Differential and Integral Calculus

Volume 2

Chapter I: Introduction

Contents

Preliminary Remarks on Analytical Geometry and Vector Analysis

  

1.2 THE AREA OF A TRIANGLE, THE VOLUME OF A TETRAHEDRON, THE VECTOR MULTIPLICATION OF VECTORS

 

1.3.2 Application to Linear Equations

1. Rectangular Co-ordinates and Vectors

  

1.2.1 The Area of a Triangle

  

Exercises 1.3
1.1.1 Co-ordinate Axes   1.2.2 Vector Multiplication of two Vectors  

1.4 AFFINE TRANSFORMATIONS AND THE MULTIPLICATION OF DETERMINANTS
1.1.2 Directions and Vectors. Formulae for Transforming Axes   1.2.3 The Volume of a Tetrahedron   1.4.1. Affine Transformations of the Plane and Space
1.1.3 Scalar Multiplication of Vectors  

Exercises 1.2

   1.4.2 The Combination of Affine Transformations and the Resolution of the General Affine Transformation
1.1.4 The Equations of the Straight Line and of the Plane  

1.3 SIMPLE THEOREMS ON DETERMINANTS OF THE SECOND AND THIRD ORDER

  1.4.3 The Geometrical Meaning of the Determinant of Transformation, and the Multiplication Theorem

Exercises 1.1

   1.3.1 Laws of Formation and Principal Properties   Exercises 1.4