# Treatise on differential calculus by Isaac Todhunter

By Isaac Todhunter

This Elibron Classics booklet is a facsimile reprint of a 1864 variation through Macmillan and Co., Cambridge and London.

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Additional info for Treatise on differential calculus

Sample text

How much heavier is the first pack than the second? 3. One pack of books weighs 7 kg which is 3 kg heavier than a second pack. How much does the second pack weigh? In the second half of the year, students are given missing subtrahend and missing addend problems, and are required to compare the solution of these problems with the way they solved familiar problems. Examples given are: (a) A girl had some postcards. She gave a friend 4 and then had 6 left. How many did she have to begin with? (b) A girl had some postcards.

Fractions also are introduced in CAP2 in Grade 1, but students are expected only to find halves of discrete sets and to estimate halves of some measures (length and volume). The fraction symbol is not introduced until Grade 2, and only after experience with the words and pictures represent­ ing one half and one fourth. There is a series of eight lessons on fractions in Grade 3. ” After lessons on finding fractional parts of sets, students are introduced to equiv­ alent fractions through pictures showing different subdivisions of the same 1.

There are lessons on multiplying and dividing whole numbers and decimal numbers by powers of ten in both text series. Because of the Soviet’s curricular emphasis on oral exercises, there is a good deal more mental math, presented in a variety of ways, in SMP. The contrast with American texts is striking, and so several examples of ex­ ercises from SMP are given here. The following is an example of an oral exercise given in Grade 1: 1 2 3 4 5 1 1 2 3 4 5 6 7 1 1 1 1 1 1 1 1 1 1 1 1 1 10 18 40 15 36 20 60 14 38 50 45 39 23 77 11 48 60 95 39 25 93 16 58 70 65 34 29 64 12 98 80 25 33 24 98 Subtract 10 from each number in row 3; from each number in the fourth column.