slides for cisc 2315: discrete structures chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/chapter...
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![Page 1: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/1.jpg)
Slides for CISC 2315: Discrete Structures
Chapters 6 & 7
CISC 2315 Discrete Structures
Professor William G. Tanner, Jr.
Fall 2008
Slides created by James L. Hein, author of Discrete Structures, Logic, and Computability, 2002, 2nd Edition, Jones & Bartlett Computer Science, ISBN 0-7637-1843-2.
![Page 2: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/2.jpg)
Chapter 6
Section 6.1 How does one reason?
CISC 2315 Discrete Structures
William G. Tanner, Jr.
Fall 2008
Slides created by James L. Hein, author of Discrete Structures, Logic, and Computability, 2002, 2nd Edition, Jones & Bartlett Computer Science, ISBN 0-7637-1843-2.
![Page 3: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/3.jpg)
Section 6.1 How does one reason?
![Page 4: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/4.jpg)
Chapter 6
Section 6.2 Propositional Calculus
CISC 2315 Discrete Structures
William G. Tanner, Jr.
Fall 2008
Slides created by James L. Hein, author of Discrete Structures, Logic, and Computability, 2002, 2nd Edition, Jones & Bartlett Computer Science, ISBN 0-7637-1843-2.
![Page 5: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/5.jpg)
Section 6.2 Propositional Calculus
![Page 6: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/6.jpg)
Section 6.2 Propositional Calculus
![Page 7: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/7.jpg)
Section 6.2 Propositional Calculus
![Page 8: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/8.jpg)
Section 6.2 Propositional Calculus
![Page 9: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/9.jpg)
Section 6.2 Propositional Calculus
![Page 10: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/10.jpg)
Section 6.2 Propositional Calculus
![Page 11: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/11.jpg)
Section 6.2 Propositional Calculus
![Page 12: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/12.jpg)
Chapter 6
Section 6.3 Formal Reasoning
CISC 2315 Discrete Structures
William G. Tanner, Jr.
Fall 2008
Slides created by James L. Hein, author of Discrete Structures, Logic, and Computability, 2002, 2nd Edition, Jones & Bartlett Computer Science, ISBN 0-7637-1843-2.
![Page 13: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/13.jpg)
Section 6.3 Formal Reasoning
![Page 14: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/14.jpg)
Section 6.3 Formal Reasoning
![Page 15: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/15.jpg)
Section 6.3 Formal Reasoning
![Page 16: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/16.jpg)
Section 6.3 Formal Reasoning
![Page 17: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/17.jpg)
Section 6.3 Formal Reasoning
![Page 18: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/18.jpg)
Section 6.3 Formal Reasoning
![Page 19: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/19.jpg)
Section 6.3 Formal Reasoning
![Page 20: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/20.jpg)
Section 6.3 Formal Reasoning
![Page 21: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/21.jpg)
Section 6.3 Formal Reasoning
![Page 22: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/22.jpg)
Chapter 6
Section 6.4 Formal Axiom Systems
CISC 2315 Discrete Structures
William G. Tanner, Jr.
Fall 2008
Slides created by James L. Hein, author of Discrete Structures, Logic, and Computability, 2002, 2nd Edition, Jones & Bartlett Computer Science, ISBN 0-7637-1843-2.
![Page 23: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/23.jpg)
Section 6.4 Formal Axiom Systems
![Page 24: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/24.jpg)
Section 6.4 Formal Axiom Systems
![Page 25: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/25.jpg)
Chapter 7
Section 7.1 First-Order Predicate Calculus
CISC 2315 Discrete Structures
William G. Tanner, Jr.
Fall 2008
Slides created by James L. Hein, author of Discrete Structures, Logic, and Computability, 2002, 2nd Edition, Jones & Bartlett Computer Science, ISBN 0-7637-1843-2.
![Page 26: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/26.jpg)
Section 7.1 First-Order Predicate Calculus
![Page 27: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/27.jpg)
Section 7.1 First-Order Predicate Calculus
![Page 28: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/28.jpg)
Section 7.1 First-Order Predicate Calculus
![Page 29: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/29.jpg)
Section 7.1 First-Order Predicate Calculus
![Page 30: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/30.jpg)
Section 7.1 First-Order Predicate Calculus
![Page 31: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/31.jpg)
Section 7.1 First-Order Predicate Calculus
![Page 32: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/32.jpg)
Section 7.1 First-Order Predicate Calculus
![Page 33: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/33.jpg)
Section 7.1 First-Order Predicate Calculus
![Page 34: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/34.jpg)
Chapter 7
Section 7.2 Equivalent Formulas
CISC 2315 Discrete Structures
William G. Tanner, Jr.
Fall 2008
Slides created by James L. Hein, author of Discrete Structures, Logic, and Computability, 2002, 2nd Edition, Jones & Bartlett Computer Science, ISBN 0-7637-1843-2.
![Page 35: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/35.jpg)
Section 7.2 Equivalent Formulas
![Page 36: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/36.jpg)
Section 7.2 Equivalent Formulas
![Page 37: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/37.jpg)
Section 7.2 Equivalent Formulas
![Page 38: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/38.jpg)
Section 7.2 Equivalent Formulas
![Page 39: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/39.jpg)
Section 7.2 Equivalent Formulas
![Page 40: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/40.jpg)
Section 7.2 Equivalent Formulas
![Page 41: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/41.jpg)
Section 7.2 Equivalent Formulas
![Page 42: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/42.jpg)
Chapter 7
Section 7.3 Formal Proofs in Predicate Calculus
CISC 2315 Discrete Structures
William G. Tanner, Jr.
Fall 2008
Slides created by James L. Hein, author of Discrete Structures, Logic, and Computability, 2002, 2nd Edition, Jones & Bartlett Computer Science, ISBN 0-7637-1843-2.
![Page 43: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/43.jpg)
Section 7.3 Formal Proofs in Predicate Calculus
![Page 44: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/44.jpg)
Section 7.3 Formal Proofs in Predicate Calculus
![Page 45: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/45.jpg)
Section 7.3 Formal Proofs in Predicate Calculus
![Page 46: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/46.jpg)
Section 7.3 Formal Proofs in Predicate Calculus
![Page 47: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/47.jpg)
Section 7.3 Formal Proofs in Predicate Calculus
![Page 48: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/48.jpg)
Section 7.3 Formal Proofs in Predicate Calculus
![Page 49: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/49.jpg)
Section 7.3 Formal Proofs in Predicate Calculus
![Page 50: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures](https://reader034.vdocuments.us/reader034/viewer/2022050115/5f4be704ec00e311773c96dd/html5/thumbnails/50.jpg)
Section 7.3 Formal Proofs in Predicate Calculus