Learning quant quickly? My review of FREE Multivariable Calculus By George Cain & James Herod

(Last Updated On: August 11, 2011)

Learning quant quickly? My review of  FREE Multivariable Calculus By George Cain & James Herod

So In finished reading this Multivariate Calculus book


It seems this book is really designed for more advanced calculus users as there are some assumptions of knowledge. Still it is a very good resource if you trying to learn quant, but when your head is spinning after Paul WIlmott or John Hull,  this would be a good resource to understand some of the calculus terminology thrown around. If you still don’t get it (like me), you may want to further investigate on good YouTube channels (like Khan Academy) some of the key terms listed below from the book’s table of contents:

Chapter One – Euclidean Three Space

1.1 Introduction

1.2 Coordinates in Three-Space

1.3 Some Geometry

1.4 Some More Geometry–Level Sets

Chapter Two – Vectors–Algebra and Geometry

2.1 Vectors

2.2 Scalar Product

2.3 Vector Product

Chapter Three – Vector Functions

3.1 Relations and Functions

3.2 Vector Functions

3.3 Limits and Continuity

Chapter Four – Derivatives

4.1 Derivatives

4.2 Geometry of Space Curves–Curvature

4.3 Geometry of Space Curves–Torsion

4.4 Motion

Chapter Five – More Dimensions

5.1 The space Rn

5.2 Functions

Chapter Six – Linear Functions and Matrices

6.1 Matrices

6.2 Matrix Algebra

Chapter Seven – Continuity, Derivatives, and All That

7.1 Limits and Continuity

7.2 Derivatives

7.3 The Chain Rule

Chapter Eight – f:Rn-› R

8.1 Introduction

8.2 The Directional Derivative

8.3 Surface Normals

8.4 Maxima and Minima

8.5 Least Squares

8.6 More Maxima and Minima

8.7 Even More Maxima and Minima

Chapter Nine – The Taylor Polynomial

9.1 Introduction

9.2 The Taylor Polynomial

9.3 Error

Supplementary material for Taylor polynomial in several variables.

Chapter Ten – Sequences, Series, and All That

10.1 Introduction

10.2 Sequences

10.3 Series

10.4 More Series

10.5 Even More Series

10.6 A Final Remark

Chapter Eleven – Taylor Series

11.1 Power Series

11.2 Limit of a Power Series

11.3 Taylor Series

Chapter Twelve – Integration

12.1 Introduction

12.2 Two Dimensions

Chapter Thirteen – More Integration

13.1 Some Applications

13.2 Polar Coordinates

13.3 Three Dimensions

Chapter Fourteen – One Dimension Again

14.1 Scalar Line Integrals

14.2 Vector Line Integrals

14.3 Path Independence

Chapter Fifteen – Surfaces Revisited

15.1 Vector Description of Surfaces

15.2 Integration

Chapter Sixteen – Integrating Vector Functions

16.1 Introduction

16.2 Flux

Chapter Seventeen – Gauss and Green

17.1 Gauss’s Theorem

17.2 Green’s Theorem

17.3 A Pleasing Application

Chapter Eighteen – Stokes

18.1 Stokes’s Theorem

18.2 Path Independence Revisited

Chapter Ninteen – Some Physics

19.1 Fluid Mechanics

19.2 Electrostatics

George Cain & James H

Of course some of the topics do apply to quant but others do not so you can omit what you don’t want to read.

Now I got to read that 1000 page linear algebra book now I would probably start with this before even touching the above calculus book. There is some mention of algebra as well s that confusing math manipulation I can never get.


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