What are the contents of advanced mathematics studied in vocational colleges at universities?

The main content of advanced mathematics in universities is calculus. Here is an example of the catalogue of the sixth edition of Tongji University, the most popular "Advanced Mathematics".

Chapter 1 Functions and Limits.

Section 1 Mappings and Functions.

Section 2 The Limits of the Sequence.

Section 3 Limits of Functions.

Section 4 Infinitesimal and Infinite.

Section 5 Limit Algorithms.

Section 6 Criterion for the Existence of Limits Two important limits.

Section 7 Infinitesimal Comparisons.

Section 8 Continuity and Break Points of Functions.

Section 9 The operation of continuous functions and the continuity of elementary functions.

Section 10 Properties of Continuous Functions on Closed Intervals.

General Exercise 1. Chapter 2 Derivatives and Differentiation.

Section 1 The Concept of Derivatives.

Section 2 Derivation of Functions.

Section 3 Higher-order derivatives.

Section 4 Derivatives of implicit functions and functions determined by parametric equations Correlation rate of change.

Section 5 Differentiation of Functions.

General Exercise 2. Chapter 3 The Differential Median Theorem and Applications of Derivatives.

Section 1 Differential Median Value Theorem.

Section 2 The Law of Lobida.

Section 3 Taylor's Formula.

Section 4 The monotonicity of functions and the concave and convex nature of curves.

Section 5 Extremums and Maximums and Minimums of Functions.

Section 6 Depiction of Function Graphs.

Section 7 Curvature.

Section 8 Approximate Solutions of Equations.

General Exercise 3. Chapter 4 Indefinite Integrals.

Section 1: The Concept and Properties of Indefinite Integrals.

Section 2 Commutation Integral Method.

Section 3 Partial Integral Method.

Section 4 Integrals of Rational Functions.

Section 5 Use of Points Tables.

Total Exercise 4. Chapter 5 Definite Integrals.

Section 1: The Concept and Properties of Definite Integrals.

Section 2 Basic Formulas of Calculus.

Section 3 Commutation method and partial integral method of definite integrals.

Section 4 Abnormal Points.

Section 5 Convergence of Anomalous Integrals Functions.

Total Exercise 5. Chapter 6 Application of Definite Integrals.

Section 1 The Elemental Method of Definite Integrals.

Section 2 Application of definite integrals in geometry.

Section 3 Application of definite integrals in physics.

Total Exercise 6. Chapter 7 Differential Equations.

Section 1 Basic Concepts of Differential Equations.

Section 2 Differential Equations for Separable Variables.

Section 3 Homogeneous Equations.

Section 4 First-Order Linear Differential Equations.

Section 5 Reduced-Order Higher-Order Differential Equations.

Section 6 Higher-Order Linear Differential Equations.

Section 7 Homogeneous linear differential equations with constant coefficients.

Section 8 Nonhomogeneous linear differential equations with constant coefficients.

Section 9 Euler's equations.

Section 10 Examples of solutions to systems of linear differential equations with constant coefficients.

Check out the information for yourself.

It doesn't feel like a pointless question.

The university of advanced mathematics and secondary school is very varied, secondary school is the foundation, and the conceptual formulas should be familiar. Advanced Mathematics focuses on the theory of calculus.

Generally, there will be slight differences in the professional settings of different schools, let me tell you about the courses I studied A certain 985 undergraduate mathematics:

Year 1: Analytic Geometry, Mathematical Analysis (3 semesters), Advanced Algebra (2 semesters), Topology;

Year 2: Complex Variable Functions, Ordinary Differential Equations, Real Variable Functions, Partial Differential Equations, Number Theory and Algebraic Structures, Abstract Algebra, Probability Theory, Mathematical Experiments.

Junior. Year 4: Mathematical Statistics, Functional Analysis, Differential Geometry, Fundamentals of Number Theory, Fundamentals of Operations Research, Computational Methods, Numerical Calculation Methods, Principles of Automatic Control, Databases and Data Structures, Fundamentals of Mechanics, Applied Statistical Methods, Linear Systems Theory, Numerical Solution of Differential Equations, Harmonic Analysis, Statistical Software, System Identification and Parameter Estimation, Time Series Analysis, Financial Mathematics, Preliminary Algebraic Topology, Group Representation Theory, Modular Forms, Theory of Subpure Functions, Complex Dynamical Systems, Theory of Multiple Complex Variable Functions, Modern Differential Geometry, Differential Dynamical Systems, Optimal Control, Mathematical Content Methods and Meanings, History of Mathematics, Simulation and Monto-Carlo Methods, Mathematical Culture, Special Topics in Mathematics, Mathematical Models, Algebraic Representation Theory.

P.S. Mathematics majors do not study the book "Advanced Mathematics".

Mathematical Analysis, Advanced Algebra, Analytic Geometry, Ordinary Differential Equations, Numerical Algebra, Consolidation and Functional, Probability Theory and Mathematical Statistics, etc.