Engineering and Technology Calculus I

Course Description

EGN2045 – Engineering and Technology Calculus I is a 3-credit-hour applied calculus course designed specifically for engineering technology programs and applied engineering contexts. Distinct from the standard engineering calculus sequence (MAC2311 — Calculus I, MAC2312 — Calculus II, MAC2313 — Calculus III) taken by engineering majors at Florida State University System institutions, EGN2045 emphasizes applied calculus methods with reduced theoretical depth, focusing on the calculus tools needed for engineering technology applications. The course is typically intended for students in Bachelor of Applied Science (B.A.S.) engineering technology programs and similar applied technical programs.

Topics typically include functions and graphs, limits and continuity at applied level, differentiation (derivatives, rules of differentiation, applications including optimization and related rates), and introductory integration (antiderivatives, definite integrals, the fundamental theorem of calculus, applications including area and volume). The applied emphasis means greater focus on calculation, problem-solving, and engineering applications rather than the theorem-and-proof structure characteristic of MAC2311.

EGN2045 is a Florida common course offered at approximately 2 Florida institutions. Students should consult their specific program for the calculus requirement applicable to their degree path. EGN2045 typically does not articulate as the equivalent of MAC2311 for transfer to Florida State University System engineering programs (which require MAC2311 with its theoretical foundation); however, EGN2045 transfers as the equivalent course at Florida public institutions accepting the applied calculus track per SCNS articulation policy.

Learning Outcomes

Required Outcomes

Upon successful completion of this course, students will be able to:

• Apply functions and graphs, including the algebraic and graphical representation of common functions (linear, polynomial, rational, exponential, logarithmic, trigonometric); domain and range; function composition.
• Apply limits and continuity at applied level, including the intuitive concept of limit; limit evaluation through algebraic manipulation; limits at infinity; continuity and discontinuity.
• Apply differentiation, including the definition of derivative as the limit of the difference quotient; the geometric interpretation as slope of the tangent line; the physical interpretation as rate of change.
• Apply differentiation rules, including the power rule, product rule, quotient rule, and chain rule; differentiation of common functions (polynomial, exponential, logarithmic, trigonometric, inverse trigonometric).
• Apply implicit differentiation for relations not given explicitly as functions of x.
• Apply related rates problems, including the formulation of related-rate equations, identification of given and required rates, and solution.
• Apply optimization, including the use of derivatives to find maxima and minima; the first and second derivative tests; engineering applications (minimum cost, maximum capacity, optimal proportions).
• Apply curve sketching, including the integration of first and second derivative information to sketch function graphs; identification of critical points, inflection points, asymptotes.
• Apply indefinite integration, including antiderivatives; basic integration rules; substitution method at introductory level.
• Apply definite integration, including the Riemann sum interpretation; the fundamental theorem of calculus; the calculation of definite integrals.
• Apply integration applications, including the area between curves; introductory volume calculations (where included); applications to engineering technology contexts.
• Apply differentials and linear approximation at introductory level for engineering applications.

Optional Outcomes

• Apply numerical differentiation and integration at introductory level (where included), including basic numerical methods.
• Apply introductory differential equations at conceptual level (where included), including separable equations and applications.
• Apply calculus to specific engineering technology contexts (mechanical engineering technology, electronic engineering technology, civil engineering technology, etc.).
• Use computational tools (graphing calculators, MATLAB, Python, Excel) for calculus problem-solving and visualization.

Major Topics

Required Topics

• Functions and Graphs: The function concept; common function families (linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric); domain and range; function composition; transformations of graphs.
• Limits and Continuity: The intuitive concept of limit; one-sided limits; limit laws; algebraic techniques for limit evaluation; limits at infinity; the concept of continuity; types of discontinuity (removable, jump, infinite).
• The Derivative: The definition as the limit of the difference quotient (f'(x) = lim h→0 [f(x+h) - f(x)]/h); the geometric interpretation as slope of the tangent line; the physical interpretation as rate of change; differentiability and continuity.
• Differentiation Rules: The power rule (d/dx [x^n] = nx^(n-1)); the product rule (d/dx [fg] = f'g + fg'); the quotient rule; the chain rule (d/dx [f(g(x))] = f'(g(x)) g'(x)); derivatives of trigonometric functions; derivatives of exponential and logarithmic functions; derivatives of inverse trigonometric functions.
• Implicit Differentiation: Differentiating relations like x² + y² = 25; the application to problems where y is not given explicitly as a function of x.
• Related Rates: The formulation of equations relating quantities; differentiation with respect to time; identification of given rates and required rates; engineering applications (filling tanks, ladder problems, expanding spheres, pollution dispersion).
• Maxima and Minima: Critical points; the first derivative test; the second derivative test; absolute vs. relative maxima and minima; the closed interval method.
• Optimization Applications: Engineering optimization problems (minimum material for a given volume, maximum strength for a given weight, optimal aspect ratios, minimum production cost); the systematic approach (define variables, express objective function, find domain, optimize, verify).
• Curve Sketching: The integration of first and second derivative information; intervals of increasing and decreasing; concavity; inflection points; asymptotes; the systematic approach to sketching.
• Differentials and Linear Approximation: The differential dy = f'(x) dx; linear approximation as a tool; engineering applications (error propagation at introductory level).
• Antiderivatives: The antiderivative as the inverse of differentiation; the family of antiderivatives differing by a constant; the indefinite integral notation ∫f(x) dx = F(x) + C.
• Basic Integration Rules: The power rule for integration (∫x^n dx = x^(n+1)/(n+1) + C for n ≠ -1); integration of common functions (exponential, logarithmic, trigonometric); the substitution method (u-substitution).
• Definite Integration: The Riemann sum (limit of sums of f(x)Δx); the definite integral notation; the fundamental theorem of calculus (Part 1: derivative of an integral; Part 2: evaluating definite integrals through antiderivatives).
• Area Between Curves: The area as ∫[f(x) - g(x)] dx; the proper choice of integration variable; engineering applications.
• Volume by Slicing (Where Included): Volume by cross-sections; volume of solids of revolution (disk method, washer method); engineering applications.

Optional Topics

• Numerical Methods: Numerical differentiation; numerical integration (trapezoidal rule, Simpson's rule); the application to engineering data analysis.
• Introductory Differential Equations: Separable equations; the application to growth and decay; the application to engineering technology problems.
• Discipline-Specific Applications: Mechanical engineering technology (motion, work, energy); electronic engineering technology (circuit analysis, signal analysis); civil engineering technology (structural calculations).
• Computational Tools: Graphing calculators; MATLAB or Python for calculus visualization and computation; Excel for engineering calculations involving calculus concepts.

Resources & Tools

• Common Texts: Calculus: An Applied Approach (Larson); Brief Calculus: An Applied Approach (Larson); Applied Calculus (Hughes-Hallett); Technical Calculus with Analytic Geometry (Kuhfittig — designed specifically for engineering technology); applied calculus textbooks designed for engineering technology programs
• Online Platforms: WebAssign (Cengage — paired with Larson); MyMathLab (Pearson)
• Software: Graphing calculators (TI-84, TI-Nspire); Desmos (free graphing); MATLAB or Python for engineering applications; Excel for tabular calculation
• Reference Resources: Khan Academy Calculus (free); Paul's Online Math Notes (tutorial.math.lamar.edu, free); MIT OpenCourseWare 18.01 Single Variable Calculus (free)

Career Pathways

EGN2045 supports career pathways in engineering technology and applied engineering work:

• Mechanical Engineering Technology (B.S. or B.A.S.) — Direct application; supports careers in manufacturing, machine design, and applied mechanical work.
• Electrical/Electronic Engineering Technology — Supports careers in electronics, telecommunications, power systems work.
• Civil Engineering Technology — Supports civil construction and surveying technician work.
• Industrial Engineering Technology — Supports manufacturing and operations work.
• Engineering Technology Faculty Career — With graduate study, supports community college engineering technology faculty careers.

Students intending to pursue an engineering bachelor's degree at a Florida State University System institution should consult target programs about the calculus requirement. Most engineering programs require the standard MAC2311/MAC2312/MAC2313 sequence; EGN2045 typically does not satisfy this requirement.

Special Information

Engineering vs. Engineering Technology

EGN2045 reflects an important distinction between engineering and engineering technology:

• Engineering programs (B.S. in Engineering — typically ABET EAC accredited) emphasize the theoretical foundations of engineering and prepare graduates for the engineering profession (PE licensure pathway, graduate school, design and analysis roles). Engineering programs require the rigorous MAC2311/MAC2312/MAC2313 calculus sequence.
• Engineering technology programs (B.S. or B.A.S. in Engineering Technology — typically ABET ETAC accredited) emphasize the application of engineering principles to immediate practice and prepare graduates for technical positions in industry. Engineering technology programs may use applied calculus courses like EGN2045 alongside or instead of theoretical calculus.

Both pathways are legitimate and lead to distinct, valuable careers. Students should consult an academic advisor about the appropriate path for their goals before choosing between EGN2045 and MAC2311.

General Education and Transfer

EGN2045 is a Florida common course number. It transfers as the equivalent course at Florida public institutions accepting the applied calculus track per SCNS articulation policy. However, EGN2045 typically does not articulate as the equivalent of MAC2311 for transfer to Florida State University System engineering programs. Students considering possible transfer to engineering should consult the receiving institution about the calculus requirement well before completing EGN2045.

Course Format

EGN2045 is offered in face-to-face, hybrid, and online formats. Mathematics courses translate well to online delivery; many institutions offer fully online sections.

Position in the Engineering Technology Curriculum

EGN2045 is typically taken in the second year of engineering technology study, after foundational mathematics (algebra and trigonometry, often through MAC1140/MAC1147 or equivalent). The course is followed by EGN3046 (Engineering and Technology Calculus II) where the engineering technology calculus sequence continues.

Prerequisites

EGN2045 typically requires:

• MAC1140C (Precalculus Algebra) or MAC1147 (Precalculus Algebra and Trigonometry) with grade of C or better
• College-level reading placement

Students should have current proficiency in algebra and trigonometry before beginning EGN2045.