Spring 1996 Worksheets

Math 408D - Second Semester Calculus


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 17 [pdf] [tex] -

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 32 [pdf] [tex] -

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 37 [pdf] [tex] -

Worksheet 38 [pdf] [tex] - review: definite integral, integrability, convergence of series, Taylor polynomials, approximations/bounding error, polar coordinates, double integrals, partial fractions, series, parameterizations


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