Course Description
This course gives students a strong foundation in algebraic techniques, analytic geometry, and trigonometry, preparing them for advanced study in mathematics, engineering, and the physical sciences. Students will learn how to manipulate algebraic expressions, solve equations and inequalities, examine functions and graphs, analyze polynomial, rational, exponential, and logarithmic functions, and investigate trigonometric functions in both algebraic and geometric contexts. Additional subjects include equation systems, matrices, determinants, sequences, series, probability, and conic sections, all of which have applications in scientific and engineering problem solving.
Course Objectives
By the end of this course, students will be able to:
- Use algebraic concepts to simplify and solve expressions, equations, and inequalities.
- Analyze various functions (polynomial, rational, exponential, logarithmic, trigonometric) and their practical applications.
- Demonstrate how to graph equations and analyze graphical relationships.
- Apply trigonometric identities, rules, and equations to solve problems in geometry and applications.
- Solve problems using algebraic, graphical, and matrix approaches.
- Use sequences, series, and probability to address combinatorial and statistical issues.
- Analyze conic sections (parabolas, ellipses, and hyperbolas) and their use in analytic geometry.
- Improve logical reasoning and problem-solving abilities for advanced mathematics and practical subjects.
References
Main Textbook
- Swokowski, E. W., & Cole, J. A. (2012). Algebra and Trigonometry with Analytic Geometry (12th Edition). Brooks/Cole, Cengage Learning.
- Analytic Geometry, 6th edition by Douglas F Riddle (ISBN: 9780534948542) is the only required book.
- Larson, R., Hostetler, R. P., & Edwards, B. H. (2009). Algebra and Trigonometry. Brooks Cole.
- Barnett, R., Ziegler, M., & Byleen, K. (2014). College Algebra with Trigonometry. Pearson.
- Stewart, J., Redlin, L., & Watson, S. (2015). Precalculus: Mathematics for Calculus. Cengage Learning.
- Thomas, G. B., Weir, M. D., & Hass, J. (2018). Thomas’ Calculus (14th ed.). Pearson.
Analytic Geometry and Algebra – Course Content Outline
