Course Overview
Math 17B – Precalculus is a six-unit course designed for Bachelor of Science in Applied Physics students, with six hours of instruction per week. The course provides a comprehensive foundation in algebra, analytic geometry, functions, trigonometry, and complex numbers, preparing students for advanced mathematical studies in calculus, differential equations, and other physics-related courses. It emphasizes mathematical reasoning, analytical thinking, problem-solving, and the application of mathematical concepts to physical phenomena and scientific investigations.
The course begins with a review of fundamental algebraic concepts, including real numbers, algebraic expressions, equations, and inequalities. Students develop proficiency in manipulating algebraic expressions, solving linear and quadratic equations, and analyzing inequalities. These skills serve as essential tools for understanding more complex mathematical relationships. The course then introduces the Cartesian coordinate system, lines, circles, and conic sections, enabling students to represent and interpret geometric relationships through equations and graphs.
Students subsequently explore systems of equations and inequalities, focusing on methods for finding solutions and interpreting their graphical representations. The study of functions follows, covering their properties, domains, ranges, and graphical behavior. Particular emphasis is placed on polynomial, exponential, and logarithmic functions, which are useful in modeling mathematical relationships, growth and decay processes, and various physical phenomena.
A substantial portion of the course is devoted to trigonometry and its applications. Students study trigonometric functions, identities, and equations, as well as inverse trigonometric functions and methods for solving triangles. These topics develop their understanding of angular relationships, periodic behavior, and wave-like phenomena. Such concepts are particularly relevant to applied physics, where trigonometric models are used to describe oscillations, waves, circular motion, and other physical systems.
The course concludes with the study of complex numbers in polar form. Students learn to represent complex numbers using modulus and argument, convert between rectangular and polar forms, and perform operations involving multiplication, division, powers, and roots. These concepts provide a mathematical foundation for understanding oscillatory systems, alternating-current circuits, wave analysis, and other applications involving complex quantities.
Throughout the course, students are encouraged to connect mathematical theory with practical applications in physics and related scientific disciplines. Problem-solving exercises, graphical analysis, and mathematical modeling help develop precision, logical reasoning, and quantitative skills. By integrating algebraic, geometric, functional, trigonometric, and complex-number concepts, Math 17B – Precalculus equips BS Applied Physics students with the essential mathematical knowledge and competencies needed for success in higher-level mathematics and physics courses.
- Faculty: Juven Burlasa Corrales