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Lean Calculus
Dr. Chad Scott
Contents
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Front Matter
Preface
1
Limits
1.1
The Main Idea
1.2
Infinity Stuff
1.3
Properties
2
Continuity
2.1
Definition
2.2
Basic Properties
2.3
Intermediate Values
3
Derivatives
3.1
Tangent Problem
3.2
Definition
3.3
Basic Properties
3.4
Chain Rule
4
Derivative Applications
4.1
Inverse Functions
4.2
Implicit Functions
4.3
Intro to Optimization
4.4
Extreme Value Theorem
4.5
Modeling
5
Integration
5.1
Area Problem
5.2
Riemann’s Solution
5.3
Definition
5.4
A Full Example
6
Fundamental Theorem
6.1
The Theorem
6.2
Antiderivatives
7
Appendix
7.1
Areas
7.2
Velocity
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Chapter
7
Appendix
7.1
Areas
7.2
Velocity
