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Ch1 Limit
1-1 Def of Limit
1-2 One-Sided Limit
1-3 Continuity
1-4 Limit at Infinity
Ch2 Differentiation
2-1 Def of Derivative
2-2 Rules of Differentiation
2-3 Chain Rule and Implicit Differentiation
2-4 Derivatives of Exponential and Logarithmic F
2-5 Numerical Approximate–Differentials
2-6 Derivatives of Trigonometric Functions
2-7 Derivatives of Inverse Trigonometric Functions
Ch 3
Applications of Derivatives
3-1 Mean Value Theorem
3-2 Increasing and Decreasing Functions
3-3 Maximum and Minimum Values
3-4 The Max- Min Problems
3-5 Concavity and Points of Inflection
3-6 Asymptotes
3-7 Sketching curve
3-8 L' Hopital's Rule
3-9 Taylor Series
3-10 Applications In Marginal Analysis
3-11 Elasticity
Ch4 Indefinite Integrals
4-1 Antiderivatives and Indefinite Integrals
4-2 Integration by Changing Variables
4-3 Integration by Parts
4-4 Trigonometric Integrals
4-5 Integration by Partial Frations
4-6 Trigonometric and Half Angle Substitution
Ch5 Definite Integrals
5-1 Definition of Definite Integral
5-2 The Fundamental Theorem of Calculus
5-3 The Approximate Integration
5-4 The Improper Integrals
Ch6 Applications of Integration
6-1 Areas between Curves
6-2 Areas in Polar Coordinates
6-3 Arc Length
6-4 Volumes and The Volumes of Revolution
6-5 Area of a Surface of Revolution
6-6 Centroid of A Plane Region
6-7 Work and Problems of The Engineering
Ch7 Partial Derivatives
7-1 Limits and Continuity
7-2 Partial Derivatives
7-3 The Differentials and Chain Rules
7-4 Extrema of Functions of Two Variables
7-5 Directional Derivatives, Gradient and Tangent Plane
Ch8 Multiple Integration
8-1 Integrals over a Rectangle
8-2 Integrals over a Region
8-3 Three-Dimensional Iterated Integrals
8-4 Multiple Integration in Polar, Cylindrical and Spherical Coordinates
8-5 Applications of Multiple Integrals
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