# Math 180 SLO and CMO

**MATH 180 SLO**

- 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.