Calculus 2
Earn college credit with Calculus II—a self-paced online course covering advanced integration, techniques of integration, sequences and series, and applications. Complete short lessons, quizzes, and assignments on your schedule, then finish with a proctored final exam. Ideal for STEM degree pathways and prerequisites, with transcript options for transfer credit.
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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.
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Learning Outcomes
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.
Major Course Topics
Major topics include fundamentals of graphing; fundamentals of 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.