基本介紹
- 中文名：Calculus I
- 提供院校：電子科技大學
- 類別：慕課
- 授課老師：費銘崗
課程大綱,參考教材,
課程大綱
The First Week: 1 Introduction
1.2 What is Calculus?
1.4 How to study Calculus?
1.1 Why study Calculus?
1.3 Why in English?
The First Week: 2 Limits and Continuity
2.2 Limit of a Function
2.1 Rate of change and tangents to curves
2.4 How to Find Limits
2.3 Limit Laws
The Second Week: 2 Limits and Continuity
2.6 Limit Involving sinx/x
2.9 Limits Involving Infinity
2.7 Continuity
2.8 The Intermediate Value Theorem
2.5 One-sided Limits
Unit Test-CH2
The Third Week: 3 Differentiation
3.1 Tangents of a curve
3.2 Derivative at a point
The Fourth Week: 3 Differentiation
3.5 When does a function not have a derivative
3.3 Derivative as a function
3.6 Differentiability implies continuity
3.4 Differentiable on an interval
The Fifth Week: 3 Differentiation
3.10 The Chain Rule
3.7 Differentiation rules I
3.9 Derivatives of trigonometric functions
3.8 Differentiation rules II
The Sixth Week: 3 Differentiation
3.11 L'Hopital's Law
3.12 Implicit differentiation
3.14 Differential
3.13 Linearization
Unit Test-CH3
The Seventh Week: 4 Applications of Derivatives
4.5 Corollaries of Mean Value Theorem
4.3 Rolle's Theorem
4.1 The extreme value
4.2 Where extreme values are located
4.4 Mean Value Theorem
The Eighth Week: 4 Applications of Derivatives
4.6 Monotonicity
4.9 Newton's method
4.7 Concavity
4.8 Curve sketching
4.10 Antiderivative and Indefinite integral
Unit Test-CH4
The Ninth Week: 5 Integration
5.2 Sigma notation
5.4 Riemann sum and definite integral
5.1 Area and estimating by finite sum
5.3 Limit of finite sum
The Tenth Week: 5 Integration
5.5 Integrable and nonintegrable functions
5.8 Fundamental Theorem of Calculus-Part 1
5.7 Mean Value Theorem of definite integral
5.9 Fundamental Theorem of Calculus-Part 2
5.6 Area under curve
The Eleventh Week: 6 Applications of Definite Integral
6.3 Washer method for volume
6.2 Disk method for volume
6.1 Cross-section method for volume
The Eleventh Week: 5 Integration
5.13 Substitution method for definite integral
5.10 Relation between differentiation and integration
5.12 Substitution method for indefinite integral
5.11 Total area
Unit Test-CH5
The Twelfth Week: 7 Transcendental Functions
7.1 Inverse function and its derivative
7.2 Natural Logarithm
7.4 Indeterminate Forms
7.5 Relative rate of growth
7.3 Exponential function
Unit Test-CH6,7
The Twelfth Week: 6 Applications of Definite Integral
6.5 Arc Length
6.6 Areas of surfaces of revolution
6.4 Cylindrical shells for volume
The Thirteenth Week: 8 Techniques of Integration
8.3 Trigonometric substitution
8.2 Trigonometric integrals
8.6 Improper integrals II
8.1 Integration by parts
8.4 Integration of rational functions
8.5 Improper integrals I
Unit Test-CH8
The Fourteenth Week: 9 Ordinary Differential Equations
9.6 Second-order linear differential equations-homogenous II
9.2 Separable differential equations
9.7 Nonhomogenous differential equations
9.4 Bernoulli equations
9.8 Euler equations
9.5 Second-order linear differential equations-homogenous I
9.3 First-order linear differential equations
9.1 General first-order differential equations and solutions
Unit Test-CH9
參考教材
《Thomas' Calculus》, G. B. Thomas, M. D. Weir and J. R. Hass, 12th edition, Pearson's company, 2010
