MATH135 Lecture : Lecture 1 Notes Winter 2009 Lecture 1 notes

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scarletimpala173

16 Oct 2011

School

University of Waterloo

Department

Mathematics

Course

MATH135

Professor

Mike Eden

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Document Summary

Two of the main purposes of math 135 are to teach you about proof (what it means, how to prove things, etc. ) and to teach you about precision in mathematics. A rigorous mathematical argument which unequivocally demonstrates the truth of a given statement. In other words, in mathematics a proof is a sequence of steps, starting with one or more hypotheses, which follow logically from each other, using the axioms of mathematics, leading to the desired con- clusion. We want to know if a statement is always true. Mathematics is cumulative we use old results to prove new results. If it turned out that one result that we thought was true actually failed sometimes, the results following from it could also be false. What kinds of professions rely on mathematics: engineering, actuarial science, accounting, weather forecasting, banking. Actually, just about every profession relies on math somehow! This is why proof is very important from a practical point of view.

Related Questions

I need help on number 2. I can't seem to find alocal max or min let alone the absolute.

Overview: You will identify, solve, and fully analyzea "real world" optimization problem of your choosing. It should bea problem that we did not cover in class, but you are free toconsult other sources for inspiration. If you get your idea fromanother source, you should both cite it and add some originalthoughts to your write-up.

Details: What you hand in to me should consist of thefollowing parts:

(1) An introduction clearly stating theproblem to be solved, including any necessary explanation of theset-up as well as clearly defined variables, parameters, etc. Theportion should be written out in full sentences. In particular, youshould identify the quantity to optimized (i.e., maximized orminimized) and identify any constraints or boundary conditions. Thequantity being optimized should be a function of two or morevariables.

WHAT I NEED HELP ON----->(2) A translationof the story problem in part (1) to a purely mathematical problem.You should then fully solve the mathematical problem by (i) findingand classifying all critical points, (ii) analyzing the boundariesor constraints, and (iii) deciding the absolute max/min value andwhere it occurs.

(3) A brief conclusion in which you discussthe implications of the mathematics in part (2) for the originalstory problem. This portion should also be written in fullsentences.

---so far what I have done--

The pool is an open top consisting of a rectangle and a semicircle. I put a constraint on volume and set it equal to10000 m^3 . So What I am trying to figure out is whatdimensions create the lowest surface area. I found a local minat r= 7.815,w=15.631 but that means that their would be noheight for the box. does that make sense? are theirother points I should be checking?