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This text is an introduction to the use of vectors in a wide range of undergraduate disciplines. It is written specifically to match the level of experience and mathematical qualifications of students entering undergraduate and Higher National programmes and it assumes only a minimum of mathematical background on the part of the reader. Basic mathematics underlying the use of vectors is covered, and the text goes from fundamental concepts up to the level of first-year examination questions in engineering and physics. The material treated includes electromagnetic waves, alternating current, rotating fields, mechanisms, simple harmonic motion and vibrating systems. There are examples and exercises and the book contains many clear diagrams to complement the text. The provision of examples allows the student to become proficient in problem solving and the application of the material to a range of applications from science and engineering demonstrates the versatility of vector algebra as an analytical tool.

Preface

1 Vector algebra I: Scaling and adding vectors

- INTRODUCTION TO SCALARS, NUMBERS AND VECTORS
- Scalars and numbers
- Introducing vectors
- Displacements and arrows
- Vector notation
- SCALING VECTORS AND UNIT VECTORS
- Scaling a vector or multiplication of a vector by a number
- Unit Vectors
- VECTOR ADDITION-THE TRIANGLE ADDITION RULE
- LINEAR COMBINATIONS OF VECTORS
- CARTESIAN VECTORS
- Cartesian coordinates of a point-a review
- Cartesian unit vectors and cartesian components of a vector
- MAGNITUDES AND DIRECTIONS OF CARTESIAN VECTORS
- SCALING AND ADDING CARTESIANVECTORS
- VECTORS IN SCIENCE AND ENGINEERING
- Definition of a vector and evidence for vector behavior
- Vector problems in science and engineering

- Vector algebra II: Scalar products and vector products
- THE SCALAR PRODUCT
- Definition of the scalar product and projections
- The scalar product in vector algebra
- CARTESIAN FORM OF THE SCALAR PRODUCT
- THE ANGLE BETWEEN TWO VECTORS
- THE VECTOR PRODUCT
- Definition of the vector product
- The vector product in vector algebra
- CARTESIAN FORM OF THE VECTOR PRODUCT
- TRIPLE PRODUCTS OF VECTORS
- The scalar triple product
- The vector triple product

This text is an introduction to the use of vectors in a wide range of undergraduate disciplines. It is written specifically to match the level of experience and mathematical qualifications of students entering undergraduate and Higher National programmes and it assumes only a minimum of mathematical background on the part of the reader. Basic mathematics underlying the use of vectors is covered, and the text goes from fundamental concepts up to the level of first-year examination questions in engineering and physics. The material treated includes electromagnetic waves, alternating current, rotating fields, mechanisms, simple harmonic motion and vibrating systems. There are examples and exercises and the book contains many clear diagrams to complement the text. The provision of examples allows the student to become proficient in problem solving and the application of the material to a range of applications from science and engineering demonstrates the versatility of vector algebra as an analytical tool.

Preface

1 Vector algebra I: Scaling and adding vectors

- INTRODUCTION TO SCALARS, NUMBERS AND VECTORS
- Scalars and numbers
- Introducing vectors
- Displacements and arrows
- Vector notation
- SCALING VECTORS AND UNIT VECTORS
- Scaling a vector or multiplication of a vector by a number
- Unit Vectors
- VECTOR ADDITION-THE TRIANGLE ADDITION RULE
- LINEAR COMBINATIONS OF VECTORS
- CARTESIAN VECTORS
- Cartesian coordinates of a point-a review
- Cartesian unit vectors and cartesian components of a vector
- MAGNITUDES AND DIRECTIONS OF CARTESIAN VECTORS
- SCALING AND ADDING CARTESIANVECTORS
- VECTORS IN SCIENCE AND ENGINEERING
- Definition of a vector and evidence for vector behavior
- Vector problems in science and engineering

- Vector algebra II: Scalar products and vector products
- THE SCALAR PRODUCT
- Definition of the scalar product and projections
- The scalar product in vector algebra
- CARTESIAN FORM OF THE SCALAR PRODUCT
- THE ANGLE BETWEEN TWO VECTORS
- THE VECTOR PRODUCT
- Definition of the vector product
- The vector product in vector algebra
- CARTESIAN FORM OF THE VECTOR PRODUCT
- TRIPLE PRODUCTS OF VECTORS
- The scalar triple product
- The vector triple product

This text is an introduction to the use of vectors in a wide range of undergraduate disciplines. It is written specifically to match the level of experience and mathematical qualifications of students entering undergraduate and Higher National programmes and it assumes only a minimum of mathematical background on the part of the reader. Basic mathematics underlying the use of vectors is covered, and the text goes from fundamental concepts up to the level of first-year examination questions in engineering and physics. The material treated includes electromagnetic waves, alternating current, rotating fields, mechanisms, simple harmonic motion and vibrating systems. There are examples and exercises and the book contains many clear diagrams to complement the text. The provision of examples allows the student to become proficient in problem solving and the application of the material to a range of applications from science and engineering demonstrates the versatility of vector algebra as an analytical tool.

Preface

1 Vector algebra I: Scaling and adding vectors

- INTRODUCTION TO SCALARS, NUMBERS AND VECTORS
- Scalars and numbers
- Introducing vectors
- Displacements and arrows
- Vector notation
- SCALING VECTORS AND UNIT VECTORS
- Scaling a vector or multiplication of a vector by a number
- Unit Vectors
- VECTOR ADDITION-THE TRIANGLE ADDITION RULE
- LINEAR COMBINATIONS OF VECTORS
- CARTESIAN VECTORS
- Cartesian coordinates of a point-a review
- Cartesian unit vectors and cartesian components of a vector
- MAGNITUDES AND DIRECTIONS OF CARTESIAN VECTORS
- SCALING AND ADDING CARTESIANVECTORS
- VECTORS IN SCIENCE AND ENGINEERING
- Definition of a vector and evidence for vector behavior
- Vector problems in science and engineering

- Vector algebra II: Scalar products and vector products
- THE SCALAR PRODUCT
- Definition of the scalar product and projections
- The scalar product in vector algebra
- CARTESIAN FORM OF THE SCALAR PRODUCT
- THE ANGLE BETWEEN TWO VECTORS
- THE VECTOR PRODUCT
- Definition of the vector product
- The vector product in vector algebra
- CARTESIAN FORM OF THE VECTOR PRODUCT
- TRIPLE PRODUCTS OF VECTORS
- The scalar triple product
- The vector triple product

Preface

1 Vector algebra I: Scaling and adding vectors

- INTRODUCTION TO SCALARS, NUMBERS AND VECTORS
- Scalars and numbers
- Introducing vectors
- Displacements and arrows
- Vector notation
- SCALING VECTORS AND UNIT VECTORS
- Scaling a vector or multiplication of a vector by a number
- Unit Vectors
- VECTOR ADDITION-THE TRIANGLE ADDITION RULE
- LINEAR COMBINATIONS OF VECTORS
- CARTESIAN VECTORS
- Cartesian coordinates of a point-a review
- Cartesian unit vectors and cartesian components of a vector
- MAGNITUDES AND DIRECTIONS OF CARTESIAN VECTORS
- SCALING AND ADDING CARTESIANVECTORS
- VECTORS IN SCIENCE AND ENGINEERING
- Definition of a vector and evidence for vector behavior
- Vector problems in science and engineering

- Vector algebra II: Scalar products and vector products
- THE SCALAR PRODUCT
- Definition of the scalar product and projections
- The scalar product in vector algebra
- CARTESIAN FORM OF THE SCALAR PRODUCT
- THE ANGLE BETWEEN TWO VECTORS
- THE VECTOR PRODUCT
- Definition of the vector product
- The vector product in vector algebra
- CARTESIAN FORM OF THE VECTOR PRODUCT
- TRIPLE PRODUCTS OF VECTORS
- The scalar triple product
- The vector triple product

Preface

1 Vector algebra I: Scaling and adding vectors

- INTRODUCTION TO SCALARS, NUMBERS AND VECTORS
- Scalars and numbers
- Introducing vectors
- Displacements and arrows
- Vector notation
- SCALING VECTORS AND UNIT VECTORS
- Scaling a vector or multiplication of a vector by a number
- Unit Vectors
- VECTOR ADDITION-THE TRIANGLE ADDITION RULE
- LINEAR COMBINATIONS OF VECTORS
- CARTESIAN VECTORS
- Cartesian coordinates of a point-a review
- Cartesian unit vectors and cartesian components of a vector
- MAGNITUDES AND DIRECTIONS OF CARTESIAN VECTORS
- SCALING AND ADDING CARTESIANVECTORS
- VECTORS IN SCIENCE AND ENGINEERING
- Definition of a vector and evidence for vector behavior
- Vector problems in science and engineering

- Vector algebra II: Scalar products and vector products
- THE SCALAR PRODUCT
- Definition of the scalar product and projections
- The scalar product in vector algebra
- CARTESIAN FORM OF THE SCALAR PRODUCT
- THE ANGLE BETWEEN TWO VECTORS
- THE VECTOR PRODUCT
- Definition of the vector product
- The vector product in vector algebra
- CARTESIAN FORM OF THE VECTOR PRODUCT
- TRIPLE PRODUCTS OF VECTORS
- The scalar triple product
- The vector triple product

Preface

1 Vector algebra I: Scaling and adding vectors

- INTRODUCTION TO SCALARS, NUMBERS AND VECTORS
- Scalars and numbers
- Introducing vectors
- Displacements and arrows
- Vector notation
- SCALING VECTORS AND UNIT VECTORS
- Scaling a vector or multiplication of a vector by a number
- Unit Vectors
- VECTOR ADDITION-THE TRIANGLE ADDITION RULE
- LINEAR COMBINATIONS OF VECTORS
- CARTESIAN VECTORS
- Cartesian coordinates of a point-a review
- Cartesian unit vectors and cartesian components of a vector
- MAGNITUDES AND DIRECTIONS OF CARTESIAN VECTORS
- SCALING AND ADDING CARTESIANVECTORS
- VECTORS IN SCIENCE AND ENGINEERING
- Definition of a vector and evidence for vector behavior
- Vector problems in science and engineering

- Vector algebra II: Scalar products and vector products
- THE SCALAR PRODUCT
- Definition of the scalar product and projections
- The scalar product in vector algebra
- CARTESIAN FORM OF THE SCALAR PRODUCT
- THE ANGLE BETWEEN TWO VECTORS
- THE VECTOR PRODUCT
- Definition of the vector product
- The vector product in vector algebra
- CARTESIAN FORM OF THE VECTOR PRODUCT
- TRIPLE PRODUCTS OF VECTORS
- The scalar triple product
- The vector triple product