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Math 418– Analysis and Applications of Functions Sample Syllabus
Textbook: Precalculus, 4th edition, Mathematics for Calculus, by Stewart, Redlin, and Watson, Brooks/Cole. Course Goals The main goals for the course are: To provide you with the mathematical foundation
needed to advance to calculus. The secondary goals for the course are: To improve your ability to carry out essential
operations such as graphing functions, solving equations, simplifying
complex algebraic expressions, factoring polynomials, finding the
inverse of a function, manipulating logarithmic and trigonometric
identities, etc. Expectations and Philosophy: This is a college level course with the intent of preparing you to take Calculus in the coming semesters. I will expect a great deal from you, which will include substantial time outside of class working on problems and class material. We believe one of the better ways to learn mathematics is to discuss mathematics; hence we will do everything possible to include class discussions and group discussions daily. I strongly suggest that you work together outside of class to help each other better understand the material. Homework: Working regularly – daily! – on homework
is essential in order to keep up in the course and to succeed in the
course’s assessments (homework, quizzes and exams). Homework will
be assigned every class meeting. Homework will be due every Tuesday and
Thursday on Quizzes There will be a total of six quizzes. The lowest quiz grade will be dropped. There are no make-up quizzes. Exams There will be three semester exams and a comprehensive final exam. Their dates are:
Makeup exams are allowed but only for legitimate compelling non-academic reasons supported by letters from the appropriate authority (e.g., doctor, athletic coach, family emergency). If possible, you must inform us before something is due to be allowed to make up any assignment. Class Attendance Class Attendance is required. Class Participation is part of your grade. Grading:
Total 100% At the end of the semester we assign letter grades as follows: 90% and above for an A-, A, 80% for a B-, 70% for a C-, 60% for a D-. Tutoring Peer tutoring is available in the Mathematics Center (MaC) in G33 Christensen Hall. Calculators We do suggest that you have a graphing calculator. The demonstrations in class will use a TI-83 calculator. If you are planning to get a graphing calculator we recommend that you buy one in the TI series. We reserve the right to prohibit calculator use on certain exam and/or quiz questions. Cell phones Cell phones and beepers must be turned off during class.
Math 418– Analysis and Applications of Functions Date Material M 9-1 Labor Day T 9-2 Welcome students, hand out syllabus and discuss it, Ask student to purchase the text book and activity book Give pretest W 9-3 Briefly discuss the use of Blackboard and WeBWorK, start section 1.1 Real Numbers R 9-4 section 1.1 review of Real Numbers F 9-5 section 1.2 Exponents and Radicals M 9-8 section 1.2 Exponents and Radicals T 9-9 section 1.3 Algebraic Expressions W 9-10 section 1.4 Fractional Expressions R 9-11 section 1.5 Equations F 9-12 open / Quiz 1 M 9-15 section 1.6 Problem-solving and Modeling with Equations T 9-16 section 1.7 Inequalities and Solving Equations with Inequalities W 9-17 section 1.8 Coordinate Geometry, Exploring the Equation of a Circle R 9-18 section 1.10 Lines F 9-19 Start section 2.1 What is a Function / Quiz 2 M 9-22 section 2.1 What is a Function? Project: Estimating the Arc Length of a Function. Introduce summation notation T 9-23 section 2.2 Graphing Functions W 9-24 section 2.3 Applied Functions, Exploring the Concept of Variation and Proportionality R 9-25 section 2.4 Average Rates of Change F 9-26 More on Average Rates of Change / Quiz 3 M 9-29 section 2.4 More on Average Rates of Change T 9-30 section 2.5 Transformation of Functions W 10-1 section 2.6 Extreme Values of Functions, Project on Optimization R 10-2 section 2.7 Modeling with Functions F 10-3 section 2.8 Composition and Decomposition of Functions M 10-6 Review T 10-7 TEST 1 - Covering sections 1.1 – 2.8 W 10-8 section 2.9 One-to-one Functions and their Inverses Homework Project: Crickets – Nature’s Thermometer R 10-9 section 3.1 Polynomial Functions and their Graphs F 10-10 open Math 418– Analysis and Applications of Functions Date Material M 10-13 Fall Break T 10-14 section 3.2 Dividing Polynomials W 10-15 section 3.3 Real Zeros of Polynomials, Discovery Project -Zeroing in on a Zero R 10-16 section 3.4 Complex Numbers F 10-17 open / Quiz 4 M 10-20 section 3.5 Complex Roots and Fundamental Theorem of Algebra T 10-21 section 3.6 Rational Functions W 10-22 section 4.1 Exponential Functions, Discovery Project -Exponential Explosion R 10-23 section 4.2 The Natural Exponential Function F 10-24 open M 10-27 section 4.3 Logarithmic Functions T 10-28 section 4.4 Exponential and Logarithmic Equations W 10-29 Project on Logarithmic or Exponential Applications R 10-30 section 4.5 Modeling with Exponential and Logarithmic Function F 10-31 open / Quiz 5 M 11-3 section 5.1 The Unit Circle T 11-4 section 5.2 Trigonometric Functions of Real Numbers / Election Day W 11-5 Review R 11-6 TEST 2 covering sections 2.9 – 4.5 F 11-7 section 5.3 Trigonometric Graphs M 11-10 section 5.3 Trigonometric Graphs cont. Discovery Project –Predator/Prey Models T 11-11 Veterans’ Day, University Holiday W 11-12 5.4 More Trigonometric Graphs R 11-13 Choose problems from Focus on Modeling – Harmonic Motion Include a problem like 23 p. 469 in class and give problem 15 p. 468 and problem 24, p. 470 as part of a homework F 11-14 open / Quiz 6
M 11-17 section 6.1 Angle Measure T 11-18 section 6.2 Trigonometry of Right Triangles W 11-19 section 6.3 Trigonometric Functions of Angles R 11-20 section 6.4 Law of Sines F 11-21 section 6.5 Law of Cosines
Math 418– Analysis and Applications of Functions Date Material M 11-24 section 7.1 Trigonometric Identities T 11-25 section 7.2 Addition and Subtraction Formulas W 11-26 Project Modeling Trigonometric (Follows a Monday Schedule) Going back to Focus on Modeling – Harmonic Motion would fit well here R 11-27 THANKSGIVING F 11-28 Holiday
M 12-1 section 7.3 Double Angle, Half Angle, Product-Sum Formulas T 12-2 section 7.4 Inverse Trigonometric Functions W 12-3 Review R 12-4 TEST 3 covering all of trigonometry, chapters 5, 6 and up to 7.4 F 12-5 section 7.5 Trigonometric Equations M 12-8 section 7.6 Trigonometric Form of Complex Numbers, DeMoivre’s Theorem T 12-9 section 7.7 Vectors W 12-10 open R 12-11 Review F 12-12 LAST DAY OF CLASS … REVIEW
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