A math primer for engineers /

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Mathematics and engineering are inevitably interrelated, and this interaction will steadily increase as the use of mathematical modelling grows. Although mathematicians and engineers often misunderstand one another, their basic approach is quite similar, as is the historical development of their res...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Cryer, Colin W. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Amsterdam : Ios Press, 2014.
Colección:Studies in health technology and informatics ; v. 195.
Temas:
Engineering mathematics.
Mathématiques de l'ingénieur.
TECHNOLOGY & ENGINEERING > Engineering (General)
TECHNOLOGY & ENGINEERING > Reference.
Engineering mathematics
Matematik.
Ingenjörsvetenskap.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Title Page
  • Preface
  • Contents
  • 1 Numbers and Their Representation
  • 1.1 Introduction
  • 1.2 Real Numbers
  • 1.3 The Representation of Real Numbers
  • 1.4 Complex Numbers
  • 2 Sequences of Numbers
  • 2.1 Introduction
  • 2.2 The Convergence of Sequences
  • 2.3 The Convergence of Sequences (continued)
  • 2.4 A Criterion for Convergence: Cauchy Sequences
  • 2.5 Infinite Series
  • 2.6 Speed of Convergence
  • 2.7 Some Generalizations
  • 3 Functions of One Variable
  • 3.1 Sets
  • 3.2 Functions
  • 3.3 Elementary Functions
  • 3.3.1 Polynomials
  • 3.3.2 Rational Functions3.3.3 Trigonometric Functions
  • 3.3.4 Exponential and Logarithmic Functions
  • 3.3.5 Hyperbolic Functions
  • 3.4 Piecewise Continuous Functions
  • 3.5 Composite Functions
  • 3.6 Special Functions
  • 3.7 Functions of a Complex Variable
  • 4 Two-dimensional Analytic Geometry
  • 4.1 Introduction
  • 4.2 Two-dimensional Analytic Geometry
  • 4.3 Lines
  • 4.4 Triangles and Polygons
  • 4.5 Conic Sections
  • 4.5.1 The Circle
  • 4.5.2 The Ellipse
  • 4.5.3 The Hyperbola
  • 4.5.4 The Parabola
  • 4.6 Other Two-dimensional Curves
  • 4.7 Inside or Outside?5 Linear Algebra
  • 5.1 Introduction
  • 5.2 Vectors and Matrices
  • 5.3 Vector and Matrix Norms
  • 5.4 Inner products and Orthogonality in Rn
  • 5.5 Linear Algebraic Equations
  • 5.6 Determinants
  • 5.7 Eigenvalues and Eigenvectors
  • 5.8 Dimension and Bases
  • 5.9 Sequences of Vectors and Matrices
  • 6 Functions of Several Variables
  • 6.1 Introduction
  • 6.2 Inverse Mappings
  • 7 Calculus
  • 7.1 Differential Calculus
  • 7.1.1 Differentiation in One Dimension
  • 7.1.2 Partial Differentiation
  • 7.1.3 The Weierstrass Example
  • 7.2 Differentiation in Rn7.3 Applications of Differentiation
  • 7.3.1 Taylor Series
  • 7.3.2 Calculation of Extrema
  • 7.3.3 Newton's Method
  • 7.3.4 Spline Functions
  • 7.4 Integral Calculus
  • 7.4.1 Riemann Integrals in One Dimension
  • 7.4.1.1 Indefinite Integrals
  • 7.4.1.2 Definite Integrals
  • 7.4.1.3 The Connection between Definite and Indefinite Integrals
  • 7.4.1.4 Integration by Parts
  • 7.4.1.5 The Differentiation of Integrals with Parameters
  • 7.4.1.6 Improper Riemann Integrals
  • 7.4.1.6.0.1 One Endpoint Equal to
  • 7.4.1.6.0.2 The Integrand is Unbounded7.4.1.6.0.3 The Integrand is Discontinuous
  • 7.4.1.7 Evaluation of Integrals
  • 7.4.2 Riemann Integrals in Several Dimensions
  • 7.5 Integration by Substitution in n Dimensions
  • 7.6 The Relationship between Integrals in 1D and 2D
  • 7.7 The Riemann-Stieltjes Integral
  • 7.8 Analytic Functions
  • 7.8.1 Analytic Continuation
  • 7.8.2 Complex Integration
  • 7.8.3 The Calculus of Residues
  • 7.9 The Calculus of Finite Differences
  • 8 Linear Spaces
  • 8.1 Introduction
  • 8.2 The Linear Space C[a, b]

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