The first is to obtain a thorough understanding of the real number system and of calculus of a single real variable. The second is to learn to express the ideas studied in the course clearly in written form. For a detailed list of learning objectives, see the Math 341 wiki page.

Math 341 Website. Review Sheets and Sample Exams Exam 1. Exam 1 Study Guide; Fall 2018 Exam 1 without solutions

Math 341 – Lecture Notes on Chapter 1 What is Math 341 about? In this class we will study the major theorems of calculus from a theoretical point of view. A major goal of the class is to improve your ability to read and write mathematical proofs. Section 1.2 – Preliminaries N = {1,2,3,...} the set of natural numbers

Math 341 – Lecture Notes on Chapter 2 Sequences and Series § 2.2 – The Limit of a Sequence Definition of a Sequence A sequence is a function whose domain is N. Examples 1 (1,1/2,1/3,1/4,...) where f: N →R is given by f(n) = 1/n. 2 (an) where an= sin(n) for n∈N. 3 Sometimes we begin the index at an integer other than 1: (b 0,b 1,b 2 ...

Math 341 Section 1 Summer 2024 Math 341 – HW 1 Exercises 1.2: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, Bonus Exercise 1.2.0 I read section 1.2 of the textbook. Exercise 1.2.1 (a)Prove that √ 3 is irrational. Does a similar argument work to show that √ 6 is irrational? (b)Where does the proof of Theorem 1.1.1 break down if we try to ...

An approximate schedule is given below. Adjustments may be necessary as the term progresses. Write homework solutions in the style of textbook examples. **Words like find, solve, show, or prove mean that you should provide a complete explanation and not merely write a final answer. Sometimes exercises are stated as a question with a Yes or No answer.

Math 341 – Lecture Notes on Chapter 7 The Riemann Integral §7.2: Definition of the Riemann Integral Definitions A partition of [ , ]is a finite set of points from[ , ]that includes both and . We will write ={ 0, 1, 2,..., } where = 0 < 1 < 2 <···< = . Let be a bounded function on [ , ].

Math 341 — Summer 2024 — Midterm 3 Review Sheet 1. The exam will have questions emphasizing the material in sections 4.3–4.5, 5.2–5.3, 6.2–6.4. 2. To receive full credit you should show your work and write neatly. The solutions should be clearly presented. Try to use correct spelling and punctuation. 3.

Math 341 – Lecture Notes on Chapter 6 Sequences and Series of Functions §6.2: Uniform Convergence of a Sequence of Functions Definition (Pointwise Convergence) For each ∈N, let : →Rbe a real-valued function on . The sequence ( )of functions converges pointwise on to a function if, for all ∈ ,

Math 341 – Lecture Notes on Chapter 8 Sequences and Series of Functions §8.6: Constructing R from Q We’ll assume we already have Q. From Q, we’ll construct R. The purpose of this section is to prove the following theorem: Theorem (Existence of the Real Numbers) There exists an ordered field in which every nonempty set that is bounded