Student Learning Outcomes

• Evaluate indefinite integrals and definite integrals using the Fundamental Theorem of Calculus. Evaluate integrals using the substitution rule and integration by parts.
• Apply derivatives to rates of change and related rates problems, linear approximations and differentials, increasing and 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.
• Compute first and higher order derivatives of polynomial, exponential, logarithmic, trigonometric, and inverse trigonometric functions. Evaluate derivatives using the product, quotient and chain rules and implicit differentiation.
• 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.
• Represent functions verbally, algebraically, numerically and graphically. Construct mathematical models of physical phenomena. Graph functions with transformations. Use logarithmic and exponential functions in applications. Solve calculus problems using a computer algebra system.
• Students will feel that mathematics is a beneficial part of their education
• Math students feel they have the resources necessary for their success.
• Students can solve optimization problems.
• Students can differentiate algebraic and transcendental functions
• Students can evaluate integrals of elementary functions using the method of substitution.
• Students can compute instantaneous rates of change in applications