高等数学G1
王阳
目录
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1 chap.0 Preliminaries
1.1 real numbers
1.2 inequalities
1.3 coordinate system
1.4 slope
1.5 line equations
1.6 graphs of equations
1.7 functions and their graphs
1.8 operations on functions
1.9 trigonometric functions
1.10 chapter review
2 Chap.1 Limits
2.1 intuitive meaning of limit
2.2 one sides limit
2.3 main limit theorem
2.4 substitution limit
2.5 limits of trigonometric functions
2.6 limits at infinity
2.7 limits of sequences
2.8 infinite limits
2.9 continuity at a point
2.10 continuity of familiar functions
2.11 chapter review
3 Chap.2 The Derivative
3.1 The Tangent Line
3.2 Velocity
3.3 definition of derivative
3.4 equivalent forms for the derivative
3.5 increments
3.6 rules for finding deviratives
3.7 product rule
3.8 quotient rule
3.9 derivatives of trigonometric functions
3.10 chain rule
3.11 Higher-Order Derivatives
4 Chap.3 Applications of the Derivative
4.1 max&min existence theorem
4.2 critical point theorem
4.3 what are extreme values
4.4 monotonicity theorem
4.5 concavity
4.6 first derivative test
4.7 second derivative test
4.8 definition of antiderivative
4.9 power rule
4.10 indefinite integral is a linear operator
4.11 generalized power rule
5 Chap. 4 The Definite Integral
5.1 introduction to area
5.2 sigma notation
5.3 Inscribed/Circumscribed Polygons
5.4 Riemann sun
5.5 definition of definite integral
5.6 first fundamental theorem
5.7 second fundamental theorem
5.8 method of substitution
5.9 substitution rule for definite integral
5.10 chapter review
Inscribed/Circumscribed Polygons
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