MAT 371 - Advanced Calculus I
Spring 2010

Homework & Reading Assignments

Assignments are due at the beginning of class on the day listed.

January
Tuesday
 Thursday
21 First Class Day
23 Read the course syllabus.
Read §0.1: Sets
Read §0.2: Relations and Functions
Read §0.3: Mathematical Induction and Recursion
Read §0.4: Equivalent and Countable Sets
Note: This reading is review. If you struggle with these sections, make sure you have taken the appropriate prerequisites (in particular MAT 300).
28 Read §0.5: Real Numbers
HW1 Chapter 0: #6, 10, 14, 17, 19
(Solutions)
Note: Focus especially on the content and notation related to functions and index sets. Confusion with these two ideas are a leading source of difficulties later in this course.
30 Read §1.1: Sequences and Convergence
HW2 Chapter 0: #39, 41, 43, 44, Project 0.2
(Solutions)
Note: §0.5 is a crucial foundation for the rest of the course. The l.u.b. property is the central property of the real numbers that distinguishes it from other fields, such as the rational numbers, and will be a key tool that we use repeatedly in this course. Your goal should be to read and reread the definitions and proofs in this section until you can reproduce them without looking at the book.

February
Tuesday
 Thursday
2 Chapter 0 Quiz (See details)
4 Read §1.2: Cauchy Sequences
HW3 Write complete answers to Questions 4, 6, & 10 in the  Section 0.5 Study Guide and to Question 1 in the Chapter 1 Study Guide.
9 Read §1.3: Arithmetic Operations on Sequences
11 Read §1.4: Subequences and Monotone Sequences
HW4 Chapter 1: #3, 6, 7,  9
16 Read §2.1: Definition of the Limit of a Function
18 HW5 Chapter 1: #14, 15, 17, 22, 24, 35, 36, 39, 45
23 Read §2.2:  Limits of Functions and Sequences
25 Exam 1 (Chapter 1)

March
Tuesday
 Thursday
2 Read §2.3: Algebra of Limits
Read §2.4: Limits of Monotone Functions
4 HW6 Chapter 2: #2, 4, 5, 7, 11, Project 2.4 parts 1 & 4
9 Read §3.1: Continuity of a Function at a Point
Read §3.2: Algebra of Continuous Functions
11 Read §3.4: Properties of Continuous Functions
HW7 Chapter 2: #19, 20, 26
Chapter 3: #3, 5, 15, 20, 21
16 ASU Spring Break
18 ASU Spring Break
23 Read §4.1: The Derivative of a Function
Read §4.2: The Algebra of Derivatives
25 Read §4.3: Rolle's Theorem and the Mean Value-Theorem
HW8 Chapter 3: #23, 27, 34, 36, 40, 41, 44
Also: Prove that a function with domain D is continuous if and only if the preimage of every open set is relatively open in D.
30 Read §5.1: The Riemann Integral
Read §5.2: Classes of Integrable Functions


April
Tuesday
 Thursday


1 Read §5.3: Riemann Sums
HW9 Chapter 4: #3, 4, Project 4.1
6
 Exam 2 (Chapters 2 & 3)
8
 Read §5.4: The Fundamental Theorem of Integral Calculus
HW10 Chapter 4: #16, 18, 21
13
 Read §5.5: Algebra of Integrable Functions
15
 Read §5.6: Derivatives of Integrals
HW11 Chapter 4: #23, 30, 32
20
 Read §5.7: Mean-Value and Change of Variable Theorems
22
 HW12 Chapter 5: #2, 3, 6
27
 Exam 3 (Chapter 4)
29
 HW13 Chapter 5: #18, 30, 35

May
Tuesday
 Thursday
4
 Last Class Day


11
 Final Exam (Comprehensive but emphasizing Chapter 5)




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