Chapter 8 Differential Calculus of Multivariable Functions 8.1 Limits and Continuity of Multivariable Functions 8.2 Partial Derivatives and Higher—Order Partial Derivatives 8.3 Linear Approximations and Total Differentials 8.4 The Chain Rule 8.5 Implicit Differentiation 8.6 Applications of Partial Derivatives to Analytic Geometry 8.7 Extreme Values of Functions of Several Variables 8.8 Directional Derivatives and The Gradient Vector 8.9 Examples Exercises 8
Chapter 9 Multiple Integrals 9.1 Double Integrals 9.2 Calculating Double Integrals 9.3 Calculating Triple Integrals 9.4 Concepts and Calculations of The First Type Curve Integral 9.5 The First Type Surface Integral 9.6 Application of Integrals 9.7 Examples Exercises 9
Chapter 10 The Second Type Curve Integral, Surface Integral,and Vector Field 10.1 The Second Type Curve Integral 10.2 The Green's Theorem 10.3 Conditions for Plane Curve Integrals Being Independent of Path, Conservative Fields 10.4 The Second Type Surface Integral 10.5 The Gauss Formula, The Flux and Divergence 10.6 The Stokes' Theorem, Circulation and Curl 10.7 Examples Exercises 10
Chapter 11 Infinite Series 11.1 Convergence and Divergence of Infinite Series 11.2 The Discriminances for Convergence and Divergence of Infmite Series with Positive Terms 11.3 Series With Arbitrary Terms, Absolute Convergence 11.4 The Discrinunances for Convergence of Improper Integral, г Function 11.5 Series with Function Terms, Uniform Convergence 11.6 Power Series 11.7 Expanding Functions as Power Series 11.8 Some Applications of The Power Series 11.9 Fourier Series 11.10 Examples Exercises 11
Appendix Ⅳ Change of Variables in Multiple Integrals Appendix Ⅴ Radius of Convergence of Power Series
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