Math 2400 Lecture Notes: Integration
نویسنده
چکیده
1. The Fundamental Theorem of Calculus 1 2. Building the Definite Integral 5 2.1. Upper and Lower Sums 5 2.2. Darboux Integrability 7 2.3. Verification of the Axioms 10 2.4. An Inductive Proof of the Integrability of Continuous Functions 12 3. Further Results on Integration 13 3.1. The oscillation 13 3.2. Discontinuities of Darboux Integrable Functions 14 3.3. A supplement to the Fundamental Theorem of Calculus 17 3.4. New Integrable Functions From Old 19 4. Riemann Sums, Dicing, and the Riemann Integral 23 4.1. Riemann sums 24 4.2. Dicing 25 4.3. The Riemann Integral 27 5. Improper Integals 29 5.1. Basic definitions and first examples 29 5.2. Non-negative functions 29 References 32
منابع مشابه
Math 117 Lecture Notes
This is the set of lecture notes for Math 117 during Fall quarter of 2017 at UC Santa Barbara. The lectures follow closely the textbook [1].
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تاریخ انتشار 2012