- Course Number:
- CMET 123
- Course Title:
- Technical Algebra with Analytic Geometry
- Credit Hours:
- Lecture Hours:
- Lecture/Lab Hours:
- Lab Hours:
- Special Fee:
Course DescriptionCovers algebra and geometry of special interest to engineering technicians including solving higher order equations, determinants, matrix operations, logarithms and trigonometric identities. Introduces plane analytical geometry in preparation for calculus, emphasizing development of skills and confidence to solve advanced pre-calculus problems. Prerequisites: CMET 112 or MTH 111. Audit available.
Intended Outcomes for the course
Upon completion of this course, students will be able to:
• Solve applied problems involving trigonometric functions.
• Solve applied algebra problems involving polynomial, exponential, radical, and logarithmic functions.
• Solve applied problems involving analytic geometry and the conic sections.
• Graph conic sections and exponential, logarithmic, and trigonometric functions; both by hand and by using calculator operations and/or computer software.
• Solve systems of equations, graphically and analytically.
• Communicate analysis and results clearly: orally, in writing, and through diagrams and calculations.
Course Activities and Design
Lectures and text reading will be the primary presentation methods. The course material is presented in an informal style using the intuitive approach. Formal proofs or theorems are given when they help clarify the presentation. The use of a programmable calculator, as designated by the department, is required for this course to solve certain algorithms.
Outcome Assessment Strategies
Based on homework and examination covering appropriate types of quantitative problems. Grading details will be expounded upon by the instructor at the first meeting.
Course Content (Themes, Concepts, Issues and Skills)
Upon successful completion of this course, the student will have satisfactorily accomplished the goals and objectives listed in this course content guide. The course content guides are developed by collegewide subject area curriculum committee faculty and approved by management.
1.0 APPLIED ALGEBRA
1.1.0 The goal is to continue developing an understanding of algebra and its application to technical subject matter.
1.1.1 To solve algebraic equations and formulas using addition, subtraction, multiplication, and division of monomials and polynomials.
1.1.2 To describe functions and graphs.
1.1.3 To present graphical solutions of algebraic equations.
1.1.4 To describe the laws of exponents and radicals. To demonstrate techniques in applying these laws.
1.1.5 To illustrate the use of exponential and logarithmic functions and show applications in the technical fields.
1.1.6 To describe polynomial and other higher degree functions and present methods for finding both rational and irrational solutions for these functions.
1.1.7 To describe the methods for solving systems of equations. Demonstrate the use of algebraic, matrix, and determinant
methods for solving n x n systems of equations.
1.1.8 To present the techniques used in solving inequalities. Demonstrate algebraic and graphical solutions of inequalities.
1.1.9 To illustrate the use of each of the above on solving practical problems.
1.1.10 To demonstrate the use of functional notation and to define associated concepts, including dependent and independent variables, domain and range, set notation, and interval notation. To evaluate composite functions and find the inverse of various functions. To define a relationship.
1.1.11 To explore and analyze functions expressed graphically, symbolically, or in tabular form. This will include the identification of the x & y intercepts, asymptotes, slopes, concavity, and the general shapes of common functions.
2.0 APPLIED TRIGONOMETRY
2.1.0 The goal is to develop an understanding of the trigonometric functions and their use in technology.
2.1.1 To demonstrate the use of radian measure of angles and present technical applications.
2.1.2 To demonstrate the solution of oblique triangles in applied technology.
2.1.3 To derive the fundamental trigonometric identities. Demonstrate techniques for proving trigonometric identities.
2.1.4 To demonstrate the methods used in solving trigonometric equations.
2.1.5 To describe the periodic functions. To present graphs of the trigonometric functions. Demonstrate uses of the sine and cosine curves.
2.l.6 To apply each of the above to solving practical problems.
3.0 ANALYTIC GEOMETRY
3.1.0 The goal is to develop an understanding of the conic sections and their use in technology and applied mathematics.
3.1.1 To describe methods of graphing the conic sections. To present the definition and use of polar coordinates.
3.1.2 To demonstrate the mathematical methods involved in graphing the conic sections.
3.1.3 To recognize the conic sections in their general form.
3.1.4 To demonstrate the methods used in the translation of axes.
3.1.5 To state the definition of the polar coordinates system. To demonstrate the use of polar coordinates and polar equations.
3.1.6 To use each of the above in solving practical problems.