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我以前自己做的几门课的syllabus,有些名词表达,看能不能帮上你
1.Mathematical Analysis(A)Ⅰ: Limit of function and series, Continuity of function, One variable differential calculus (derivative, differential, differential mean-value theorems, Taylor Formula)
2.Mathematical Analysis(A)Ⅱ: One variable integral calculus (indefinite integral, the fundamental theorem of calculus, integral mean-value theorems, the sufficient and necessary conditions for integrability, improper integrals), Number series, Function sequence and series, Power series, Fourier series.
3.Mathematical Analysis(A) Ⅲ: The theorems of the completeness of real numbers (Cauchy convergence theorem, nested intervals theorem, Weierstrass cluster point theorem, Heine-Borel finite covering theorem, supremum principle, bounded monotonic series theorem, and the proofs of their equivalence), Multivariable calculus (implicit function theorem, the integral with parameters, Gauss/Stokes Formula and field theory, introduction to the calculus on manifolds)
4.Linear AlgebraⅠ: Operations of determinant, Linear equations, Matrix theories, Linear space and linear transformation.
5.Linear AlgebraⅡ: Bilinear function and quadratic form (Matrix congruence), Canonical forms of matrices and space decomposition (Jordan form, Matrix similarity, Cayley-Hamilton theorem, cyclic decomposition theorem), Euclidean space and unitary space, Orthogonal and symplectic geometric space, Introduction to tensor product.
6.Probability Theory: Event and probability, Random variable and distribution function, Numerical characteristic and characteristic function, Limit theory (Helly theorems, inverse limit theorem, central limit theorems, the laws of large numbers).
7.Stochastic Processes: Poisson processes, Markov processes, Stationary processes, Random walk, Brownian motion, Introduction to stochastic calculus. |
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