Elementary Mathematical Analysis: A Text Book for First Year College StudentsThis book is not intended to be a text on "Practical Mathematics" in the sense of making use of scientific material and of fundamental notion» not already in the possession of the student, or in the sense of making the principles of mathematics secondary to its technique. On the contrary, it has been the aim to give the fundamental truths of elementary analysis as much prominence as seems possible in a working course for freshmen. The emphasis of the book is intended to be upon the notion of functionality. Illustrations from science are freely used to make this concept prominent. The student should learn early in his course that an important purpose of mathematics is to express and to interpret the laws of actual phenomena and not primarily to secure here and there certain computed results. Mathematics might well be defined as the science that takes the broadest view of all of the sciences-an epitome of quantitative knowledge. The introduction of the student to a broad view of mathematics can hardly begin too early. |
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abscissa algebraic amplitude angle arithmetical arithmetical progression axes axis called centimeters circle common logarithm complex number computation constant construction coördinate paper corresponding cos² cosine cubic cubical parabola curve decimal diameter distance divided double scale Draw ellipse equal Exercises expression factor feet Find the equation formula geometrical progression given graph graphically Hence horizontal hyperbola inches latus rectum length locus logarithms negative ordinates parabola parametric equations perpendicular plane polar coördinates polar equation positive power function quadrant radians ratio rectangle rectangular coördinates represented result revolutions per minute roots rotation seiche Show side sin² sine sinusoid Sketch slope Solve squared paper straight line student Substituting tangent theorem tion trigonometric trigonometric functions units variable velocity vertical wave Write the equation X-axis Y-axis Y-intercept zero ΙΟ
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Page 323 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.
Page 130 - At a point 200 feet from, and on a level with the base of a tower, the angle of elevation of the top of the tower is observed to be 60° : what is the height of the tower?
Page 321 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides by the projection of the other upon that side.
Page 374 - Hence the product of two complex numbers is a complex number whose modulus is the product of the moduli and whose amplitude is the sum of the amplitudes of the two complex numbers.
Page 248 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.
Page 321 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other...
Page 461 - A term may be transposed from one member of an equation to the other by changing its sign.
Page 408 - A conic is the locus of a point whose distance from a fixed point called the focus is in a constant ratio to its distance from a fixed line called a directrix.
Page 12 - ... function. A magnitude so related to another magnitude that for any value of one there is a corresponding value of the other. For instance, the area of a circle is a function of its radius. The radius is also a function of the area. functional reserves. The ability of the body to accomplish additional muscular or other activity and useful work beyond the normal level of activity of an individual.
Page 413 - Parabola is the locus of a point whose distance from a fixed point is always equal to its distance from a fixed straight line.