目录 Chapter 7 Infinite Series 7.1 Series Exercises 7.1 7.2 Series with Positive Terms 7.2.1 The Comparison Tests 7.2.2 The Root and Ratio Tests Exercises 7.2 7.3 Alternating Series and Absolute Convergence 7.3.1 Alternating Series 7.3.2 Absolute Convergence Exercises 7.3 7.4 Power Series Exercises 7.4 7.5 Differentiation and Integration of Power Series Exercises 7.5 7.6 Taylor Series 7.6.1 The Taylor Polynomials at x=0 (or Maclaurin Polynomials) 7.6.2 The Taylor’s series(or Maclaurin series) for function f at 0 7.6.3 The Taylor’s series for function f at a (an arbitrary real number) Exercises 7.6 Chapter 8 Partial Derivatives and Double Integrals 8.1 Functions of Two Variables Exercises 8.1 8.2 Limits and Continuity 8.2.1 Limits 8.2.2 Continuity Exercises 8.2 8.3 Partial Derivatives 8.3.1 Definition 8.3.2 Economical Interpretations of Partial Derivatives 8.3.3 Geometric Interpretations of Partial Derivatives Exercises 8.3 8.4 Strategy for Finding Partial Derivatives 8.4.1 The Chain Rule 8.4.2 Implicit Differentiation 8.4.3 Higher Derivatives Exercises 8.4 8.5 Total Differentials 8.5.1 Definition 8.5.2 Relations between Continuity, Partial Derivatives, and Differentiability 8.5.3 Rules for Finding Total Differentials 8.5.4 The Invariance of First Order Total Differential Form Exercises 8.5 8.6 Extremum of Functions of Two Variables 8.6.1 Locating Maxima and Minima 8.6.2 Methods of Finding Absolute Maxima and Minima 8.6.3 Methods of Finding Conditional Extremum Exercises 8.6 8.7 Directional Derivatives and The Gradient Vector 8.7.1 Vectors and Vector Operations
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