Students can differentiate algebraic and transcendental functions.

Students can solve optimization problems.

Students can compute instantaneous rates of change in applications.

Students can evaluate integrals of elementary functions using the method of substitution.

MATH 180 CMO

Represent functions verbally, algebraically, numerically and graphically. Construct
mathematical models of physical phenomena. Graph functions with transformations on
known graphs. Use logarithmic and exponential functions in applications. Solve calculus
problems using a computer algebra system.

Prove limits using properties of limits and solve problems involving the formal definition
of the limits. Solve problems involving continuity of functions. Evaluate limits at
infinity and represent these graphically. Use limits to find slopes of tangent lines,
velocities, other rates of change and derivatives.

Compute first and higher order derivatives of polynomial, exponential, logarithmic,
hyperbolic, trigonometric, and inverse trigonometric functions. Evaluate derivatives
using the product, quotient and chain rules and implicit differentiation.

Use derivatives to compute rates of change in applications. Apply derivatives to related
rates problems, linear approximations and differentials, increasing the decreasing
functions, maximum and minimum values, inflections and concavity, graphing, optimization
problems, and Newton's Method. Apply the Mean Value Theorem in example problems. Use
L'Hospital's Rule to evaluate limits of indeterminate forms. Use a Computer Algebra
Systems in applications of calculus.

Use anti-derivatives to evaluate indefinite integrals and the Fundamental Theorem
of Calculus to evaluate definite integrals. Evaluate integrals using the substitution
rule and integration by parts.