Welcome to the homepage of Calculus Ⅰ !
Tips: 凌波能信步，苦海岂无边。
Course Introduction
Course number: 00010011A Credit: 5
The teaching content of this course is as follows:
Section
Content
1. Review of Basic Elementary Mathematics
Fundamental concepts of set theory
Mappings and functions
Basic elementary functions
Composite functions and elementary functions
Complex numbers and polar coordinates
2. Limits and Continuity
Sequences and limits of functions
Continuity and discontinuities of functions
Properties of continuous functions on closed intervals
3. Differential Calculus
Definition of derivatives and arithmetic operation rules
Derivative rules for inverse functions, composite functions, and basic derivative formulas
Logarithmic differentiation, implicit function differentiation, and derivative rules for parametric equations
Definition and properties of differentials
Mean value theorems (L'Hôpital's rule, Lagrange's mean value theorem, Cauchy's mean value theorem)
Taylor's formula
4. Integral Calculus
Primitive functions, definitions, and properties of indefinite integrals
First and second substitution methods, integration by parts, and basic integration formulas for indefinite integrals
Definitions and properties of definite integrals, Newton-Leibniz formula
Substitution and integration by parts for definite integrals
Method of evaluating definite integrals using infinitesimals
Geometric applications of definite integrals (area of plane figures, volume via cross-sectional areas, curve arc length, volumes/surface areas of rotating surfaces, curve curvature, etc.)
