JeffGroah

Vectors in space, direction angles, direction cosines, the Euclidean dot product, projections, the orthogonal compliment, work

Vectors, vector space, vector space axioms, norm, normalization, direction angle, applications

Final Exam Review

Exam 4 Review

Conic sections, ellipse, parabola, hyperbola, polar form of conic sections, To Infinity and Beyond, Johannes Kepler, Riemann sphere, Alexandroff one-point compactification of the plane.

Calculus in Polar Coordinates, tangent lines, area, arc length, surface area

Polar coordinates, limacon, lemniscate, foliation

Parametric equations, parametric curves, cycloid curve, smooth, epicycloid, arc length, speed

Exam 3 Review

Power series, radius of convergence, interval of convergence, analytic functions, C-infinity functions

Ratio Test, Root Test

Alternating series, absolute convergence, conditional convergence, Remainder Theorem, Alternating Series Test

Direct Comparison Test, Limit Comparison Test

Final Exam Review

Taylor Series, analytic functions, Maclaurin series

Taylor Polynomial, Maclaurin polynomial, Taylor Remainder Theorem, Taylor's Theorem, Taylor Remainder Formula

Integral Test, p-Series Test, Harmonic Series

Infinite Series, geometric series, Geometric Series Test, convergence, divergence, Divergence Test, The n-th Term Test for Divergence, converse, contrapositive, inverse, telescoping sums

Sequences, initial segments of the natural numbers, infinite sequences, finite sequences, limits, monotone, strictly monotone, monotone increasing, monotone decreasing, upper bounds, lower bounds, least upper bounds, greatest lower bounds, completeness axiom, Weierstrass Theorem,

Differential equations, initial value problems, initial data, Euler's Method

Numerical integration, approximate integrals, quadrature, right-hand rule, left-hand rule, midpoint rule, trapezoid rule, trapezoidal rule, Simpson's rule, error formula

Improper integrals, Gabriel's trumpet, Gabriel's horn

Numerical integration, approximate integrals, quadrature, right-hand rule, left-hand rule, midpoint rule, trapezoid rule, trapezoidal rule, Simpson's rule, error formula

Partial fractions, other methods, computer algebra systems, tables

Integration of trigonometric functions. Trigonometric substitutions, or trig substitutions, trig subs.