Spring 13 Classes:

480, 430

Courses taught in the past: Pre-Calculus and Calculus Sequences:151, 252,126, 140,  Linear algebra (460) Advanced Calc. 431.

Remember:

Be sure to get all your homework done as soon as possible after class as this will lead to better grades.

Links:

- Flash Movies: Chile 07, Chile 05, Korea 05.
- eJMT
- ATCM
- E-mail Me

-Math Applets.

Walker 203; Phone: (540) 831-5232

 

Math 430    Mathematical Analysis (Some call this Real Analysis or Advanced Calculus.)
  • Implicit Differentiation (A flash)
  • Derivative of a polar equation (A flash)
  1. Course Contract
  2. Officially, we will cover from Chapter 5. You need to preview chapters 3 and 4 on your own.
  3. NOTES ON SYMBOLIC LOGIC
  4. A link to an online advanced calculus course.
  5. Proving 1=2 (what went wrong?)
  6. Proving All People in Canada are the Same Age (what went wrong? (Need principle of induction)
  7. Interactive Real Analysis.
  8. Maple command to mean value theorem.
  9. Page 46-47 (Maple file)
  10. Homework: page 25, page 28, page 31.
  11. A problem from page 65 (Maple file).
  12. Homework: pages 41, 43, 48
  13. Mathematical Induction.
  14. Countable and uncountable sets (1)
  15. Page 58; pages 66-68
  16. Page68#17(b).mws 
  17. (0,1) is uncountable. (there is a typo in this page!)
  18. Definition of field/ring.
  19. Solving inequalities graphically. (page 83).
  20. homework page 83
  21. homework page 87
  22. homework page 89
  23. homework page 96
  24. homework page 97
  25. Explore the set of rational number is dense in R. (a Maple file). 
  26. homework page 105
  27. homework page 110
  28. homework page 120.
  29. homework on limit points. (page 124)
  30. homework on limits and partial limits (page 136)
  31. limit points and closed set.
  32. Hints for problems on Final.
  33. Hints to a homework.
  34. homework page 142.
Math 431
  1. Hint on Test 1. (Added March 21, 2011).
  2. Using Maple to learn sequences.
  3. About Recursive Sequence. (PDF file-include a 2d FTC example-Nov. 12)
  4. Using Fixed Point or Newton's method? When will 2^x>x^10? (November 12)
  5. More about Fixed Point and Newton's methods.
  6. Newton's Method
  7. Homework page 150
  8. Homework page 155
  9. Cauchy Sequence
  10. The speed of convergence of two series. (Maple file)
  11. A link to an online Real Analysis course.
  12. Using Maple to explore the limit of a function at  point. (Maple file). 
  13. Epsilon-delta concept.
  14. A ruler function
  15. Taylor polynomial, Fourier Series and Bernstein Polynomial.
  16. Another look at exploring the limit of a function at  point. (Maple file). 
  17. A proof to the squeezing principle. 
  18. Homework set 1 (Exercises on Cantor Theorem)
  19. Recall the relationship between a closed set and its limit points.
  20. Solution to page 175.
  21. Solution to page 195
  22. Understand the proofs of the followings:
    • A continuous function sends a closed and bounded set to a closed and bounded set.
    • If  f  is continuous on a closed and bounded set, then  f  assumes its maximum and minimum.
    • If  f  is continuous on a closed and bounded set, then  f  assumes all its intermediate value.
  23. Solution to (continuous functions on closed and bounded set).
  24. Solution to page 216.
  25. Some exercises on uniform continuous functions.
  26. About continuity and uniform continuity of a function.
  27. More about uniform continuity
  28. Continuity and Differentiability
  29. A nowhere differentiable function
  30. Converse of Mean Value Theorem (Dr. Yang's).
  31. Mean Value and Cauchy Mean Value Theorems (Dr. Yang's).
  32. Java applet on Mean Value Theorem.
  33. Cauchy Mean Value Theorem and L'Hopital's Rule
  34. Solution to page 237
  35. Taylor's Theorem.
  36. Second Partial Derivative Test (html).
  37. Fourier Series approximation is global but not local (Maple).
  38. Homework on Taylor Polynomial and its Remainder. (PDF)
    • Maple solution.
  39. Riemann Integration Theory
  40. Uneven partition and numerical integrations with singularities
  41. My own adaptive quadratures, good for functions that are monotone with singularities or highly oscillatory.
    • 1 dimensional closed quadrature (Maple, Matlab)
      • f(x)=1/sqrt(1-x^2) in [-1,0] Maple
    • 1 dimensional open quadrature (Maple, Matlab)
    • 2 dimensional closed quadrature (Maple, Matlab)
    • 2 dimensional open quadrature (Maple)
  42. Romberg Integration
  43. About Fubini's Theorem 1
  44. About Fubini's Theorem, double integral and etc.
  45. Animations for numerical integration
  46. Numerical Method.
  47. Animation on sequence of functions. (Maple file)
  48. Introduction to Topology.
  49. Hilbert space and Banach space.
  50. Cauchy Completeness and Hilbert space and Banach space.
  51. Online Mathematical Analysis
  52. Online Multivariable Calculus
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