- 1 Number and Arithmetic To the Student xi
- 1.1 Review
- 1.2 Revision
- 1.3 Reinforcement
- 1.4 Applications
- Answers to reinforcement exercises
- 2 Algebra
- 2.1 Review
- 2.2 Revision
- 2.3 Reinforcement
- 2.4 Applications
- Answers to reinforcement exercises
- 3 Functions and Series
- 3.1 Review
- 3.2 Revision
- 3.3 Reinforcement
- 3.4 Applications
- Answers to reinforcement exercises
- 4 Exponential and Logarithm Functions
- 4.1 Review
- 4.2 Revision
- 4.3 Reinforcement
- 4.4 Applications
- Answers to reinforcement exercises
- 5 Geometry of Lines, Triangles and Circles
- 5.1 Review
- 5.2 Revision
- 5.3 Reinforcement
- 5.4 Applications
- Answers to reinforcement exercises
- 6 Trigonometry Contents
- 6.1 Review
- 6.2 Revision
- 6.3 Reinforcement
- 6.4 Applications
- Answers to reinforcement exercises
- 7 Coordinate Geometry
- 7.1 Review
- 7.2 Revision
- 7.3 Reinforcement
- 7.4 Applications
- Answers to reinforcement exercises
- 8 Techniques of Differentiation
- 8.1 Review
- 8.2 Revision
- 8.3 Reinforcement
- 8.4 Applications
- Answers to reinforcement exercises
- 9 Techniques of Integration
- 9.1 Review
- 9.2 Revision
- 9.3 Reinforcement
- 9.4 Applications
- Answers to reinforcement exercises
- 10 Applications of Differentiation and Integration
- 10.1 Review
- 10.2 Revision
- 10.3 Reinforcement
- 10.4 Applications
- Answers to reinforcement exercises
- 11 Vectors
- 11.1 Introduction – representation of a vector quantity
- 11.2 Vectors as arrows
- 11.3 Addition and subtraction of vectors
- 11.4 Rectangular Cartesian coordinates in three dimensions
- 11.5 Distance in Cartesian coordinates
- 11.6 Direction cosines and ratios
- 11.7 Angle between two lines through the origin
- 11.8 Basis vectors
- 11.9 Properties of vectors
- 11.10 The scalar product of two vectors
- 11.11 The vector product of two vectors
- 11.12 Vector functions Contents
- 11.13 Differentiation of vector functions
- 11.14 Reinforcement
- 11.15 Applications
- 11.16 Answers to reinforcement exercises
- 12 Complex Numbers
- 12.1 What are complex numbers?
- 12.2 The algebra of complex numbers
- 12.3 Complex variables and the Argand plane
- 12.4 Multiplication in polar form
- 12.5 Division in polar form
- 12.6 Exponential form of a complex number
- 12.7 De Moivre’s theorem for integer powers
- 12.8 De Moivre’s theorem for fractional powers
- 12.9 Reinforcement
- 12.10 Applications
- 12.11 Answers to reinforcement exercises
- 13 Matrices and Determinants
- 13.1 An overview of matrices and determinants
- 13.2 Definition of a matrix and its elements
- 13.3 Adding and multiplying matrices
- 13.4 Determinants
- 13.5 Cramer’s rule for solving a system of linear equations
- 13.6 The inverse matrix
- 13.7 Eigenvalues and eigenvectors
- 13.8 Reinforcement
- 13.9 Applications
- 13.10 Answers to reinforcement exercises
- and All That 14 Analysis for Engineers – Limits, Sequences, Iteration, Series
- 14.1 Continuity and irrational numbers
- 14.2 Limits
- 14.3 Some important limits
- 14.4 Continuity
- 14.5 The slope of a curve
- 14.6 Introduction to infinite series
- 14.7 Infinite sequences
- 14.8 Iteration
- 14.9 Infinite series
- 14.10 Tests for convergence
- 14.11 Infinite power series
- 14.12 Reinforcement
- 14.13 Applications
- 14.14 Answers to reinforcement exercises
- 15 Ordinary Differential Equations Contents
- 15.1 Introduction
- 15.2 Definitions
- variables 15.3 First order equations – direct integration and separation of
- 15.4 Linear equations and integrating factors
- 15.5 Second order linear homogeneous differential equations
- 15.6 The inhomogeneous equation
- 15.7 Reinforcement
- 15.8 Applications
- 15.9 Answers to reinforcement exercises
- 16 Functions of More than One Variable – Partial Differentiation
- 16.1 Introduction
- 16.2 Function of two variables
- 16.3 Partial differentiation
- 16.4 Higher order derivatives
- 16.5 The total differential
- 16.6 Reinforcement
- 16.7 Applications
- 16.8 Answers to reinforcement exercises
- 17 An Appreciation of Transform Methods
- 17.1 Introduction
- 17.2 The Laplace transform
- 17.3 Laplace transforms of the elementary functions
- 17.4 Properties of the Laplace transform
- 17.5 The inverse Laplace transform
- 17.6 Solution of initial value problems by Laplace transform
- 17.7 Linear systems and the principle of superposition
- 17.8 Orthogonality relations for trigonometric functions
- 17.9 The Fourier series expansion
- 17.10 The Fourier coefficients
- 17.11 Reinforcement
- 17.12 Applications
- 17.13 Answers to reinforcement exercises
- Index
やまだぃちぅ
(やまだぃちぅ)
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