Mathematics for Electronic Technology

Preface


1 Introductory Concepts


1.1 Differentiation


1.2 Integration


1.3 Partial Differentiation


1.4 Infinite Series


1.4.1 Convergent and Divergent Series


1.4.2 Taylor's and Maclaurin's Series


1.5 Vectors and Vector Algebra


1.6 Surface, Volume and Line Integrals


1.7 Examples


2 Determinants


2.1 The Solution of Linear Simultaneous Algebraic Equations


2.2 General Properties of Determinants


2.2.1 The Effect of Interchanging Rows and Columns


2.2.2 The Laplace Development


2.2.3 Other Theorems


2.3 Methods for Evaluating Determinants


2.3.1 Evaluating a Third-Order Determinant


2.3.2 Solution by Reduction to Triangular Form


2.3.3 Pivotal Condensation


2.4 Examples


3 Differential Equations


3.1 Fundamental Theorems for Linear Equations


3.1.1 Complementary Function and Particular Integral


3.2 Linear Differential Equations with Constant Coefficients


3.2.1 First-Order Equation with f(t) Zero


3.2.2 nth-Order Equation with f(t) Zero


3.2.3 The Operator D


3.2.4 Particular Integrals Derived Using the Operator D


3.3 Linear Equations with Variable Coefficients


3.3.1 Higher-Order Linear Differential Equations


3.4 Non-linear Differential Equations


3.4.1 Equations Soluble by the Separation of Variables


3.4.2 Homogeneous Equations


3.4.3 Bernoulli's Equation


3.4.4 Ricatti's Equation


3.4.5 General Observations on Non-linear Equations


3.5 Partial Differential Equations


3.6 Examples


4 Matrix Analysis


4.1 Definition and Properties of a Matrix


4.2 Some Network Manipulations


4.3 Inverse Matrices


4.4 Matrix Partition


4.5 Diagonalizing Matrices


4.6 Examples


5 The Complex Variable


5.1 The Complex Number


5.2 The Complex Plane


5.3 Complex Functions


5.3.1 Differentiation


5.4 Mapping


5.5 Integration


5.6 Circuit Applications


5.7 Examples


6 Topography and Graph Theory


6.1 Examples


7 Numerical Analysis


7.1 Introduction


7.2 Errors and Their Source


7.3 Calculation of the Roots of f(x)=0


7.3.1 Roots of Polynomials


7.4 Solution of Sets of Linear Algebraic Equations


7.4.1 Calculation of the Matrix Inverse


7.4.2 Calculation of the xi


7.5 The Solution of Differential Equations


7.6 Numerical Integration


7.7 Examples


8 Fourier Methods for Harmonic Analysis


8.1 The Dirichlet Conditions


8.2 The Evaluation of Fourier Coefficients


8.3 Wave Symmetry


8.4 Rate of Convergence of the Fourier Series


8.5 Fourier Spectra


8.6 Truncated Fourier Series and the Gibbs Phenomenon


8.7 The Exponential Series


8.8 The Fourier Integral


8.9 Examples


9 The Laplace Transform


9.1 The Limitations of the Fourier Transform


9.2 Differentiation and Integration of f(t)


9.3 A Table of Laplace Transforms


9.4 The Solution of Differential Equations


9.5 Circuit and System Analysis


9.6 The Convolution Theorem


9.7 Application to Other Forms of Differential Equation


9.8 Examples

Solutions

References

Index