MIAMI DADE COLLEGE WOLFSON CAMPUS MAC 1147 Pre-Calculus Algebra and Trigonometry 5 Credits Summer B Term 2007-3 (2nd six weeks) Instructor : Bernard Mathon Office : Room 1526 Office Hours : Will be posted on the office door. Telephone : (305) 237-3491 E-mail : [email protected] Textbook : Precalculus, 3rd Edition, by Lial, Hornsby and Schneider. Technology : A graphing calculator is required. Students will be allowed to use calculators on most exams. PREREQUISITE: MAC 1105 with a grade of C or better, or the equivalent. Introduction MAC 1147, Pre-Calculus Algebra and Trigonometry is intended primarily for students majoring in mathematics, science or engineering. The competencies acquired in MAC 1147 will prepare students for Calculus I, the next course in the sequence of mathematics courses offered at the college. To be successful in this course, students should have performed very well in College Algebra, or should have a strong high school background in Algebra and Trigonometry. Course Description MAC 1147 is a combination of two courses: MAC 1140 (Pre-Calculus Algebra) and MAC 1114 (Trigonometry). It includes the following topics: functions and models, polynomial and rational functions, real and complex zeros of polynomial functions, exponential and logarithmic functions and their applications, conic sections, systems of linear and non linear equations, sequences and series, trigonometric functions and their graphs, inverse trigonometric functions, identities and conditional equations, solving right and oblique triangles, polar graphs, vectors and De Moivre’s theorem. Course Goals The goals of the course are to provide the student with an understanding of • The properties and graphs of piecewise, polynomial, rational and other algebraic functions • Exponential and logarithmic functions, their graphs and properties; • Trigonometric functions, their graphs and properties; • Trigonometric identities and trigonometric equations; • The trigonometric form of complex numbers; • Vectors, vector operations and applications; • The use of matrices to solve systems of linear equations; • Conic sections and their applications; • Sequences and series; • The binomial theoremCourse Objectives Upon successful completion of the course, the student will show a good understanding of the topics covered. The student will also be able to apply the concepts or procedures studied in the course to solve related problems. How do the course objectives relate to the Miami-Dade Learning Outcomes? What follows below is a list of the ten learning outcomes that have recently been prepared by Miami Dade faculty and administrators. As graduates of Miami Dade College, students will be able to: 1. Communicate effectively using listening, speaking, reading, and writing skills. 2. Use quantitative analytical skills to evaluate and process numerical data. 3. Solve problems using critical and creative thinking and scientific reasoning. 4. Formulate strategies to locate, evaluate, and apply information. 5. Demonstrate knowledge of diverse cultures, including global and historical perspectives. 6. Create strategies that can be used to fulfill personal, civic, and social responsibilities. 7. Demonstrate knowledge of ethical thinking and its application to issues in society. 8. Use computer and emerging technologies effectively. 9. Demonstrate an appreciation for aesthetics and creative activities. 10. Describe how natural systems function and recognize the impact of humans on the environment. Each course taken at the college addresses some of these learning outcomes. Pre Calculus Algebra and Trigonometry addresses outcomes 1, 2, 3, 4, 5, 8, 9. • Communicate effectively using listening, speaking, reading, and writing skills. This course requires reading and understanding the material covered in the textbook. Students will need to pay attention in class and may periodically be asked to explain a concept discussed in class. • Use quantitative analytical skills to evaluate and process numerical data. The student will have the opportunity to develop these skills in solving real world applications using polynomial, piece wise, exponential, logarithmic and trigonometric functions. A good understanding of arithmetic sequences and series will also give students the ability to process and analyze patterns in numerical data. • Solve problems using critical and creative thinking and scientific reasoning. Some of the applications discussed in the course will require the use of critical and creative thinking. Students will have to understand the problem and use newly acquired concepts to come up with a mathematical model for the situation; then use the model to solve the problem.• Formulate strategies to locate, evaluate, and apply information. The areas that will provide students with this opportunity are applications of exponential, logarithmic and trigonometric functions. • Demonstrate knowledge of diverse cultures, including global and historical perspectives. This course touches lightly on the role played by different cultures in the development of mathematics, as well as the use made by people in these cultures of mathematical concepts or applications. Examples include the subdivision of the circumference of a circle into 360 parts believed to have been introduced by the Babylonians and contributions of mathematicians such as Euler, Napier, Gauss, Fibonacci, Pascal. • Use computer and emerging technologies effectively. Most homework assignments and quizzes will be posted on line on the Course Compass/My Math Lab website. Students will develop the ability to use these computer resources to monitor their progress in the course and to help them reach a better understanding of the concepts, ideas and applications discussed in the course. They will also have the opportunity to use graphing calculators to explore the graphs and properties of functions studied in the course and create mathematical models using real world data. • Demonstrate an appreciation for aesthetics and creative activities. Students will have the opportunity to learn about the connection between the high resolution computer graphics and complex numbers. This will help students develop an appreciation for the beauty of mathematics, as well as an appreciation for