Lecture_1_Sept_3.pdf - Math 264 Lecture 1 Notes Biji Wong September 2 2019 1\/27 Lecture 1 Outline 1 Go over course outline that\u2019s also on myCourses 2

Lecture_1_Sept_3.pdf - Math 264 Lecture 1 Notes Biji Wong...

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1/27 Math 264 Lecture 1 Notes Biji Wong September 2, 2019
2/27 Lecture 1 Outline 1. Go over course outline that’s also on myCourses 2. Learning goals for the course 3. Prerequisites 4. Review of the gradient
3/27 Why this course? 1. If you want to model or analyze any complex system where the variables take on a continuum of values, then you need Calculus. 2. Calculus gives you good training in abstract and quantitative thinking.
4/27 Advice You should try not to view the material as simply symbolic manipulation of mathematical symbols and objects in order to get the right answer. Instead you should focus on: 1. an understanding of what these symbols and object mean 2. how they relate to concrete physical or geometric problems 3. why they are useful 4. how you can couple your understanding with existing technology to solve concrete problems.
5/27 Concrete example of advice Problem 1: Solve this pair of equations for x and y : x + 2 = y - 2 2 x - 4 = y + 2 .
6/27 Concrete example of advice Problem 2: I Laurel and Wren have just finished picking apples, and each holds up their basket of apples. I Laurel looks at Wren and says: “If you give me two of your apples, then we will have the same number of apples.” I Wren responds with: “No, if you give me two of your apples, then I will have double the number of apples as you.” I How many apples did each pick?
7/27 Concrete example of advice I These are equivalent problems. I If a student can do the first problem, but not the second problem, then unfortunately in today’s modern world, they have learned a useless skill. I Perhaps 100 years ago, equation solving could only be performed by hand, and hence such a skill would’ve been useful. Today, there are programs that will do it quickly and accurately. I However, there aren’t programs that know how to analyze, interpret, and manipulate answers to mathematical problems (yet), so that’s still relevant.
8/27 Learning Goals 60-70% of the Course will be about integration. Integration in Calculus 2 and 3: I single integrals Z b a f ( x ) dx I double integrals ZZ R f ( x , y ) dxdy , where R is a either a rectangle or a more complicated domain (region) in R 2 .
9/27 Learning Goals I triple integrals ZZZ S f ( x , y , z ) dxdydz , where S is some domain (region) in R 3 .

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