math - 1 Math Review Mathematics Review PHY 2053-2054...

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Math Review 1 Mathematics Review PHY 2053-2054 Introduction In a sense, mathematics is the language of physics. Since the goal or physics is to describe the world quantitatively (usually), mathematics is the natural language. Even when only qualitative descriptions are needed, the concepts are frequently couched in the language of mathematics. It is necessary to be conversant with simple mathematics to successfully understand physics. The idea that physics consists of "formulas" from which one calculates results is totally incorrect. Physics requires attaching a physical meaning to the symbols, developing a "feeling" for these quantities, and some intuition is usually required in the solution of problems. The problems you will be doing during this course are similar to the "word" problems you have done in some of your math courses. Only elementary mathematics is required: algebra, geometry, and trigonometry. While all students in this course will have had courses in these subjects, frequently these skills have not been exercised since the courses were taken. During the first few laboratory sessions the concepts most used in elementary physics will be reviewed, and you will work problems, which should help you to overcome difficulties generated by being "stale" in mathematics.
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Math Review 2 Algebra A first requirement is that you be able to carry out simple algebraic manipulations and rearrangements with ease, and to attach physical meaning to the variables. The algebraic rules you will need are in the "summary of math review". These exercises are designed to give you practice in the kind or manipulations and thinking required for physics. A . Evaluate the following expressions for a = 3, b = -2, c = 4, d = -1, x = 5, and y = - 3. 1. c x a - - 3 2. y d b a + - + 3 2 3. c b x c + - + 2 2 4. y d y - + 2 5 5. y ac d a xy 2 2 ) 3 4 ( + - 6. ) )( 8 3 ( ) 2 2 )( 3 2 ( d c a c c a d c - + - - B . Add the following expressions; 1. (2a + 7b - 15c) + (6a+ 2b + 6c) + (2a + 3b + 4c) - (2a- 3b+ 6c) 2. (3x- 4y + 7z + 4c) + (-2x + 4y - 8z - 2c) - (3x -7z - 3c) C . Carry out the following multiplications and raising to a power: 1. (3x - 2y) (6x + 3y) 2. (2a + 3b) (a - 2b + c) 3. (2x - 3y) 2 D . Solve the following equations for the unknown variable: 1. 0 7 4 = + x 2. y y 6 ) 4 3 ( 3 = - 3. ) 8 4 ( 2 ) 4 3 ( 3 - = - y y 4. ) 1 2 ( 4 . 0 2 . 1 7 . 0 - = - x x 5. x x 5 6 3 4 - = - 6. 11 8 2 3 = - + q q q
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Math Review 3 E. "Word" problems. Solving such problems is very similar to much of the problem solving in physics. They require a certain amount of creative thought and a clear understanding of the representation of physical quantities in algebraic form. No "recipe" or rigid set of rules can be given which will solve all such problems, but certain guidelines can be helpful: 1. Read the problem carefully, frequently several readings will be required. Identify the given facts and the unknown quantity to be determined.
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math - 1 Math Review Mathematics Review PHY 2053-2054...

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