Curriculum
0. Introduction
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1 FUNCTIONS AND LIMITS
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- 1.1 Four ways to Represent a Function (42:21)
- 1.2 Mathematical Models (66:22)
- 1.3 New Functions from old function (48:01)
- 1.4 The tangent and velocity Problems (19:24)
- 1.5 The Limit of a Function (29:05)
- 1.6 Calculating Limits Using the Limit Laws (30:49)
- 1.7 The Precise Definition of a Limit (21:40)
- 1.8 Continuity (25:56)
2 DERIVATIVES
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- 2.1 Derivatives and Rate of Change (36:32)
- 2.2 The Derivative as a Function (33:45)
- 2.3 Differential Formulas (35:30)
- 2.4 Derivatives of Trigonometric Functions (23:02)
- 2.5 Chain Rule (18:39)
- 2.6 Implicit Differentiation (20:27)
- 2.7 Rates of change in the nature and social science (15:43)
- 2.8 Related Rates (34:03)
- 2.9 Linear Approximation and Differentials (24:28)
3 APPLICATIONS OF DIFFERENTIATION
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- 3.1 Maximum and Minimum Values (27:54)
- 3.2 Mean Value Theorem (26:03)
- 3.3 What derivatives tell us the shape of a graph (41:13)
- 3.4 Limit at Infinity(Horizontal Asymptotes) (30:01)
- 3.5 Summary of Curve Sketching (46:45)
- 3.6 Graphing with Calculus and Technology (33:46)
- 3.7 Optimization Problems (31:34)
- 3.8 Newton's Method (22:40)
- 3.9 Antiderivative (30:49)
4 INTEGRALS
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