Syllabus and Course Structure: Calculus for Business and Social Sciences (MATH 1325)

Course Overview

Course Description

This course provides a foundational study of calculus with a focus on applications in business, economics, and social sciences. Topics include limits and continuity, differentiation, optimization, graphing, and integration of elementary functions. Emphasis is placed on practical applications relevant to business and social sciences. This course is not a substitute for Calculus I (MATH 2413).

• Prerequisite: College Algebra (MATH 1314) or Finite Mathematics (MATH 1324), or equivalent.

• Required Tools: Graphing calculator (TI-83 or TI-84; calculators with CAS such as TI-89 or TI-92 are not permitted on tests).

• Textbook: Lial, Greenwell, and Ritchey, 12th Edition, Pearson Education, 2022.

• Online Homework: MyLab Math (Pearson MyMathLab).

Course Topics and Calendar

Major Topics Covered

• Limits and Continuity (Ch. 3.1–3.2)

• Definition and Techniques of Differentiation (Ch. 3.3–4.4)

• Product, Quotient, and Chain Rules (Ch. 4.2–4.3)

• Derivatives of Exponential and Logarithmic Functions (Ch. 4.4–4.5)

• Applications of the Derivative (Ch. 5.1–6.6, 12.7)

• Optimization and Extrema (Ch. 6.1–6.3)

• Implicit Differentiation and Related Rates (Ch. 6.4–6.5)

• Differentials and L'Hospital's Rule (Ch. 6.6, 12.7)

• Integration and the Fundamental Theorem of Calculus (Ch. 7.1–7.4, 8.2)

• Volumes, Average Value, and Differential Equations (Ch. 8.2, 10.1)

Course Calendar (Selected Weeks and Topics)

Week	Topics
1	Limits, Continuity, Introduction to the Derivative
2	Related Rates, Definition of the Derivative, Graphical Differentiation
3	Techniques for Finding Derivatives, Product and Quotient Rules
5	Chain Rule, Derivatives of Exponential Functions
6	Derivatives of Logarithmic Functions, Increasing/Decreasing Functions
7	Concavity, Second Derivative Test, Curve Sketching
9	Absolute Extrema, Applications of Extrema
10	Further Business Applications, Implicit Differentiation
11	Related Rates, Differentials, L'Hospital's Rule
13	Antiderivatives, Substitution Method
14	Area and the Definite Integral, Fundamental Theorem of Calculus
15	Volumes, Average Value, Solutions of Differential Equations

Student Learning Outcomes

• Apply calculus to solve problems in business, economics, and social sciences.

• Use differentiation techniques for various functions, including logarithmic and exponential functions.

• Solve application problems involving implicit differentiation and related rates.

• Solve optimization problems with emphasis on business and social sciences applications.

• Determine and apply appropriate techniques of integration.

• Integrate functions using substitution and, where appropriate, integration by parts.

• Solve application problems using integration techniques.

Assessment and Grading

Assessment Type	Weight	Notes
CORE Quizzes	6%	Critical Thinking, Communication, Empirical & Quantitative Skills
Online Homework	10%	Problems from each section
Test #1	16%	Limits, Continuity, Derivatives, Product/Quotient Rules
Test #2	16%	Chain Rule, Exponential/Logarithmic Derivatives, Curve Sketching
Test #3	16%	Applications of Extrema, Implicit Differentiation, L'Hospital's Rule
Test #4	16%	Integration, Fundamental Theorem, Differential Equations
Final Exam	20%	Comprehensive

Grading Scale: A = 90–100%; B = 80–89%; C = 70–79%; D = 60–69%; F = 0–59%

Key Course Policies

• Attendance: Regular attendance and participation are expected.

• Homework: Completed online via MyLab Math; lowest two scores dropped; no late homework accepted.

• Exams: Four in-class exams and a comprehensive final; make-up exams only for documented emergencies.

• Technology: Only approved calculators allowed; electronic devices must be silenced and put away unless used for class activities.

• Academic Integrity: Cheating, plagiarism, and use of generative AI tools are strictly prohibited and subject to disciplinary action.

• Accommodations: Students requiring accommodations must contact the ACCESS Office and provide documentation.

Mathematical Concepts and Techniques (as outlined in the syllabus)

Limits and Continuity

• Limit: The value that a function approaches as the input approaches a certain value.

• Continuity: A function is continuous at a point if the limit exists and equals the function value at that point.

• Notation: $\lim_{x \to a} f(x) = L$

The Derivative

• Definition: The derivative of a function at a point measures the instantaneous rate of change of the function with respect to its variable.

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

• Applications: Marginal cost, marginal revenue, and optimization in business contexts.

Techniques of Differentiation

• Product Rule: $(fg)' = f'g + fg'$

• Quotient Rule: $\left( \frac{f}{g} \right)' = \frac{f'g - fg'}{g^2}$

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

Derivatives of Exponential and Logarithmic Functions

• Exponential: $\frac{d}{dx} e^{x} = e^{x}$

• Logarithmic: $\frac{d}{dx} \ln(x) = \frac{1}{x}$

Applications of the Derivative

• Optimization: Finding maximum and minimum values of functions in business applications.

• Related Rates: Determining how rates change with respect to time in applied problems.

• Concavity and Inflection Points: Using the second derivative to analyze the shape of graphs.

• L'Hospital's Rule: Used to evaluate limits of indeterminate forms: $\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}$ (if the limit exists).

Integration

• Antiderivative: A function whose derivative is the given function.

• Definite Integral: Represents the area under a curve from $a$ to $b$.

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

• Substitution Method: Used to simplify integration by changing variables.

Differential Equations

• Elementary and Separable Differential Equations: Equations involving derivatives that can be solved by separation of variables or other elementary techniques.

• Application: Modeling growth and decay in business and economics.

Additional Information

• Students are encouraged to begin studying early and consistently, as topics build upon each other.

• All institutional and course policies regarding academic integrity, accommodations, and classroom conduct apply.

• Important dates (census, withdrawal, exams) are provided in the course calendar and are subject to change with notice.

Additional info: This syllabus outlines the structure, expectations, and mathematical content for a standard Business Calculus course, matching the topics listed in the reference chapter titles. Students should refer to the official textbook and MyLab Math for detailed examples and practice problems.