Math 410, Advanced Calculus , Spring 2011


Course Outline

Textbook

Patrick M. Fitzpatrick, Advanced Calculus, 2-nd edition.

Tests

  • Test 1. Feb. 24
  • Material: Ch.1. Ch.2 Sections 2.1-2.4. Instead of Section 2.5: Theorem : A set S is compact if and only if it is closed and bounded. Ch.9: Section 9.1.
  • Test 2. April 7.
  • Material: Ch.3,4,5 . In section 3.6 consider the inverse of a continuous strictly monotone function. From Chapter 5 need to know properties of related functions, and use them to find derivatives and limits. In particular find limits by using L'Hopital's rule.
  • Quiz 1. Feb 15. Sections 1.1-2.4.
  • Quiz 2. March 15. Chapter 3. In Section 3.6 Theorem : The inverse of a continuous strictly monotone function is continuous and strictly monotone.
  • Quiz 3. April 21. Chapter 6 and Sections 7.2,7.3.
  • Final exam. May 16. 10:30-12:30.
  • Material: Chapters 1-7 see material for exams 1,2 and quizzes 1-3. Chapter 8: Sections 1-4 and 6. Chapter 9: Sections 1-5.

    Homework problems

  • Homeworks are normally assigned on Thursday and due next Tuesday.
  • HW 1. Section 1.1: Ex. 2,14,19. Section 1.2 : Ex.4. Section1.3: Ex. 17,19.
  • HW 2. Section 2.1 : Ex. 1,2,6,14,16. Due Feb. 7
  • HW 3. Section 2.2 : Ex. 4. Section 2.3 : Ex. 8,9. Section 2.4 : Ex. 10,12.
  • HW 4. Section 9.1: Ex. 1,2,3,6,8.
  • HW 5 Section 3.1 : Ex. 6, 9, 13. Section 3.3 : Ex. 3,7
  • HW 6 Section 3.4: Ex. 7. Section 3.5: Ex. 3 ( for f(x) = x^4 ), 9, 10. Section 3.6 : Ex.6.
  • HW 7. due march 17. Section 4.1: Ex. 8,11,12,17. Section 4.2: Ex. 4.
  • HW 8. due March 29. Section 4.3: Ex. 7, 10, 20, 21. Section 4.4: Ex. 5, 7.
  • HW 9. due April 12. Section 6.1: Ex.1. Section 6.2: Ex.3,5,9. Section 6.3: Ex. 6. Section 6.4: Ex.1,2
  • HW 10. due April 19. Section 6.5: Ex.5,6. Section 6.6: Ex.5,6. Section 7.3: Ex.3,4,9.
  • HW 11. due April 26. Section 8.1: Ex.4. Section 8.2: Ex.1,11. Section 8.3: Ex. 3,4. Section 8.4: Ex.2.
  • HW 12. due Thursday May 5. Section 9.1: Ex.7. Section 9.2: Ex.2,3. Section 9.3: Ex. 2,3. Section 9.4: Ex.1,2. Section 9.5: Ex.5.
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