Quadratic equations, inequalities, logarithmic and exponential functions, graphs, elements of theory of equations, systems of equations. *Note: This course is designed to prepare students for Precalculus MATH 2312 (formerly 1330) and Calculus I MATH 2413 (formerly 1431) . Students with prior credit in MATH 2312 or MATH 2413 will not be allowed to enroll or receive credit in MATH 1314.
Partial differential equations and boundary value problems, Fourier series, the heat equation, vibrations of continuous systems, the potential equation, spectral methods.
Techniques and applications of integration, sequences, series, polar coordinates and parametric equations.
This course is designed to provide a college-level experience in history of mathematics. Students will understand some critical historical mathematics events, such as creation of classical Greek mathematics, and development of calculus; recognize notable mathematicians and the impact of their discoveries, such as Fermat, Descartes, Newton and Leibniz, Euler and Gauss; understand the development of certain mathematical topics, such as Pythagoras theorem, the real number theory and calculus.
An introduction to proof in mathematics: logic, sets, relations, functions and cardinality, a first look at epsilon-delta methods of proof. Writing and communication of mathematical ideas will be emphasized.
Calculus of single variable functions, limits, continuity, derivatives, mean value theorem, applications of the derivative, motion problems, optimization, antiderivatives, the definite integral, fundamental theorem of calculus, and numerical integration.
AP Calculus AB is an introductory college-level calculus course. Students cultivate their understanding of differential and integral calculus through engaging with real-world problems represented graphically, numerically, analytically, and verbally and using definitions and theorems to build arguments and justify conclusions as they explore concepts like change, limits, and the analysis of functions
In Discovery Precalculus, students will deepen and extend their knowledge of functions, graphs, and equations from their high school algebra and geometry courses so they can successfully work with the concepts in a rigorous university-level calculus course. This course is designed to push students well beyond “drill and kill” type exercises, with an emphasis on unpacking mathematical definitions and making logical arguments to their peers.
Each unit consists of a series of explorations designed to engage students and empower them to develop their problem-solving skills alongside the teacher. In each exploration, students will create connections with prior concepts in developing the current topic. Students will experience high-quality curriculum designed by the faculty at the University of Texas at Austin. The pedagogy of the course, Inquiry-Based Learning, encourages students to take an active role in the construction of their learning.