MAT 238 Calculus III

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Nándor Sieben

You probably have a copy of the following book from Calc II: Calculus early transcendentals by Jon Rogawski and Colin Adams.

Alternate online books:
Whitman , Alternate location
Michael Corral
Paul Dawkins
Gilbert Strang
Any standard printed Calculus book is useful.


Test dates are going to be announced here one week ahead of time:

Test 1: Tuesday 2/8 (see Bblearn for more details)

includes sections 12.1-12.7, 13.1, 13.2, 13.5 : vectors, vector algebra, length, unit vectors, unitization, dot product, angle between vectors, perpendicular vectors, scalar projection, vector projection, parallel and perpendicular components, distance from a line, distance from a plane, cross product, normal vectors, area using the cross product, equations of lines in planes and in space, equations of planes, cylindrical and spherical coordinates, vector functions, derivatives integrals of vector functions, motion in space

Test 2: Tuesday 3/8 (see Bblearn for more details)

includes sections 14.1-14.7 : multivariable functions, surfaces, tangent planes, contour plots, limits, partial derivatives, functions form R^m to R^n, local linearization, derivative, chain rule, directional derivatives, gradient, critical points, local extrema, second derivative test, global extrema, optimization

Test 3: Tuesday 4/5 (see Bblearn for more details)

includes sections 14.8-15.6 : Lagrange multipliers, multiple integrals, iterated integrals, changing order of integration, change of variables, integration using polar cylindrical spherical coordinates, applications, volume, average value, mass, center of gravity

New material on the final

includes sections 16.1-17.3 : line integral of scalar and vector fields, surface integral of scalar and vector fields, applications (length of curves, surface area, mass, center of gravity, work), conservative vector fields, potential, curl=rot=circulation density, divergence=flux density, Green/Stokes Theorem, Divergence Theorem
Bblearn has the course sylabus, handouts, summary sheets, discussion forum, etc.

Our department computer lab is in AMB 222. Computers and free tutoring are also available in AMB 137. Math Achievement Program Tutoring options.

Mathematica notebooks

Mathematica is available in many NAU computer labs and on NAU's virtual desktop

You can install it on your computer following the instructions.

You should be able to use Wolfram Cloud in your browser.

You can always call NAU ITS help line 928-523-9294 or and ask how you can have access to Mathematica.

Introduction to Mathematica

Quadratic surfaces: notebook pdf
Intersection of surfaces: notebook pdf
Webwork 14.1 Problem 12: notebook
Limit: notebook pdf
Gradient: 2D notebook pdf 3D notebook pdf
Second derivative test: notebook pdf
Global extrema: notebook pdf
Global extrema: notebook pdf
Optimization: notebook pdf
Lagrange multipliers with one constraint: notebook pdf
Lagrange multipliers with two constraints: notebook pdf
Volume as double integral or triple integral: notebook pdf
Square to parallelogram: notebook pdf
Centroid of solid paraboloid: notebook pdf
Flux and circulation density 2D: notebook pdf
div rot: notebook pdf
Surface area of sphere: - rectangular notebook pdf - cylindrical notebook pdf - spherical notebook pdf
Flux density 3D: notebook pdf
Surface area of triangle: notebook pdf
Centroid of surface of hemisphere: notebook pdf
Flux through surface of paraboloid: notebook pdf
Flux through surface of cone: notebook pdf
Green: notebook pdf
Stokes on hemisphere: notebook pdf
Gauss on cylinder: notebook pdf

Resources with videos:

Follow the link.


3D tetris
Problem Of The Week
Mooculus lectures.
Online function grapher.
Graphcalc, a free graphing calculator
Calculus tools on the web.
LyX a word processor for writing mathematics
2D vector field applet
3D vector field applet