Advanced Calculus Exercises Fall 2017
Course Textbook: Principle of Mathematical Analysis, 3rd edition, by Walter Rudin
Fall Semester :
Exercises 1 (p. 21): Do 1, 2, 3, 4, 5
Exercises 2 (p. 22): Do 6, 12, 13, 14
Exercises 3 (p. 43): Do 6, 12, 13, 14
Exercises 4 (p. 44-46): Do 10, 11, 16, 19, 22
Exercises 5 (p. 78): Do 3, 4, 5, 6, 7
Exercises 6 (p. 79-82): Do 9, 14 (a) (b), 16 (a)
Read: Theorem 3.20 (p. 57-58), Theorem 3.43-3.44 (p. 70-71) and Examples 3.35 (p.67)
Exercises 7 (p. 98-102): Do 1, 2, 3, 4, 5, 6
Exercises 8 (p. 98-102): Do 8, 9, 13, 20, 21, 22
Exercises 9 (p. 114-119): Do 1, 2, 3, 4, 5, 6
Exercises 10 (p. 114-119): Do 22 (a), (b), (c); 25 (a), (b), (c); 26, 27
Exercises 11 (p. 165-171): Do 1, 2, 4, 7, 15, 16
Spring Semester 2018:
Exercises 1 : Chapter 6 (p. 138-142): Do 1, 2, 4, 5, 10 (a), (b), (c), 11, 15;
Chapter 7 (p. 167): Do 12, 18, 20
Exercises 2 : Chapter 8 (p. 196-203): Do 1, 7, 12, 13, 14, 15
Exercises 3 : Chapter 9 (p. 239-244): Do 1, 3, 5, 6, 7, 8, 9
Exercises 4 : Chapter 9 (p. 239-244): Do 16, 17, 18, 19, 23, 27
Advanced Calculus Exercises (Continued) Fall 2017
Reference: The Elements of Real Analysis 2nd edition, by Robert G. Bartle
Exercises 5 : Section 44 (p. 432): Do A, B, C, D, E, F, G
Exercises 6 : Section 45 (p. 451-454): Do A, B, C, D, E, F, G, N
Exercises 7 : Exercise Problems for Study Guide 14:
Section 5.2 Green’s Theorem (p.227-228) 1, 3, 4 ; Section 5.5 The Divergence Theorem (p.242) 1, 3 ; Section 5.7 Stokes’s Theorem (p.257) 1, 2.
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