Business Calculus: Course Syllabus and Topic Overview

Course Overview

Introduction to Business Calculus

This course provides an introduction to differential and integral calculus, focusing on applications in business, economics, biology, and social sciences. The curriculum is designed for students who require calculus for their major but are not pursuing a mathematics or physical sciences degree.

• Course Code: Math 152: Calculus for the Life and Social Sciences

• Prerequisites: Completion of specified mathematics courses with required grades or placement exam.

• Textbook: Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Expected Learning Outcomes

• Interpret and evaluate limits of algebraic, exponential, and logarithmic functions.

• Apply derivatives to analyze and solve problems involving rates of change and optimization.

• Utilize differentiation techniques for various function types.

• Apply derivatives of exponential and logarithmic functions to solve business and life science problems.

• Analyze properties and graphs of selected functions.

• Apply antiderivatives to problems involving optimization.

• Calculate areas under curves using definite integrals.

• Solve differential equations and growth/decay problems.

Course Topics and Schedule

Review of Functions

The course begins with a review of linear, quadratic, exponential, and logarithmic functions, which are foundational for understanding calculus concepts.

• Linear Functions: Functions of the form $f(x) = mx + b$

• Quadratic Functions: Functions of the form $f(x) = ax^2 + bx + c$

• Exponential Functions: Functions of the form $f(x) = a e^{bx}$

• Logarithmic Functions: Functions of the form $f(x) = a \\log_b(x)$

Limits and Continuity

Limits are essential for defining derivatives and integrals. The course covers the concept of limits, infinite limits, and limits at infinity, as well as continuity of functions.

• Limit Definition: $\\lim_{x \\to a} f(x)$

• Infinite Limits: Limits where $f(x)$ increases or decreases without bound as $x$ approaches a value.

• Limits at Infinity: $\\lim_{x \\to \\infty} f(x)$

• Continuity: A function $f(x)$ is continuous at $x=a$ if $\\lim_{x \\to a} f(x) = f(a)$

Differentiation

Differentiation is the process of finding the rate at which a function changes. The course covers basic differentiation rules, the derivative, and applications in business and economics.

• Derivative Definition: $f'(x) = \\lim_{h \\to 0} \\frac{f(x+h) - f(x)}{h}$

• Basic Differentiation Properties: Linearity, product rule, quotient rule, chain rule.

• Applications: Marginal analysis in business and economics.

Advanced Differentiation Techniques

Students learn the chain rule, implicit differentiation, and related rates, which are essential for handling more complex functions and real-world problems.

• Chain Rule: $\\frac{d}{dx} f(g(x)) = f'(g(x)) \\cdot g'(x)$

• Implicit Differentiation: Used when functions are not explicitly solved for one variable.

• Related Rates: Problems involving rates of change of related quantities.

Applications of Derivatives

Key applications include elasticity of demand, curve sketching, and optimization problems.

• Elasticity of Demand: $E = \\frac{dQ}{dP} \\cdot \\frac{P}{Q}$

• First and Second Derivative Tests: Used to determine local maxima, minima, and points of inflection.

Integration

Integration is the process of finding the area under a curve. The course covers antiderivatives, definite and indefinite integrals, and the Fundamental Theorem of Calculus.

• Antiderivative: If $F'(x) = f(x)$, then $F(x)$ is an antiderivative of $f(x)$.

• Indefinite Integral: $\\int f(x) dx$

• Definite Integral: $\\int_a^b f(x) dx$

• Fundamental Theorem of Calculus: $\\int_a^b f(x) dx = F(b) - F(a)$, where $F$ is an antiderivative of $f$.

Differential Equations

The course introduces basic differential equations, including those modeling growth and decay, which are important in business and life sciences.

• Growth/Decay Equation: $\\frac{dy}{dt} = ky$

• Solution: $y(t) = y_0 e^{kt}$

Assessment and Grading

Exams and Quizzes

Students are assessed through in-class exams, quizzes, and online homework assignments. The lowest quiz score is dropped, and the average of the remaining quizzes contributes to the final grade.

Assessment	Weight
Exams	80%
Quizzes	10%
MyLabMath Homework	10%

Letter Grade Scale

Grade	Percentage
A+	97.5-100
A	92.5-97.4
A-	90.0-92.4
B+	87.5-89.9
B	82.5-87.4
B-	80.0-82.4
C+	77.5-79.9
C	70.0-77.4
D	60-69.9
F	0-59.9

Additional Information

• Calculator Policy: Only basic scientific calculators are permitted; graphing calculators and devices with advanced functions are not allowed during exams.

• Academic Integrity: Students must adhere to college policies regarding academic honesty.

• Support Services: The Dolciani Mathematics Learning Center offers tutoring and resources for students.

Additional info: The syllabus includes policies on disabilities, sexual misconduct, and emergency procedures, which are standard for college courses but not directly related to calculus content.