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atheMatical

hysics

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atheMatical

hysics

An Introduction

Derek Raine, PhD et al.

ERCURY

EARNING AND

NFORMATION

Dulles, Virginia

Boston, Massachusetts

New Delhi

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Original title and copyright:

Mathematical Methods for Physical Science

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Publisher: David Pallai

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D. Raine et al.

Mathematical Physics.

ISBN: 9781683922056

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CONTENTS

Preface ....................................................................................

xiii

1 Derivatives and Integrals ............................................ 1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

1.10

1.11

1.12

1.13

1.14

1.15

1.16

1.17

1.18

1.19

1.20

1.21

Definition of a derivative ............................................... 1

Some basic derivatives ................................................... 4

“Function of a function” (chain rule) ............................ 5

Product (and quotient) rule ........................................... 8

Implicit differentiation ................................................. 11

Piecewise differentiable functions ............................... 12

Higher order derivatives .............................................. 14

Stationary points ........................................................... 15

Integrals of elementary functions ................................ 18

Integrals of combinations of functions ........................ 20

Integration by substitution ........................................... 21

Integration by parts ...................................................... 25

Integration of rational functions .................................. 27

Definite integrals .......................................................... 28

Area under a graph ....................................................... 29

Continuous and discontinuous functions .................... 30

Estimates of integrals ................................................... 32

Derivatives of integrals................................................. 33

Reduction formulae...................................................... 35

Exercises ....................................................................... 40

Problems ....................................................................... 44

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