Calculus

CALCULUS NOTES


Name:




MATHEMATICS


Hilary Dorgan
Leaving Certificate

Higher Level

2020 - 2021

CALCULUS
NOTES




© H Dorgan IOE Maths HL 1

,CALCULUS NOTES




CONTENTS

Syllabus Page 3

Limits Page 4

Trigonometrical Limits Page 5

Differentiation from First Principles Page 5

Rules of Differentiation (Product, Quotient, Chain) Page 6

Practising the Rules of Differentiation Page 7

Differentiating Trig, Exponential & Log Functions Page 8

Differentiating Inverse Sine & Inverse Tan Functions Page 9

Second Derivatives Page 10

Applications of Calculus Page 11

Slope of a Tangent to a Curve Page 12

Finding Maxima, Minima and Points of Inflection Page 13

Curve Sketching Page 14

Displacement, Velocity, Acceleration Page 14

Rates of Change Page 16

Maxima & Minima Page 17

Sketching Derivative Curves Page 21

Implicit Differentiation Page 22

Points to Remember Page 23




© H Dorgan IOE Maths HL 2

, CALCULUS NOTES



Differential Calculus Paper 1 SYLLABUS
Functions and Calculus




© H Dorgan IOE Maths HL 3