Calculus II for the Social Sciences

At the end of the course, students will be expected to be able to:

• find an indefinite integral using the antiderivatives of a given function.
• verify the properties of an antiderivative through differentiation.
• solve initial value problems using indefinite integrals.
• find an indefinite integral using substitution.
• evaluate definite integrals using the Fundamental Theorem of Calculus.
• use integrals to solve problems involving area, net change and average value.
• find integrals using integration by parts.
• find integrals using integral tables.
• evaluate improper integrals or describe reasons for divergence.
• estimate definite integrals using numerical techniques.
• use integrals to solve problems from business and science.
• create a symbolic formula to represent a given description of a function of two variables.
• sketch the domain and level curves for a given function of two variables.
• compute all first and second order partial derivatives of a given function of two variables.
• give a qualified interpretation of a partial derivative.
• find critical points of a function of two variables.
• classify the critical points of a function of two variables.
• use the method of Lagrange multipliers to optimize a function of two variables under constraints.
• use the method of least squares to find the regression line relating one variable to another.
• set-up and evaluate double integrals.
• rearrange the order of integration variables to evaluate a double integral.
• use partial derivatives and/or double integrals to solve problems from business and science.
• solve elementary separable and linear differential equations.
• use Euler's Method to approximate solutions to differential equations.
• use differential equations to model and solve problems from business and science.
• use Taylor’s formula to approximate functions and estimate definite integrals.