Synopses & Reviews
Excerpt from The Calculus
Although care has been exercised to secure a consistent order of topics, some teachers may desire to alter it; for example, an earlier introduction of transcendental functions and of por tions of the chapter on Approximations may be desired, and is entirely feasible. But it is urged that the comparatively early introduction of Integration as a summation process be retained, since this further impresses the usefulness of the subject, and accustoms the student to the ideas of derivative and integral before his attention is diverted by a variety of formal rules.
Purely destructive criticism and abandonment of coherent arrangement are just as dangerous as ultraconservatism. This book attempts to preserve the essential features of the Calculus, to give the student a thorough training in mathematical rea soning, to create in him a sure mathematical imagination, and to meet fairly the reasonable demand for enlivening and eu riching the subject through applications at the expense of purely formal work that contains no essential principle.
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