# Math Analysis

Welcome to Honors Math Analysis.

In these course pages you will find the course syllabus and a weekly schedule of assignments. Additionally, I will post fundamental definitions, axioms, theorems or interesting ideas developed in class. Remember that the class notes will be the most comprehensive and your primary reference.

 Day Assignment 1 Meet and Greet – Course Bureaucracy 2 Day 1 continued: Review Real Number System. Natural numbers and integers are subsets of the rational numbers. Can you describe geometrically, what makes a rational number different from an irrational number? 3 Review of the real number system continued. Review factoring. HW: R.2 (pg 885); 3,8,12, 14,17, 19, 21,24,30, 42,47, 62,66, for 68-88 choose a few that you would not want to see on a quiz or test. 4 2.1 Basic Functions – Definition and some properties. HW: 2.1; 11-22, 24-34e 5 2.1 Basic Functions – Definition and some properties. HW: 2.1; 35-46, 54-76 6 2.1 Basic Functions – Definition and some properties HW: Review and Retry problems with which you had difficulty. 7 In class investigation with functions. Introduction to LaTeX HW: TBA 8 2.2 Function Transformations and Their Graphs. Initially we will consider function transformations analytically (without a calculator) and develop some experience with transformations. Developing analytical skills are important for doing well on non-calculator based tests, as well as, and more importantly, having the ability to know if the answer that a computer produced is reasonable. HW: 2.2; 11-19, 25-30, 31-42 9 2.2 Function Transformations and Their Graphs. HW: 2.2; 47-62 10 2.2 Function Transformations and Their Graphs. Using the graphing calculator to obtain correct answers. HW: Choose a few of the previous homework problems and solve using the graphing calculator. 11 2.3 Function Transformations Continued. HW: 2.3; 1-8, 11-12, 19,20,21, 33,34, 36,38,46,48 12 2.3 Function Transformations Continued.HW: 52-53, 59-60, We’ll need to pay attention to the language used in the instructions for problems 63-74. 13 2.1-2.3: Reviewing the Basics HW: 1-10 14 2.4 Absolute Value. HW: 2.4; 1-20 15 2.4 Absolute Value. HW: 2.4; 29-32, 39,40,44, 51,52,58,59,64 16 2.4 Absolute Value. HW: 2.4; 68,71,74,78 17 2.4 Absolute Value. Review of the Previous Lessons. HW: Redo or retry problems you initially found difficult in order to ensure that you can correct solve them. Try some problems not assigned 18 2.5 Piecewise Functions. HW: 2.5; 1-4, 6,8, 10,13,16,19, 21-24, 33-38 19 2.5 Piecewise Functions. HW: 2.5; 39,40, 50,52,55,58 20 2.5 Piecewise Functions. HW:57,59,60,62 21 2.4-2.5 Review: Consider how the graph of $$f$$ changes when added to the greatest integer function. Is there a discernible pattern? What assumptions are you making about $$f$$ ? 22 2.4-2.5 Review 23 2.4-2.5 Review 24 2.4-2.5 Review 25 2.4-2.5 26 2.6 Operations on Functions and Function Compositions. HW: 2.6; 2-34e 27 2.6 Operations and Composition. HW: 2.6; 35-46 28 2.6 Operations and Composition. HW: 2.6; 47-52, 59-72 29 2.6 30 2.6 31 Chapter 2 Review 32 Chapter 2 Test 33 3.2 Quadratic Functions and Graphs. HW: 6,9,15, 17,18, 20,24, 26,29,32 34 3.2-3.3 Quadratic Equations & Inequalities HW: Section 3.3: 18,22,26,30,55, 95,96,102 35 3.3 Quadratic Equations & Inequalities HW: Really focus on being able to represent your answers from this section both graphically and analytically. Feel free to use your graphing calculator to check your answer. 36 3.1: Structure of the Complex Plane. We will consider a few significant ways in which complex numbers are different from real numbers. The properties do not appear in the text and will not be tested per se, however, I think it is important that you are exposed to these differences. 37 3.1 Complex Numbers and their operations. HW: 2-14e, 15-20, 22,26,28,32, 39,43,44, 46,50,54, 56,62,68,69,72, 74,79,86, 100,101,103 38 3.1 Review Operations on Complex Numbers. HW: In class problems with answers given. 39 3.4 Applications of Quadratics & Models. HW: 11,13,16,18,23,30 40 3.4-3.5 Higher Degree Polynomial Functions. HW: Section 3.5: 10-20even, 33-46 41 3.5 Higher Degree Polynomial Functions. HW: 59-66 42 3.5 Higher Degree Polynomial Functions. HW: Review 43 3.6 Topics in the Theory of Polynomial Functions. HW: 6-14e, 23,23,31, 24-28e 44 3.6 Topics in the Theory of Polynomial Functions. HW: 38-42e, 50-54e 45 3.6 Topics in the Theory of Polynomial Functions. HW: 66-76e, 88-92e 46 3.7 Topics in the Theory of Polynomial Functions. HW: 2-18e 47 3.7 Topics in the Theory of Polynomial Functions. HW: 26-38e, 41-46 48 3.7 Topics in the Theory of Polynomial Functions. HW: 52, 54, 58, 62, 68, 74, 78 49 3.8 Polynomial Equations and Inequalities. HW: 2-18e, 20-32e 50 3.8 Polynomial Equations and Inequalities. HW: 38-56e, 62,65,68,69 51 3.8 Polynomial Equations and Inequalities.HW: 52 Review HW: 53 Test HW: 54 4.1/4.2 HW: 55 4.1/4.2 HW: 56 4.1/4.2 HW: 57 4.3HW: 58 4.3HW: 59 HW: 60 HW: 61 HW: 62 HW: 63 3.1-3.4 HW: 64 3.1-3.4 HW: 65 3.1-3.4 HW: 66 3.1-3.4 HW: 67 3.1-3.4 HW: 68 3.1-3.4 HW: 69 3.1-3.4 HW: 70 3.1-3.4 HW: