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