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## Math 20C Calculus & Analytic Geometry for Science and Engineering Winter 2013 Course Syllabus

### Updated 1/1/13

Course:  Math 20C

Title:  Calculus & Analytic Geometry for Science and Engineering

Credit Hours:  4  (2 credits if taken after Math 10C)

Prerequisite:  AP Calculus BC score of 3, 4, or 5;   or, Math 20B with a grade of C- or better

Catalog Description:  Vector geometry, vector functions and their derivatives.   Partial differentiation.  Maxima and minima.  Double integration.

Textbook:  Calculus: Early Transcendentals, second edition, by Jon Rogawski; published by W.H. Freeman and Company; 2012.

• If you do not already have the above textbook, the multivariable portion suffices:
Multivariable Calculus: Early Transcendentals, second edition, by Jon Rogawski; published by W.H. Freeman and Company; 2012
• The Student Solutions Manual (available in the Bookstore) is optional. It has complete solutions for odd-numbered problems in the text.

Subject Material:  We will cover parts of Chapters 11-15 of the text.

The course concerns 3-dimensional (parameter) calculus, and the goal is to prepare you to work in 1000s or millions of parameter, since that is where most technolgy lies. How can anybody do this? Well first you must understand 2 and 3 dimensions very well both in pictures and algebraically and especially how the two fit together. Much of the algebra extends in a natural way to higher dimensions, but some does not. For example, vectors and dot products extend to any dimension, but cross products do not do so readily. So this course while following the syllabus will emphasize three dimensional methods which naturally extend to any dimension.
As you learn a formula or technique think about what form it might take in 4 dimensions of 5 dimensions, etc.
(As your career progresses that is probably where you will be using it.)
The advanatage of pictures over algebra is that it is easier to get ideas and see how things fit together in terms of pictures. So when an engineer works on a problem in 15 variables often they think of an anolog in 3 variables, solve it there and then extend the algebra involved to 15 variables. In all these pursuits matrices (M20F) are a major tool. A major part of the course is how one approximates a function in many variables by a linear function (effectively a matrix).

A weakness of the text is that it draws word problems and examples from an exteremly narrow range of science. It does only physics and leaves out much of the technological world.

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