([[.:mvorderold|old version]])

=== Introduction ===

== Warmup ==

  * [[..:prereq:mvpre:mvpresurface|Prerequisite Ideas]]
  * Introduction
  * [[courses:pretest:mvtest:mvpretest|Pretest]] and/or [[courses:pretest:mvtest:mvskills|Skills Test]] (Pretest: 15 min)
  
== Representations of Multivariable Functions ==

  * [[swbq:mvsw:mvswpizza|Pizza and Cola]] (SWBQ: 10 min)
  * [[..:activities:mvact:mvsurfaces|Surfaces]] (SGA: 30+ min)
  * [[swbq:mvsw:mvswsurface|Surfaces]] (SWBQ: 10 min)
  * [[..:lecture:mvlec:mvlecsurfrep|Representations of surfaces]] (Lecture)
  * [[bb>book:math:msurfaces|Surfaces]] (Lecture)
  * [[bb>book:math:level|Contour Maps]] (Lecture)
  * [[..:activities:mvact:mvheater|The Heater]] (SGA: 30--45 min)

=== Multiple Integrals ===

== Review of Single Variable Integration ==

  * [[..:activities:mvact:mvcylinder|The Cylinder]] (SGA: 30 min)
  * [[swbq:mvsw:mvswintegrate|Integration]] (SWBQ)
  * Activity: chop (single integrals)
  * Wrap up: chop (double integrals)
  * [[..:lecture:mvlec:mvlecchop|Chop, Multiply, and Add]] (Lecture)
  * [[bb>book:math:single|Single Integrals]] (Lecture)
  * [[..:lecture:mvlec:mvlecchoc|Chocolate]] (Lecture)

== Double Integrals ==

  * [[..:activities:mvact:mvpark|The Park]] (SGA)
  * [[..:activities:mvact:mvcake|The Cake]] (SGA)
  * [[bb>book:math:double|Double Integrals]] (Lecture)
  * [[swbq:mvsw:mvswlim|Constant limits]] (SWBQ: ConcepTest)
  * [[..:activities:mvact:mvchop|Chop, Multiply, and Add]]
  * [[..:activities:mvact:mvtriangle|The Triangle]] (SGA)
  * [[bb>book:math:order|Order of Integration]] (Lecture)
  * [[..:activities:mvact:mvdouble|Reverse order of integration]] (SGA)
  * [[swbq:mvsw:mvswmatch|Match region to limits]] (SWBQ: ConcepTest)
  * [[bb>book:math:limits|Non-constant limits]] (Lecture)
  * Example: Computation
  * Activity: Chop (Mass)
  * [[bb>book:math:triple|Triple Integrals]] (Lecture)
  * [[bb>book:math:mass|Mass]] (Lecture)
  * [[..:lecture:mvlec:mvlecintquest|Questions for integrals]] (Lecture)

== Polar and Curvilinear Coordinates ==

  * [[swbq:mvsw:mvswcircle|The Area of a Circle]] (SWBQ: 10 min)
  * [[bb>book:math:polar|Polar Coordinates]]
  * [[bb>book:math:coords2|Curvilinear Coordinates]]
  * [[..:activities:mvact:mvdscoord|Area and Volume Elements]] (SGA)
  * [[..:activities:mvact:mvcone|The Cone]] (SGA: 1 hour)
  * [[bb>book:math:polarint|Integrals in Polar Coordinates]] (Lecture)
  * [[bb>book:math:curvint|Integrals in Curvilinear Coordinates]] (Lecture)

=== Partial Derivatives I ===

== Review of Differentiation ==

  * [[swbq:mvsw:mvswdiff|Derivatives?]] (SWBQ)
  * [[..:lecture:mvlec:mvlecderivrep1|Representations of Derivatives]] (Lecture)
  * [[swbq:mvsw:mvswdiffex|Differentiate]] (SWBQ: 10 min)
  * [[courses:pretest:mvtest:mvskills|Skills test]] (15 min)
  * [[swbq:mvsw:mvswdrule|Derivative Rules]] (SWBQ)

== Differentials and Derivatives ==

  * [[..:lecture:mvlec:mvlecdrules|Derivative Rules from Differentials]] (Lecture: ?? min)
  * [[bb>book:math:zap|Derivative]] and [[bb>book:math:single|Integration]] rules (Lecture: ?? min)
  * [[bb>book:math:partial|Differentials]] (Lecture)

== Partial Derivatives ==

  * [[..:activities:mvact:mvheater2|The Heater II]] (SGA)
  * Partial Derivatives? (SWBQ)
  * [[..:lecture:mvlec:mvlecderivrep2|Representations of Partial Derivatives]] (Lecture)
  * [[..:activities:mvact:mvhotplate|The Hot Plate]] (SGA)
  * [[bb>book:math:thick|Thick Derivatives]] (Lecture)
  * [[..:lecture:mvlec:mvlecdcalc|Computing Partial Derivatives]] (Lecture)
  * [[..:activities:mvact:mvdrill|Drill]] (SGA)
  * [[..:lecture:mvlec:mvlec2nd|Second-Order Partial Derivatives]] (Lecture)

== Chain Rule ==

  * [[swbq:mvsw:mvswchain2|Chain Rule]] (SWBQ)
  * [[bb>book:math:chain|Chain Rule]] (Lecture)
  * [[bb>book:math:chaindiag|Tree Diagrams]] (Lecture)
  * [[..:activities:mvact:mvchain|Chain Rule]] (SGA)
  * [[..:lecture:mvlec:mvlecchainrule|Summary and Examples]] (Lecture)
  * [[..:activities:mvact:mvresistors|Resistors]] (SGA)
  * [[..:activities:mvact:mvpchain|Chain Rule Measurements]] (SGA)

=== Vectors I ===

== Introduction ==

  * [[swbq:mvsw:mvswvec|Vectors]] (SWBQ)
  * [[bb>book:math:vectors|Vectors]] (Lecture)

== Dot Product ==

  * [[swbq:mvsw:mvswdot|The Dot Product]] (SWBQ)
  * [[bb>book:math:dot|The Dot Product]] (Lecture)
  * [[..:lecture:mvlec:mvlecgeoalg|Geometry and Algebra]] (Lecture)

=== Partial Derivatives II ===

== Gradient and Directional Derivatives ==

  * [[..:activities:mvact:mvhillside|The Hillside]] (SGA)
  * [[..:lecture:mvlec:mvlecmaster|The Master Formula]] (Lecture)
  * [[bb>book:math:grad|The Gradient]] (Lecture)
  * [[bb>book:math:gradprop|Properties of the Gradient]] (Lecture)
  * [[..:activities:mvact:mvdderiv|Directional Derivatives]] (SGA)
  * [[bb>book:math:directionderiv|Directional Derivatives]] (Lecture)
  * [[..:activities:mvact:mvpuddle|The Puddle]] (SGA)

== Optimization ==

  * [[swbq:mvsw:mvswmaxmin|Maxima and Minima]] (SQBQ)
  * [[swbq:mvsw:mvsw2nd|The Second-Derivative Test]] (SWBQ)
  * [[..:lecture:mvlec:mvlecmaxmin|Max/min]] (Lecture)
  * [[bb>book:math:maxmin|Second-Derivative Test]] (Lecture)
  * [[..:activities:mvact:mvgoldmine|The Gold Mine]] (SGA)
  * [[..:activities:mvact:mvwater|The Water Table]] (SGA)
  * [[..:activities:mvact:mvcoaster|The Roller Coaster]] (SGA)
  * [[bb>book:math:lagrange|Lagrange multipliers]] (Lecture)
  * [[..:activities:mvact:mvmaxmin|Optimization]] (SGA)

=== Vectors II ===

== Applications ==

  * [[bb>book:math:cross2|The Cross Product]] (Lecture)
  * [[..:activities:mvact:mvcross|Cross Product]] (SGA)
  * [[..:activities:mvact:mvcube|The Cube]] (SGA)
  * [[bb>book:math:curves|Curves]] (Lecture)
  * [[bb>book:math:motion|Parametric Curves]] (Lecture)
  * [[bb>book:math:arclength|Arclength]] (Lecture)
  * [[bb>book:math:cov|Change of Variables]] (Lecture)
  * [[..:activities:vcact:vccov|Change of Variables]] (SGA)

=== Extra ===

  * [[..:activities:mvoutcomes:mvoutcomesd2|Learning Outcomes]]
  * [[..:activities:mvact:mvdifferentiate|Differentiation]] (SWBQ: 10 min)