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《麻省理工开放课程:18.01SC 单变量微积分(87集更新完毕!)》(Single Variable Calculus)开放式课程[MP4]

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中文名麻省理工开放课程:18.01SC 单变量微积分(87集更新完毕!)
英文名Single Variable Calculus
资源格式MP4
课程类型数学
学校MIT
版本开放式课程
发行日期2011年1月1日
地区美国
对白语言英语
简介

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本微积分课程涵盖了一个变量的函数的分化和整合,并与无穷级数的一个简短的讨论结束。微积分是许多科学学科,包括物理学,工程学和经济学的基本知识。



目录

1.Recitation Introduction
2.Graphing a Derivative Function
3.Smoothing a Piece-wise Function
4.Definition of the Derivative
5.Tangent Line to a Polynomial
6.Constant Multiple Rule
7.Derivatives of Sine and Cosine
8.Quotient Rule
9.Product Rule
10.Chain Rule
11.Implicit Differentiation
12.Graphing the Arctan Function
13.Arccos
14.Log and Exponent Derivatives
15.Rules of Logs
16.Hyperbolic trig functions
17.Implicit differentiation and linear approximation
18.Quadratic Approximation
19.Quadratic Approximation of a Product
20.Sketching a curve
21.Closest Point to the Origin
22.Maximum Surface Area
23.Minimum Triangle Area
24.Related rates 1
25.Using Newton's Method
26.Related rates 2
27.Mean Value Theorem
28.Mean value theorem 1
29.Computing Differentials
30.Antidiff. With Discontinuity
31.Linear approx. with differentials
32.Computing Antiderivatives
33.Differential Equation
34.Antidifferentiation by substitution
35.Differential Equation With Graph
36.Riemann sum
37.Computing the Volume of a Paraboloid
38.Definite Integrals of tan(x)
39.Summation Notation Practice
40.Definite Integral by Substitution
41.Applying the Second Fundamental Theorem
42.Second fundamental theorem and chain rule
43.Area Between the Graphs of Sine and Cosine
44.Second fundamental theorem and quadrdrtic approximation
45.Volume of a Paraboloid via Disks
46.Area Between y=x^3 and y=3x-2
47.Volume of Revolution via Shells
48.Average Velocity
49.Average x-Coordinate in a Region
50.Explanation of Simpson's rule
51.Using the Trapezoid and Simpson's ru
52.Trig Integral Practic
53.Trig Integrals and a Volume of Revolution
54.Integral of tan^4 (theta)
55.Integration by completing the square
56.Hyperbolic Trig Sub
57.Finding u and v' When Integrating by Parts
58.Partial Fractions Decomposition
59.Arc Length of y=x^(2_3)
60.Integrating sin^n(x) Using Reduction
61.Parametric Arclength
62.Surface Area of a Torus
63.Polar to Cartesian
64.Integration Practice I
65.Graph of r = 1 + cos(theta/2)
66.Integration Practice II
67.Integration Practice III
68.l'Hospital Practice
69.Integration Practice IV
70.Failure of L'Hospital's Rule
71.A Solid With Finite Volume and Infinite Cross Section
72.Integral of x^n e^(-x)
73.Limit of a Series
74.Improper Integrals
75.Comparison Tests
76.Ratio Test for Convergence
77.Integral Test
78.Ratio Test -- Radius of Convergence
79.Power Series Practice
80.Taylor's Series of a Polynomial
81.Finding Taylor's Series
82.Taylor's Series for sec(x)
83.Integration of Taylor's Series
84.Series Calculation Using a Riemann Sum
85.4J3, Diffusion of a Chemical
86.Indeterminate forms
87.Integral Test as Estimation

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