MA 117 - Calculus for Business and Liberal Arts
Limits, the derivatives of functions of one variable, differentiation rules, and applications of the derivative. Definite integrals for functions of one variable, antiderivatives, the Fundamental Theorem, integration techniques, and applications of the integral.
Prerequisites: MA 116
The one-semester course is intended to be a terminal one-semester introduction to the basic concepts and methods of elementary calculus, including the most basic elements of multivariable calculus. The course covers topics similar to Ma115 and parts of Ma116 but with less depth.
- Limits of Indeterminate Forms: Understand the concept of a limit and evaluate elementary examples of indeterminate forms.
- Continuity: Demonstrate a working knowledge of continuity for functions of one variable.
- Derivative–First Principles: State and apply the fundamental definition of the derivative and understand its relationship to the tangent line; recognize when a function is not differentiable.
- Derivative–Evaluation: Calculate the derivative of functions constructed via composition, multiplication, division, and addition of elementary functions.
- Application of Differentiation: Determine the behavior of a function through the analysis of its derivative information (intervals of increase/decrease, local extrema, concavity, and asymptotes).
- Optimization: Formulate and solve optimization problems that can be reduced to maximizing (minimizing) a function in one variable.
- Anti-derivatives and indefinite integrals: Know what is meant by the most general anti-derivative and be able to solve elementary initial value problems of the form x′(t) = g(t).
- Integration Techniques: Successfully apply formal techniques such as Method of Substitution or Integration by Parts to express anti-derivatives in terms of elementary functions.
- Definite Integral–First Principles: Understand the definite integral as the signed area under the curve y = g(x) and its definition as the limit of Riemann sums that approximate this area.
- Definite Integral–Evaluation: Evaluate definite integrals using the Fundamental Theorem.
- Application of Integration: Recognize elementary applications for which the definite integral is the appropriate tool; apply the definite integral to describe the area of arbitrary planar regions.
- Introduction to Differential Equations: understand the concepts of general and particular solutions, initial value problem. Be able to find solutions of separable differential equations.
- Functions of Two Variables: Determine the domain for functions f(x,y).
- Partial Derivatives: Evaluate first and second order partial derivatives, including simple cases of the chain rule; understand geometric interpretation of partial derivatives.
- Relative Extrema: Find the critical points of scalar-valued functions of two variables (simple cases) and apply the second derivative test to identify and characterize local extremum.
- Optimization: Solve simple (constrained) optimization problems in two variables.
- Double integrals: Evaluate double integrals over rectangular and simple nonrectangular regions. Compute area of a region in the plane.
Hoffman, Laurence D. and Gerald L. Bradley, Calculus for Business, Economics, and the Social and Life Sciences, Brief Edition, ninth edition, McGraw-Hill, 2006.