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Math 2210-3
2210-3 home page
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Lecture notes will be posted by noon the day before class, and it will be your responsibility to bring a copy to class. Most people find it useful to have the notes handy so as to minimize copying directly from the blackboard, thus leaving time in class to work on and write down example details and key explanations.
Week 1: Jan 11-15
jan11.pdf 11.1 the geometry of 3 dimensional Euclidean space.
jan13.pdf 11.2 vectors
jan15.pdf 11.3 dot product algebra and geometry
Week 2: Jan 20-22
jan20.pdf 11.3 planes, work and projection, with dot product.
jan22.pdf 11.4 the cross product, and applications.
Week 3: Jan 25-29
jan25.pdf 11.4, and begin 11.5-6. cross product, parametric lines.
jan27.pdf 11.5 parametric curves and vector-valued functions. lines.
jan29.pdf 11.5 Calculus for vector-valued functions.
Week 4: Feb 1-5
feb1.pdf 11.6 tangent lines and perpendicular planes for parameteric curves
feb3.pdf 11.5: the most important *science* this semester - how Kepler's observed planetary laws are ONLY consistent with Newton's deduced inverse square law of gravitational attraction; one of the greatest scientific deductions ever.
feb5.pdf 11.7: the geometry of curves and the physics of particle motion.
Week 5: Feb 8-12
feb8.pdf 11.7-11.8: finish curve geometry/physics; then understand quadric surfaces in 3-space.
feb10.pdf 11.9: polar, cylindrical and spherical coordinates
feb12.pdf review sheet for Wednesday exam
pracexam1.pdf actual exam from 2005 - NOTE that this exam does not cover all possible topics on your exam! Solutions are posted on our exam page
Week 6: Feb 17-19
feb19.pdf 12.1 functions of 2 or more variables
Week 7: Feb 22-26
feb22.pdf 12.2 partial derivative computations and geometry.
feb24.pdf 12.3 limits and continuity for functions of 2 or more variables.
feb26.pdf 12.4 differentiability means good linear approximation, in higher dimensions.
Week 8: March 1-5
mar1.pdf 12.5 directional derivatives.
mar3.pdf 12.6 multivariable chain rule!
mar5.pdf 12.7 applications of chain rule and differential approximation.
Week 9: March 8-12
mar8.pdf 12.8 multivariable max-min problems.
mar10.pdf 12.9 Lagrange multipliers for constrained max-min problems
mar12.pdf 13.1-13.2 double integrals
Week 10: March 15-19
mar15.pdf 13.3 double integrals over non-rectangular domains
mar17.pdf 13.4 double integrals using polar coordinates
mar19.pdf 13.5 double integral applications
Week 11: March 29-April 2
mar29.pdf 13.6 surface area for graphs and parametric surfaces.
mar31.pdf 13.7 triple integrals and applications
apr2.pdf 13.8-13.9 triple integrals in spherical and cylindrical coordinates; the general change of variables formula.
Week 12: April 5 - April 9
April 5: finish Friday's notes and answer questions about Wednesday midterm.
apr9.pdf 14.1 vector fields, divergence, curl.
Week 13: April 12 - April 16
apr12.pdf 14.2 curve and line integrals
apr14.pdf 14.3 path-independent line integrals and gradient vector fields.
apr16.pdf 14.3-14.4 and Green's Theorem
Week 14: April 19 - April 23
apr19.pdf 14.4 Green's Theorem, the 2-d divergence theorem, and the geometric meaning of n=2 curl and div.
apr21.pdf 14.5 surface integrals
apr23.pdf 14.6 3-space divergence theorem (Gauss' Theorem).
Week 15: April 26 - April 28
apr26.pdf 14.7 Stokes' Theorem
apr28.pdf Review sheet