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Han's book is suitable for students interested in the mathematical theory of partial differential equations, either as an overview of the subject or as an introduction leading to further study. The book is very well-written, the proofs are given in full detail, and each chapter ends with a list of exercises. Note that the author puts emphasis on the main ideas and methods rather than on various generalizations.
Continue Shopping Checkout. AMS Homepage. Join our email list. Sign up. Advanced search. Author s Product display : Qing Han. Abstract: This is a textbook for an introductory graduate course on partial differential equations. Volume: Publication Month and Year: Copyright Year: Page Count: Cover Type: Hardcover. Circle the leading keyword and indicate the corresponding AND that it defines.
With other leading keywords discussed in the following sections , AND can mean other things. In the direct translation strategy, you translate each word into its corresponding algebraic symbol, one at a time, in the same order as written, as shown in Example 4.
He had a gain of seventeen pounds after working out with the team for four weeks. Note: Not all numbers mentioned in a word problem should be included in the mathematical expression. You may also be wondering why the answer isn't pounds. That's because the question asks you to translate the story problem into a mathematical expression, not to evaluate the expression.
He received a raise of 25 cents an hour. Note: The hourly wage is stated in dollars, and the raise is stated in cents. Any time you are adding two numbers that have units , make sure both numbers are measured with the same units; if they aren't, convert one of the numbers to the same units as the other.
Having both numbers measured with the same units is called homogeneous units. Subtraction keywords also include leading keywords, keywords that can be translated one word at a time, and keywords that are found in story problems.
Look at the following list of subtraction keywords:. You can use the same methods of underlining and circling the keywords shown in the preceding section to translate these expressions. Note: AND is not always translated to mean addition. Example 8 is a subtraction word problem that is translated one keyword at a time, in the exact order of the expression.
Note: Keep in mind that AND does not always indicate addition. One of the most confusing keywords indicating equality is IS. In a translation problem, you may see more than one IS, as Example 2 demonstrates.
Example 2: Translate the following sentences into an algebraic equation: When a number is subtracted from twelve, the result is five. What is the number?
Any IS placed directly in front of a keyword for an operation does not indicate equality. When a number directly follows IS, however, IS does indicate equality. Remember: Mark the turnaround word to remind you to translate in the correct order. What operation should replace AND in this equation? Note : The first expression is translated, then the equal sign is translated, and then the expression on the right of the equal sign.
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