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Lecture 1: Course Outline

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 1: Course Outline. Original formulas, diagrams, and example problems are retained.

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1.1 Advanced Mathematics

Outline

  • Differential Calculus of Single-variable Functions (Calculus in one variable is thefoundation, key point, and difficulty)
  • Calculus
  • Functions, limits (Difficulty), continuity
  • Derivatives and differentials
  • Mean value theorem for differential (Difficulty) and the application of derivatives
  • Integral Calculus
  • Indefinite integral
  • Definite integrals (Difficulty) and improper integrals
  • Application of Definite Integrals (Key Point)
  • Multivariable Differential Calculus
  • Calculus
  • Functions, limits (heavy limits, but not tested), continuous
  • Partial Derivatives and Total Differentials (Focuses on Total Derivatives)
  • Applications of differential calculus (Extrema and Extrema, Multivariate Has No Differential Mean Value Theorem)
  • Integral Calculus
  • Multiple integrals (double integral (difficulty) and triple integral)
  • Linear area division
  • Points application
  • Spatial analytic geometry and vector algebra
  • Differential equations
  • First-order equation
  • Reduced-order equation
  • Higher-order linear equations
  • Infinite series
  • Series of Constant Terms (Difficulty)
  • Power Series (Difficulty)
  • Fourier series