## UPI Study, Inc. | Evaluated Learning Experience

## Math 265: Calculus 2

Varies (self-study, self-paced).

March 2021 - Present.

Upon the successful completion of this course, students will be able to: define limits and continuity and apply limit notation in various contexts; estimate limit values using graphical, numerical, and algebraic methods; analyze functions to determine limit behavior, types of discontinuities, and asymptotes; apply differentiation rules to find derivatives of basic functions and compositions; solve practical problems involving rates of change, optimization, and related rates; understand the fundamental theorem of calculus and apply integration techniques to find areas, volumes, and accumulation functions; solve differential equations, including initial value problems and growth models; utilize parametric equations, polar coordinates, and vector-valued functions in modeling motion and other contexts; and analyze sequences and series, determine convergence, and represent functions as power series.

The course is self-paced. Instruction is delivered through online video and text lessons. Students are assessed through quizzes, assignments and a proctored final exam. Major topics include: Fundamentals of Graphing; Fundamentals of Functions; Graphing Fundamental Functions; Function Limits; Continuity of Functions; Mastering Exponentials and Logarithms; Mastering Exponents and Polynomials; Advanced Functions - Parametric, Polar, and Vector; Derivatives: Foundational Concepts; Derivatives at Specific Points; Understanding the Derivative as a Function; Higher-Order Derivatives; Applications of Derivatives; Calculating Derivatives; Characteristics of Definite Integrals; Integral Applications; Applying the Fundamental Theorem of Calculus; Mastering Integration Methods; Estimating Definite Integrals; Exploring Sequences and Series; Constant Series; and Expansion of Functions with Taylor Series.

In the lower division baccalaureate/associate degree category OR in the upper division baccalaureate degree category, 4 semester hours in Calculus, Mathematics, or Computer Science (5/24).