Calculus for Business and Social Sciences
Mathematics 151
Course Objectives
Objective of Math 151 course is to gain proficiency in the topics listed below.
1. Functions and Graphs
a) Polynomial and rational functions:
 Domain and range, properties and graphing techniques, horizontal and vertical
asymptotes.
 Applications to mathematical models in sciences, business and economics.
b) Exponential and Logarithmic functions:
 Their properties and graphs, solving exponential and logarithmic equations, concepts of
doubling time and half-time in mathematical models, interest rate models.
 Applications in sciences, business and economics.
2. Differential Calculus
a) Limits and continuity of functions:
 Concept of limit, rules of limits, use of graphical and numerical evidence to estimate
limits, identify situations where limits fail to exist.
 Concept of continuity, identify the points of continuity, applications to mathematical
models.
b) Derivative of functions:
 Concepts of average rate of change and instantaneous rate of change, average velocity
and instantaneous velocity, applications to mathematical models.
 Derivative as a limit concept, tangent line of a graph, derivative as rate of change,
graphical and numerical methods to estimate derivatives. applications in business and
economics; cost analysis, marginal costs, and rates of change.
c) Differentiation techniques:
Linearity property of the derivatives, product and quotient rules, chain rules, power rule,
differentiation of exponential and logarithmic functions, applications of these techniques.
d) Graphs and derivatives:
 Connection between the shape of graphs of functions and their derivatives, horizontal
tangent lines, increasing and decreasing functions, relative extrema,
 Finding critical points and use them to identify relative extrema, higher order
derivatives, concavity of graphs, first derivative test and second derivative test for
relative extrema, sketching the graphs of functions, applications to mathematical
models.
e) Applications of derivatives:
 Computation of absolute extrema of functions, implicit differentiation, related rates,
differentials and linear approximations.
 Use of derivatives to solve optimizations problems, applications of differential calculus
in mathematical models.
3. Integral Calculus
a) Anti-derivatives:
Computing anti-derivatives, chain rule and the method of substitution, applications.
b) Definite integral:

Define integral as a limit of approximating sums, definite integral and the area under a
curve, linearity property, the fundamental theorem of calculus, computation of definite
integrals using anti-derivatives.
c) Techniques of integration:
Method of substitution, integration by parts, integrals with logarithmic and exponential
functions, numerical methods to approximate definite integrals.
d) Applications of integration:
The area between two curves, average value of a function, applications to mathematical
models.