Multivariable Calculus

A Linear Algebra Based Approach

Häftad, Engelska, 2022

Av Michael Olinick, Olinick

2 909 kr

Beställningsvara. Skickas inom 5-8 vardagar

Fri frakt för medlemmar vid köp för minst 249 kr.

A linear algebra based approach, covering topics including vector differential calculus, multiple integrals and vector field theory.

Produktinformation

Utgivningsdatum2022-02-21
FormatHäftad
SpråkEngelska
Antal sidor310
FörlagKendall/Hunt Publishing Co ,U.S.
ISBN9798765705070

Tillhör följande kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Preface1 Remembrance of Things Past1.1 Calculus1.1.1 Limits, Continuity, and the Derivative1.1.2 Properties and Uses of the Derivative1.1.3 The Definite Integral1.1.4 Fundamental Theorem of Calculus1.1.5 Taylor’s Theorem1.2 Linear Algebra1.2.1 Vectors1.2.2 Linear Independence1.2.3 Matrices1.2.4 Eigenvalues and Eigenvectors1.3 Exercises and Projects2 Vector-Valued Functions of One Variable2.1 Curves in the Plane and Space2.2 Limits and Continuity2.3 Derivatives2.4 Velocity, Speed, and Acceleration2.5 Integrals2.6 Applications2.6.1 Projectile Motion2.6.2 Kepler’s Laws of Planetary Motion2.7 Exercises and Projects3 Real-Valued Functions of a Vector: The Derivative3.1 Some Examples3.2 Graphs and Level Sets3.3 Partial Derivatives3.4 Parametrized Surfaces3.5 Applications3.5.1 Utility Functions3.5.2 An Age-Structured Population Model3.6 Exercises and Projects4 Differentiable Functions4.1 Limits and Continuity4.2 Differentiability4.3 Directional Derivatives4.4 A Mean Value Theorem4.5 The Jacobian Matrix4.6 Applications4.6.1 Economic Growth4.6.2 Newton’s Method4.7 Exercises and Projects5 Vector Differential Calculus5.1 Differentiating Compositions of Functions5.1.1 The Little Chain Rule5.1.2 General Chain Rule5.2 Change of Variables5.3 Gradient Fields5.4 Normal Vectors5.5 Implicit Differentiation5.6 Extreme Values 5.6.1 Critical Values 5.6.2 Method of Lagrange Multipliers5.6.3 Second Derivative Criteria5.7 Alternative Coordinate Systems5.7.1 Polar Coordinates5.7.2 Cylindrical Coordinates5.7.3 Spherical Coordinates5.8 Applications5.8.1 Maximizing Utility With Budget Constraint5.8.2 Laplace Equation5.9 Exercises and Projects6 Multiple Integrals 6.1 The Iterated Integral6.2 The Multiple Integral 6.2.1 Definition6.2.2 Existence6.2.3 Double Integrals6.2.4 Triple Integrals 6.3 Properties of the Integral6.4 Jacobians and the Change of Variable6.5 Improper Integrals6.6 Applications6.6.1 Probability6.6.2 Density and Moments6.7 Exercises and Projects7 Calculus Along Curves7.1 Work 7.2 Vector Fields and Line Integrals 7.2.1 Line Integrals7.3 Arc Length and Weighted Curves7.3.1 Weighted Curves7.4 Surfaces of Revolution7.5 Numerical Integration 7.6 Curvature and Normals 7.6.1 Curvature 7.7 Flow Lines and Differential Equations7.7.1 Alternative Notation for Vector Fields 7.8 Applications 7.9 Exercises and Projects8 Vector Field Theory8.1 Divergence and Curl8.1.1 Divergence of a Vector Field8.1.2 Properties of Divergence8.1.3 The Del Operator8.1.4 Curl 8.1.5 Derivative Identities8.2 Conservative Vector Fields8.2.1 Potential Functions8.2.2 Equivalent Notions of Path Equivalence 8.2.3 Symmetric Jacobians and Path Independence 8.3 Green’s Theorem in the Plane8.3.1 Setting for Green’s Theorem8.3.2 A Verification of Green’s Theorem8.3.3 Proof of Green’s Theorem for a Very Simple Region8.3.4 Green’s Theorem for Simple Regions8.3.5 Green’s Theorem for More Complicated Regions8.3.6 Using Green’s Theorem to Evaluate Line Integrals8.3.7 The Divergence Theorem8.3.8 Jacobian Symmetry and Gradient Fields8.3.9 Finding Potentials Using Partial Integration8.4 Surface Integrals 8.4.1 Mass 8.4.2 Integrating Vector Fields Over Surfaces 8.4.3 Orientation 8.5 Gauss’s Theorem 8.5.1 Gauss’s Theorem for Simple Regions8.5.2 Surface Independence 8.5.3 Meaning of Divergence8.6 Stokes’ Theorem 8.6.1 Proving Stokes’ Theorem 8.6.2 Simply Connected Surfaces and Conservative Fields8.6.3 Interpreting Curl 8.6.4 Independence of Surface 8.6.5 An Historical Note 8.7 Applications 8.7.1 Geometry: Shoelace Theorem 8.7.2 Newton’s Law of Gravitational Attraction8.8 Exercises and Projects9 Differential Forms and Vector Calculus9.1 What Are Differential Forms?9.1.1 0-Forms9.1.2 1-Forms9.1.3 Integrating a 1-Form Over a Curve9.1.4 2-Forms 9.1.5 Integrating a 2-Form Over a Surface 9.1.6 3-forms 9.1.7 Integrating a 3-Form Over a Region9.2 Algebra of Forms 9.3 Differentiating Forms9.4 Generalizing the Fundamental Theorem of Calculus 9.4.1 Gauss’ Theorem9.4.2 Stokes’ Theorem 9.5 Exercises and ProjectsIndex

Mer från samma författare

Mathematical Modeling in the Social and Life Sciences

Mathematical Modeling in the Social and Life Sciences

Michael Olinick

1 149 kr

Simply Turing

Del 21

Simply Turing

Michael Olinick

119 kr

Du kanske också är intresserad av

Simply Turing

Del 21

Simply Turing

Michael Olinick

119 kr

Mathematical Modeling in the Social and Life Sciences

Mathematical Modeling in the Social and Life Sciences

Michael Olinick

1 149 kr

Den yttersta hemligheten

Nyhet

Del 6

Den yttersta hemligheten

329 kr

Harry Potter och de vises sten

Del 1

Harry Potter och de vises sten

439 kr

Kvinnorna

4 pocket för 3

Kvinnorna

125 kr

Hon som blev kvar

4 pocket för 3

Hon som blev kvar

125 kr

Lovisas val

4 pocket för 3

Del 1

Lovisas val

Ruth Kvarnström-Jones

125 kr

Alchemised

Nyhet

Alchemised

349 kr

Hitster Christmas

Nyhet

Hitster Christmas

Jumbo

259 kr

Vitön. : Den fristående fortsättningen på Expeditionen

Nyhet

Vitön. : Den fristående fortsättningen på Expeditionen

399 kr