Chapter 7
U-Substitution
7.1: Integration by parts (be sure to know formula, be ready for problems with $\ln{x}$ and inverse trig)
7.2: Integration using trig identities (be sure to know the 6 trig identities (3 Pythagorean identities, 2 reduction identities, $sin(2\theta)$ identity) and representations for $\sec{x}$, $\csc{x}$. $\cot{x}$)
7.3: Trig Substitution (be sure to know the three cases, and you will have to go back to $x$, remember I like the answer as an algebraic expression when possible)
7.4: Partial Fractions
7.8: Improper integrals (both types)
Chapter 9 9.1: Find constant solution to a differential equation (similar to homework) Solve for constants in the solution that satisfy the differential equation (similar to homework) Find all constant solutions (similar to homework) 9.3: Solve separable differential equations (similar to homework and board problems, be sure to know to break it up $\frac{dy}{dx}=\frac{f(x)}{g(y)})$ 9.5: Solve DE using Integrating Factor (similar to homework and board problems, be sure to know what to multiply by, you must show how you "undo" the product rule)
Chapter 10 10.1 Parametric equations: parametric to Cartesian equation 10.2 Parametric Derivatives: Equation of tangent line to parametric curve, 1st and 2nd derivative of parametric equation, length of curve 10.3 Polar: graph of polar regions, polar to Cartesian equation, Cartesian to polar equation, 10.4 Polar Derivatives: derivatives in polar, equation of a tangent line, length of a curve
Chapter 11
11.1 Sequences: formula to list of numbers, list of numbers to formula, convergence, LUB, GLB
11.2 Series: sequence of partial sums, telescoping series, geometric series
11.3 Integral test, p-test (be careful it must satisfy the conditions)
11.4 Limit comparison test, direct comparison test (will not have to use this, but can if you choose), nth term test (will not have to use this, but can if you choose)
11.5 Alternating series test, absolute and conditional convergence
11.6 Ratio and Root tests
11.8 Power Series: interval of convergence
11.9 Functions of a power series
11.10 Taylor & MacLauren series
11.11 Applications of Taylor MacLauren series
*Remember on the exam to determine if a series converges/diverges you must use one of the test we learned in class
Chapter 14 14.1 Functions of Several Variables 14.2 Limits and Continuity 14.3 Partial Derivatives 14.5 The Multivariate Chain Rule - Remember you must show the multivariate chain rule formula you are using for each problem and after taking the derivative replace the inside functions to receive full credit
Chapter 15
15.1 Double Integrals over Rectangles
15.2 Double Integrals over General Regions
15.3 Double Integrals in Polar Coordinates
15.6 Triple Integral