Homework Assignments (Fall 2021)


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Chapter 6 The Riemann and Riemann Stieltjes Integral
    6.1 The Riemann Integral 1, 3(a), 4(a,c), 5, 6, 8 (* 7, 9, 11, 13) 6.2 Properties of the Riemann Integral 2 (a), 3, 5, 10 (* 4, 6) 6.3 Fundamental Theorems of Calculus 1, 3, 4, 5(a,b), 9, 11(a, c) (* 5(c,d), 7, 8, 12, 14) 6.4 Improper Riemann Integrals 1(a,d,f), 2 (a, c, e), 3(a,b), 4, 5, 7 (* 1(b,c), 2(b,d), 3(c), 6, 8)
Chapter 7 Series of Real numbers
    7.1 Convergence Tests 1, 2(a, c, d, f, h, i, k, m, n), 3(a,b), 4 (a,b,d), 5, 6, 7, 13, 14 (* 2(b,e, g,j,l), 3 (b), 4( c,e, f), 8, 10, 11) 7.2 The Dirichlet Test 1, 4, 5 (a, c, e, g), 6, 8 (* 5 (b, d, f, h), 7) 7.3 Absolute and Conditional Convergence 2, 5, 6 (a, c, e, h), 7, 8, 10, 11, 12 (* 1, 3, 4, 6 (b, d, f, g,i), 9 ) 7.4 Square Summable Sequences
Chapter 8 Sequences and Series of Functions
    8.1 Pointwise Congergence and Interchange of Limits 1 (a, c), 3, 4, 5, 6 (* 1(b,d), 2) 8.2 Uniform Convergence 2, 4, 5, 8 (a,c), 9 (a, c, e), 10, 11, 12, 16 (the first problem) (* 1, 3, 6, 7, 8 (b,d), 9 (b,d), 13, 16 (the second problem)) 8.3 Uniform Convergence and Continuity 1, 2, 4, 6, 9, 12 (* 3, 5, 7) 8.4 Uniform Convergence and Integration 1, 3, 4, 5, 9 (* 2, 6, 10) 8.5 Uniform Convergence and Differentiation 1, 2, 3, 4, 6 (a, c) (* 6 (b, d), 7) 8.6 The Weierstrass Approximation Theorem 1, 4, 6, 7, 8 (* 3, 5) 8.7 The Power Series Expansions Part I : 1 (a,c,d), 2 (a, b), 3 (a), 7, 9 (* 1 (b, e, f), 2(c), 3(b), 8) Part II : 11, 12 (b,d e), 13 (a, b) (* 10, 12(a, c, f)) 8.8 The Gamma Function 1, 3, 5 (* 2, 6)