2/27Lecture 1 Outline1.Go over course outline that’s also on myCourses2.Learning goals for the course3.Prerequisites4.Review of the gradient
3/27Why this course?1.If you want to model or analyze anycomplex systemwherethe variables take on acontinuumof values, then you needCalculus.2.Calculus gives you good training in abstract and quantitativethinking.
4/27AdviceYou should trynotto view the material as simplysymbolicmanipulationof mathematical symbols and objects in order to getthe right answer.Instead you should focus on:1.anunderstandingof what these symbols and object mean2.how they relate to concrete physical or geometric problems3.why they are useful4.how you can couple your understanding with existingtechnology to solve concrete problems.
5/27Concrete example of adviceProblem 1:Solve this pair of equations forxandy:x+ 2=y-22x-4=y+ 2.
6/27Concrete example of adviceProblem 2:ILaurel and Wren have just finished picking apples, and eachholds up their basket of apples.ILaurel looks at Wren and says: “If you give me two of yourapples, then we will have the same number of apples.”IWren responds with: “No, if you give me two of your apples,then I will have double the number of apples as you.”IHow many apples did each pick?
7/27Concrete example of adviceIThese are equivalent problems.IIf a student can do the first problem, butnotthe secondproblem, then unfortunately in today’s modern world, theyhave learned a useless skill.IPerhaps 100 years ago, equation solving could only beperformed by hand, and hence such a skill would’ve beenuseful. Today, there are programs that will do it quickly andaccurately.IHowever, there aren’t programs that know how to analyze,interpret, and manipulate answers to mathematical problems(yet), so that’s still relevant.
8/27Learning Goals60-70% of the Course will be about integration.Integration in Calculus 2 and 3:Isingle integralsZbaf(x)dxIdouble integralsZZRf(x,y)dxdy,whereRis a either a rectangle or a more complicated domain(region) inR2.
9/27Learning GoalsItriple integralsZZZSf(x,y,z)dxdydz,whereSis some domain (region) inR3.