Preparatory Mathematics for Engineers
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry, 1/e, by Michael Sullivan and Michael Sullivan III.
Course Objectives: This course is designed to help the student:
•Establish a clear understanding of numbers and their properties .
•Use graphical and algebraic methods to solve linear equations and inequalities.
•Develop the basic concepts of functions and carry out basic algebraic operations.
•Establish a clear understanding of different type of functions such as polynomials, rational, exponential, logarithmic, and trigonometric functions.
• Solve logarithmic and exponential equations.
•Explore some trigonometric identities by using the concepts of right triangle.
Course Outcomes: This course requires the student to demonstrate the following:
1. Develop the basic properties of real and complex numbers.
2. Solve linear equations and inequalities and be able to sketch the solution set .
3. Define the basic concepts of functions including and the concepts of domain and range.
4. Perform basic operations on functions and conclude new domains.
5. Perform basic tests on functions such as one-to-ones.
6. Fins the inverse of a function, if exists.
7. Make a basic sketch of polynomial and rational functions.
8. Solve logarithmic and exponential functions and examine the relationship between exponential and logarithmic expressions.
9. Sketch the graph of basic logarithmic and exponential functions.
10. Define some basic trigonometric identities.
11. Establish knowledge of the basic trig identities that are driven from the right triangle.
12. Sketch some trigonometric functions and identify the domain, periods, and amplitudes.
13. Develop skills to work out application problems.
Algebraic and fractional expressions -Equations and inequalities and some applications.
|Functions - definition, graphs, and properties.|
|Linear Functions and applications|
|Quadratic Functions and Applications|
|Polynomial and Rational Functions|
|Exponential and Logarithmic Functions|
|Introduction to Limits- numerical, graphical and algebraic approach|
Tentative Exam Schedule
|Date and Time||Percentage|
|Quizzes and Homework||TBA||10%|
Attendance is a vital part of the course work. It is the university policy that if a student is absent 15% of the class sessions (which, in our case, translates into 6 hours), he/she will be withdrawn from the course with a grade of WF.
Late attendance: Not only you are expected to be in class, but you are also expected to be there on time. Three (3) late attendances will count as one absence. Late is defined as follows: showing up to class after I have finished calling the class roster, and within the first 10 minutes of the lecture. Showing up more than 10 minutes late to the lecture counts as an absence.
You are encouraged to work in groups , discuss ideas and compare answers with other students. However, you are not allowed to work together to the extent that submitted work is indistinguishable from copied work. Your submitted work is a personal work, expressed in your own words, with your own numerical computations and algebraic steps. Copying, cheating or plagiarism, if detected will result in a WF grade in the course for all who are involved. In addition, those involved may be reported to the administration for disciplinary action.
Course Syllabus and Weekly Schedule
|1||Line in the plane and solving linear equations||F3|
|3||Graphs of Functions||1.2|
|4||Properties of Functions||1.3|
|5||Library of Functions; Piecewise-defined Functions||1.4|
|6||Graphing Techniques: Transformations||1.5|
|7||Properties of Linear Functions||2.1|
|9||Quadratic Functions and Their Zeros||2.3|
|10||Properties of Quadratic Functions||2.4|
|11||Inequalities Involving Quadratic Functions||2.5|
|12||Complex Zeros of a Quadratic Function||2.7|
|13||Equations and Inequalities Involving the Absolute Value Function||2.8|
|14||Polynomial Functions and Models||3.1|
|15||Properties of Rational Functions||3.2|
|16||The Graph of a Rational Function; Inverse and Joint Variation||3.3|
|17||Polynomial and Rational Inequalities||3.4|
|19||The Real Zeros of a Polynomial Function||3.5|
|20||Complex Zeros ; Fundamental Theorem of Algebra||3.6|
|22||One-to-One Functions; Inverse Functions||4.2|
|25||Properties of Logarithms||4.5|
|26||Logarithmic and Exponential Equations||4.6|
|27||Angles and Their Measure|
|28||Trigonometric Functions: Unit Circle Approach||5.2|
|29||Properties of the Trigonometric Functions||5.3|
|30||Graphs of the Sine and Cosine Functions||5.4|
|31||Phase Shift; Sinusoidal Curve Fitting||5.6|
|32||32 Trigonometric Identities||6.3&6.4|
|36||Trigonometric Equations (I)||6.7|
|37||Finding Limits Using Tables and Graphs||13.1|
|38||Algebra Techniques for Finding Limits||13.2|
|39||Algebra Techniques for Finding Limits||13.2|
Schedule for Fall 2008
Phone # 515-2995
|09:00||STA 202 NAB 013||STA 202 NAB 113|
|10:00||OFFICE HOUR||OFFICE HOUR||OFFICE HOUR|
|11:00||MTH 003 PHY 114||OFFICE HOUR||MTH 003 PHY 114||OFFICE HOUR||MTH 003 PHY 114|
|12:00||MTH 001 PHY 103||MTH 001 PHY 103||MTH 001 PHY 103|
|14:00||MTH 001 NAB 010||MTH 001 NAB 010||MTH 001 NAB 010|
|STA LAB CHE 110||STA LAB NAB 105|
Other office hours are available by appointment.