MATH 20500: Elements of Calculus
Career: Undergraduate
Category: Regular
Term Offered: Fall, Spring, Summer
Pre-requisites: C or better in Math 19500 or
placement
Hours/Credits: 4 HR/WK; 4 CR
Date Effective: Fall 2026
Course Supervisor: David John
Catalog Description
Limits, derivatives, rules of differentiation, differentials, graph sketching, maximum and minimum problems, related rates, exponential and logarithmic functions, differential equations, anti-derivatives, area, volume, applications to economics. This course is intended for Biology and Economics majors.
Text: Applied Calculus (1st ed.), Calaway, Hoffman, Lippman.
Schedule
| Class | Topic(s) | Section(s) | Assessment |
|---|---|---|---|
| 1 | Functions; Operations on Functions; Linear Functions | 1.1, 1.2, 1.3 | N/A |
| 2 | Linear Functions; Exponents; Exponential Functions | 1.3, 1.4, 1.7 | N/A |
| 3 | Exponential Functions; Logarithmic Functions; Prelude to the Derivative | 1.7, 1.8, 2.1 | Quiz 1: 1.1–1.4 |
| 4 | Limits and Continuity; The Derivative | 2.2, 2.3 | Quiz 2: 1.7, 1.8, 2.1 |
| 5 | The Derivative | 2.3 | Quiz 3: 2.2 |
| 6 | The Derivative | 2.3 | Quiz 4: 2.3 |
| 7 | Power and Sum Rules for Derivatives | 2.4 | Exam 1: 1.1–2.3 |
| 8 | Power and Sum Rules; Product and Quotient Rules | 2.4, 2.5 | Quiz 5: 2.4 |
| 9 | Product and Quotient Rules | 2.5 | Quiz 6: 2.4, 2.5 |
| 10 | Product and Quotient Rules; Chain Rule | 2.5, 2.6 | Quiz 7: 2.5 |
| 11 | Chain Rule; Second Derivative and Concavity | 2.6, 2.7 | Quiz 8: 2.6 |
| 12 | Second Derivative and Concavity | 2.7 | Quiz 9: 2.6, 2.7 |
| 13 | Optimization | 2.8 | Exam 2: 2.4–2.7 |
| 14 | Optimization; Curve Sketching | 2.8, 2.9 | Quiz 10: 2.8 |
| 15 | Curve Sketching; Applied Optimization | 2.9, 2.10 | Quiz 11: 2.8, 2.9 |
| 16 | Applied Optimization | 2.10 | Quiz 12: 2.9 |
| 17 | Applied Optimization; Other Applications; Implicit Differentiation and Related Rates | 2.10, 2.11, 2.12 | Quiz 13: 2.10 |
| 18 | Implicit Differentiation and Related Rates | 2.12 | Quiz 14: 2.11, 2.12 |
| 19 | Prelude to the Integral; The Definite Integral | 3.1, 3.2 | Exam 3: 2.8–2.12 |
| 20 | The Definite Integral; Fundamental Theorem and Antidifferentiation | 3.2, 3.3 | Quiz 15: 3.1, 3.2 |
| 21 | Fundamental Theorem and Antidifferentiation; Antiderivatives of Formulas | 3.3, 3.4 | Quiz 16: 3.2 |
| 22 | Antiderivatives of Formulas; Substitution | 3.4, 3.5 | Quiz 17: 3.3 |
| 23 | Substitution | 3.5 | Quiz 18: 3.4 |
| 24 | Additional Integration Techniques | 3.6 | Quiz 19: 3.5 |
| 25 | Area, Volume, and Average Value | 3.7 | Exam 4: 3.1–3.6 |
| 26 | Area, Volume, and Average Value; Applications to Business | 3.7, 3.8 | Quiz 20: 3.7 |
| 27 | Applications to Business; Differential Equations | 3.8, 3.9 | Quiz 21: 3.7, 3.8 |
| 28 | Differential Equations | 3.9 | Quiz 22: 3.8 |
Course Learning Outcomes
After taking this course, the student should be able to:
- Use limits to calculate derivatives. a, b, e1, e2
- Differentiate algebraic, logarithmic and exponential functions. a, b, e1, e2
- Solve related rates problems. a, b, c
- Apply methods of calculus to sketch curves.. a, b
- Solve maximum and minimum problems. a, b, e1, e2
- Use exponential functions to model growth and decay. a, b, e1, e2
- Anti-differentiate polynomial, logarithmic and exponential functions. a, b, e1, e2
- Use calculus to find areas. a, b
Course Assessment Tools
- Term average, based mostly on in-class examinations: 60% of grade.
- Comprehensive written final exam: 40% of grade.
Departmental Learning Outcomes
The mathematics department, in its varied courses, aims to teach students to:
a. Perform numeric and symbolic
computations.
b. Construct and apply symbolic and graphical
representations of functions.
c. Model real-life problems mathematically.
d. Use technology appropriately to analyze mathematical
problems.
e. State (e1) and apply (e2) mathematical definitions and
theorems.
f. Prove fundamental theorems.
g. Construct and present (generally in writing, but
occasionally orally) a rigorous mathematical argument.
