Calculus Ⅰ

Practice more, learn more! Wish you enjoy this course and benifit from our lectures.


Calculus Ⅰ课程简介:前往报名学习

Calculus Ⅰ课程简介:

Practice more, learn more! Wish you enjoy this course and benifit from our lectures.


Calculus Ⅰ课程目录:

Functions and Models

--Four Ways to Represent a Function

--Mathematical Models:A Catalog of Essential Functions. New Functions from Old Functions

--Exponential Functions, Inverse Functions and Logarithms

Limits and Derivatives

--The Limit of a Function. Calculating Limits Using the Limits Laws

--The Precise Definition of a Limit. Continuity

--Limits at Infinity;Horizontal Asymptotes

--Derivatives and Rates of Change. The Derivative as a Function

Differentiation Rules

--Derivatives of Polynomials and Exponential Functions

--The Product and Quotient Rules

--Derivatives of Trigonometric Functions

--The Chain Rule,Implicit Differentiation

--Derivatives of Logarithmic Functions

--Exponential Growth and Decay

--Related Rates

--Linear Approximations and Differentials

--Hyperbolic Functions

Applications of Differentiation

--Maximum and Minimum Values

--The Mean Value Theorem

--How Derivatives Affect the Shape of a Graph

--Indeterminate Froms and 1'Hospital's Rule

--Optimization Problems

--Newton's Method



--Areas and Distances,The Definite Integral

--The Fundamental Theorem of Calculus

--Indefinite Integrals and the Net Change Theorem

--The Substitution Rule

Applications of Integration

--Areas Between Curves


--Volumes by Cylindrical Shells


--Average Value of a Function

Techniques of Integration

--Integration by Patrs

--Trigonometric Integral

--Trigonometric Substitution

--Integration of Rational Functions by Parital Fractions

--Approximate Integration

--Improper Integrals

Further Applications of Integration

--Arc Length

--Area of a Surface of Revolution

--Applications to Physics and Engineering

Differential Equations

--Modeling with Differential Equations

--Separable Equations

--Linear Equations

Parametric Equations and Polar Coordinates

--Curves Defined by Parametric Equations

--Calculus with Parametric Curves

--Polar Coordinates

--Areas and Lengths in Polar Coordinates

Calculus Ⅰ授课教师:



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