Denition approach of learning new topics

2 CONTENTS
Contents
I Lecture I 4
1 Cartesian coordinate system 4
1.1 Plotting points . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Dene slope for two points . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Slope of a line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Slopes of line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Functions 8
2.1 Examples of a functions . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Finding values of function in y = f(x) form . . . . . . . . . . . . 8
2.3 Functions and their graphs . . . . . . . . . . . . . . . . . . . . . 8
2.4 Domain and range of a function . . . . . . . . . . . . . . . . . . . 9
II Lecture 2 11
3 Examples of what is a Limit? 11
3.1 Polygon becomes circle . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Bucket is full or overowing?[5] . . . . . . . . . . . . . . . . . . . 12
3.3 Rotating a marble tied to a cord . . . . . . . . . . . . . . . . . . 13
3.4 A numerical example . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.5 Denition of Limit . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.6 Formulae of limits . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.7 Worked out problems in limits . . . . . . . . . . . . . . . . . . . 15
3.8 Practise Problems in Limits . . . . . . . . . . . . . . . . . . . . . 18
III Lecture 3 19
4 Derivatives 19
4.1 Derivatives of other functions . . . . . . . . . . . . . . . . . . . . 23
4.2 Understanding the Derivative denition geometrically[1] . . . . . 23
4.3 Rate of change . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.4 Function & its examples in Physics . . . . . . . . . . . . . . . . . 25
4.5 Instantaneous rate of change[3] . . . . . . . . . . . . . . . . . . . 26
4.6 Chain Rule and friends . . . . . . . . . . . . . . . . . . . . . . . . 27
4.7 Composition of functions . . . . . . . . . . . . . . . . . . . . . . 27
4.8 Derivative of a composite function . . . . . . . . . . . . . . . . . 28
IV Lecture 4 30
5 Integration 30
5.1 Dierentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.2 Indenite Integration . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.3 Denite Integration . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.3.1 Way to evaluate Denite Integrals . . . . . . . . . . . . . 31