Calculus for the Social Sciences

Upon completion of MATH 1125 the student should be able to:

• evaluate elementary limits involving algebraic, exponential, logarithmic and trigonometric functions
• describe the concept of continuity and determine intervals upon which a function is continuous
• apply the intermediate value theorem
• find average and instantaneous rates of change
• find derivatives and relate them to tangent lines and instantaneous rates of change
• use differentiation rules to compute the derivatives of algebraic functions
• compute the derivatives of exponential, logarithmic and trigonometric functions
• compute derivatives using implicit differentiation
• formulate and solve problems involving marginal analysis, elasticity, points of diminishing returns, and other forms of economic modeling
• apply the concepts of differentials and linear approximations
• use Newton’s method to determine points of intersection
• sketch graphs of functions by applying first and second derivative techniques as well as analysis of vertical, horizontal and slant asymptotes
• use differentiation to determine the local and absolute extrema of functions

Additional topics that may be included in the course:

• apply the concept of an annuity to loans, mortgages and investments
• solving problems involving Markov Chains, Linear Programming and Game Theory
• compute the definite and indefinite integral of a function
• use integration techniques (substitution, integration by parts and others) to compute integrals
• apply the integral to problems in Business and the Social Sciences