导语

  

内容提要

  

    於嵩、吴斌主编的《数学（微积分）（英文版）》是为国际文凭课程大学预科项目（IBDP）设计的数学微积分选修辅导书，内容涵盖了IBDP数学HL微积分教学大纲的所有内容。全书分为6个模块，每个模块以知识点分节，每节包含知识点梳理、例题演示和相关习题这3部分，每个模块后有综合题练习。书中的例题和习题都力求提供详细的解题步骤或多种思考方向。本书重点在于微积分科目系统的解题训练，以及专业的IB答题思路指导。

1  Limits, continuous and differentiable functions
  1.1  Limits of sequences
  1.2  Limits of functions
  1.3  Squeeze Theorem
  1.4  Continuity of functions
  1.5  Differentiable functions
  Module one miscellaneous questions
2  Rolle's theorem and Mean Value Theorem
  2.1  Rolle's theorem
  2.2  Mean Value Theorem (MVT)
  Module two miscellaneous questions
3  Fundamental Theorem of Calculus and improper integrals
  3.1  Fundamental Theorem of Calculus
  3.2  Improper integrations of the form
  3.3  Approximation 'of improper integrals
  Module three miscellaneous questions
4  Infinite series and power series
  4.1  Sum of infinite geometric series
  4.2  Test for Divergence
  4.3  Integral Test
  4.4  Comparison Test
  4.5  Limit Comparison Test
  4.6  Alternating Series Test
  4.7  Absolute and conditional convergence
  4.8  Ratio Test
  4.9  Telescoping series
  4.10  Power series
  Module four miscellaneous questions
5  Taylor and Maclaurin series
  5.1  Revision: power series and its convergence
  5.2  Taylor and Maclaurin series
  5.3  Taylor and Maclaurin polynomials
  5.4  Taylor and Maclaurin series with their "friends"
  Module five miscellaneous questions
6  Differential equation
  6.1  Introduction to differential equation
  6.2  Solving the first order differential equations by graphical method
  6.3  Solving the first order differential equations by numerical method
  6.4  Solving the first order differential equations by analytic method
  6.5  The first order differential equation and the Taylor or Maclaurin series
  Module six miscellaneous questions
Answers of exercises