Worksheet 1 [pdf] [tex] - Review: definition of the definite integral, area, Fundamental Theorem, graphing, partitions/estimates
Worksheet 2 [pdf] [tex] - cross-sectional area, Fundamental Theorem, area (ellipse)
Worksheet 3 [pdf] [tex] - Fundamental Theorem, minimization (overhauling machinery), infinite sums
Worksheet 4 [pdf] [tex] - improper integrals, convergence/divergence, p-test, harmonic series, repeating decimal expansions, geometric series, cardinality
Worksheet 5 [pdf] [tex] - improper integrals, gamma function, integration by parts, integral comparison test, absolute convergence for integrals, Hilbert hotel
Worksheet 6 [pdf] [tex] - improper integrals, series, convergence/divergence, divergence test, alternating harmonic series, harmonic series, p-series
Worksheet 7 [pdf] [tex] - harmonic series, integral test, conditional convergence, alternating series
Worksheet 8 [pdf] [tex] - Riemann sums, improper integrals, comparison test, ratio test, estimating series, error, limit comparison test
Worksheet 9 [pdf] [tex] - tests for convergence of series, golden mean, partial fractions, telescoping series
Worksheet 10 [pdf] [tex] - power series, interval of convergence, partial sums, derivatives and coefficients
Worksheet 11 [pdf] [tex] - power series, Maclaurin series, Taylor series, non-power series
Worksheet 12 [pdf] [tex] - examples of series with bad habits, (nice) Taylor series, differentiating series, interval of convergence
Worksheet 13 [pdf] [tex] - smooth functions, taylor series, exp(-1/x^2), shortcuts for computing taylor series, even/odd functions
Worksheet 14 [pdf] [tex] - interval of convergence, shortcuts for computing taylor series, exp(-1/x^2)
Worksheet 15 [pdf] [tex] - Taylor polynomials, alternating series theorem, approximations and error
Worksheet 16 [pdf] [tex] - Taylor series computer lab
Worksheet 18 [pdf] [tex] - Tyaylor series, proof of the remainder theorem, Taylor polynomials, Bessel function, series solution to a differential equation
Worksheet 19 [pdf] [tex] - Maclaurin series, De Moivre's theorem, Taylor polynomials, remainders, error, Bessel function, geese
Worksheet 20 [pdf] [tex] - Dirac's belt trick, rotations in 3-space, "proof" that pi_1(SO_3)=Z_2
Worksheet 21 [pdf] [tex] - parameterizations, vectors, velocity/speed, curvature, osculating circles
Worksheet 22 [pdf] [tex] - parameterizations: involute, cycloid, epicycloid, hypocycloid
Worksheet 23 [pdf] [tex] - vectors, norm, angle, orthogonality, dot product, doomed idiots, velocity, acceleration
Worksheet 24 [pdf] [tex] - vectors, orthogonality, parallelism, prophetic idiots
Worksheet 25 [pdf] [tex] - vectors, dot product, cross product, parameterization, helix, curvature, Lie algebras (nonassociativity, Jacobi identity)
Worksheet 26 [pdf] [tex] - vectors, nautical navigation, force, components, work, moment of a force, angular velocity
Worksheet 27 [pdf] [tex] - parameteriztion, velocity, acceleration, polar idiots
Worksheet 28 [pdf] [tex] - polar coordinates, Archimedes' spiral, arclength
Worksheet 29 [pdf] [tex] - polar coordinates, symmetry, arclength, polar distance formula, planet orbits
Worksheet 30 [pdf] [tex] - functions of several variables, graph of a function, level sets, polar coordinates
Worksheet 31 [pdf] [tex] - vector valued functions, continuity, algebra of continuous functions, limits
Worksheet 33 [pdf] [tex] - multivariable functions, level sets, gradient vector field, gradient flow, rate of change, chain rule
Worksheet 34 [pdf] [tex] - multivariable functions, gradient, directional derivatives, chain rule
Worksheet 35 [pdf] [tex] - double integrals, order of integration, exp(-1/x^2), integrating in polar coordinates
Worksheet 36 [pdf] [tex] - double integrals, volumes, integrating with polar coordinates, Jacobian
Worksheet 38 [pdf] [tex] - review: definite integral, integrability, convergence of series, Taylor polynomials, approximations/bounding error, polar coordinates, double integrals, partial fractions, series, parameterizations