Solve equations and manipulate expressions using properties of algebraic (e.g., polynomial, power, and rational functions)
Solve equations and manipulate expressions using properties of transcendental functions (e.g., trigonometric, exponential, and logarithmic functions)
Compute derivatives of algebraic and transcendental functions
Use and apply appropriate differentiation rules and techniques (power, product, chain, quotient, implicit diff., logarithmic diff.)
Use derivatives to solve related rate problems, optimization problems, linear approximation problems, and compute limits using L'HĂ´pital's Rule
Explain the meaning and mathematical notation of the definite integral and Riemann sums
Compute antiderivatives of standard functions and use them to compute areas with the Fundamental Theorem of Calculus
Compute antiderivatives with the substitution method and use them to compute areas with the Fundamental Theorem of Calculus
Describe the difference between derivatives and integrals, and identify when each is needed in a real-world application.
Have fun and gain confidence in your mathematical reasoning and skills
Improve as a learner, teacher, communicator, and mathematician by working individually and as part of a community to further not only your personal growth, but also our collective knowledge and understanding of the world around us
read and communicate (verbally and in writing) clearly, concisely, and correctly using relevant vocabulary, notation, and colloquial language of modern mathematics
understand and appreciate philosophical and conceptual ideas of modern mathematics, and how they lead to models for, and solutions of, common (and uncommon) problems