutions**volume by surface of revolution and arc length 8.2**slides and clicker, practice sheet, solutions to part 2 of Wiley practice are on ASULearn (like they are for all the sections)**density 8.4**slides and clicker, traffic density, and**work 8.5**slides and clicker, practice sheet, and group work solutions-
**sequences 9.1**slides and clickers, intro in Maple, and**geometric series 9.2**slides and clickers, and practice sheet, group work solutions **series in 9.3 including partial sums, series divergence when terms not getting smaller, linearity arguments, and the integral test**slides and clickers, practice sheet, integral test group work target practice, group work solutions/a>, geometric series versus p-series

- class review
**substitution**slides and clickers, and solutions to group target practice**parts**slides and clickers, and solutions to group target practice**partial fractions**slides and clickers, and solutions to group target practice**trigonometric substitution**slides and clickers, primer, and solutions to group target practice**improper integrals**slides and clickers, group target practice, solutions to group target practice**numerical integration**slides and clicker, and group target practice, solutions to group target practice, sample questions- algebra missteps

numerical integration via rectangles

area between two curves via rectangles

volume by cylindrical disk or rectangular box slices

total work via the work for each slice = force for each slice x displacement of that slice

series diverges when sequence terms do not get smaller

slope fields in DEs