Calculus with Analytic Geometry I

Course Description

MAC2311 / MAC2311C – Calculus with Analytic Geometry I is a 4-credit lecture course in the Mathematics: Calculus and Pre-Calculus taxonomy of Florida's Statewide Course Numbering System (SCNS). The course is the first semester of the standard three-semester calculus sequence and is the foundational mathematics course for engineering, the physical sciences, mathematics, and many computer-science programs. Students develop problem-solving skills, critical thinking, computational proficiency, and contextual fluency through the study of limits, derivatives, and definite and indefinite integrals of functions of one variable, including algebraic, exponential, logarithmic, and trigonometric functions, together with their applications.

MAC2311 is part of Florida's state-mandated General Education Core in Mathematics, satisfying the Gen-Ed math requirement at every Florida public college and university. The course is offered at 49 Florida public institutions and transfers as equivalent across the state. The "C" suffix variant denotes integrated lecture and supplemental instruction; both forms count for the same Gen-Ed core credit. Successful completion (grade C or better) satisfies the math requirement for STEM transfer pathways and is the prerequisite for MAC2312 (Calculus II), MAS3114 (Linear Algebra), differential equations courses, and a wide range of upper-division STEM courses.

Learning Outcomes

Required Outcomes

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

• Evaluate limits using analytical, graphical, and numerical methods, including limits at infinity and limits involving indeterminate forms.
• Apply the formal (epsilon-delta) definition of a limit to verify simple limits.
• Determine continuity of a function at a point and on an interval; identify and classify discontinuities.
• Apply the Intermediate Value Theorem and the Squeeze (Sandwich) Theorem.
• Define the derivative as a limit; compute derivatives using the limit definition and using differentiation rules (power, product, quotient, chain).
• Compute derivatives of algebraic, trigonometric, exponential, logarithmic, and inverse trigonometric functions.
• Apply implicit differentiation and logarithmic differentiation.
• Apply derivatives to analyze and graph functions, including identifying critical points, intervals of increase/decrease, concavity, inflection points, and asymptotes.
• Solve optimization problems using derivatives, including identifying absolute and relative extrema.
• Solve related-rates problems by applying derivatives to time-varying quantities.
• Apply the Mean Value Theorem and the Extreme Value Theorem.
• Apply linearization and differentials for approximation; apply Newton's method for root finding (some institutions).
• Compute antiderivatives using basic integration rules.
• Define and compute definite integrals using Riemann sums and the Fundamental Theorem of Calculus.
• Apply u-substitution to evaluate indefinite and definite integrals.
• Apply integration to compute the area between curves.

Optional Outcomes

Depending on institutional emphasis, students may also:

• Solve separable differential equations as an introduction to differential equations.
• Compute volumes of solids of revolution using the disk/washer method (often deferred to MAC2312).
• Apply derivatives in kinematics (position, velocity, acceleration of particles in motion).
• Apply L'Hopital's Rule for indeterminate forms (sometimes introduced in MAC2311; otherwise in MAC2312).
• Use computational tools (MATLAB, Python, Wolfram Alpha, Desmos, GeoGebra) to verify analytical results.
• Apply calculus to economics, biology, or physical science through context-specific problems.

Major Topics

Required Topics

• Functions and Models (Review): Algebraic, exponential, logarithmic, and trigonometric functions; function composition; inverse functions; transformations.
• Limits: Intuitive concept of a limit; one-sided limits; limits at infinity; infinite limits and vertical asymptotes; limit laws; computing limits algebraically; limits involving indeterminate forms (0/0); the formal (epsilon-delta) definition of a limit.
• Continuity: Definition; types of discontinuities (removable, jump, infinite); Intermediate Value Theorem; continuity of common function families.
• The Derivative: Tangent lines and rates of change; the derivative as a limit; the derivative as a function; differentiability and continuity; higher-order derivatives.
• Differentiation Rules: Power rule, sum/difference rule, product rule, quotient rule, chain rule; derivatives of trigonometric functions; derivatives of exponential and logarithmic functions; derivatives of inverse trigonometric functions.
• Implicit Differentiation: Differentiation of implicitly defined relations; logarithmic differentiation; derivatives of inverse functions.
• Applications of Differentiation: Related rates; linear approximation and differentials; mean value theorem and Rolle's theorem; first and second derivative tests; concavity and inflection points; curve sketching; optimization (absolute extrema and applied optimization problems).
• Antiderivatives and Indefinite Integrals: Definition; basic integration rules (power rule, exponential, logarithmic, trigonometric); applications.
• The Definite Integral: Riemann sums (left, right, midpoint); area under a curve; definition of the definite integral; properties of definite integrals.
• The Fundamental Theorem of Calculus: Both parts (the relationship between differentiation and integration; the derivative of an integral with variable upper limit).
• Substitution (u-substitution): Application to indefinite and definite integrals.
• Area Between Curves: Integration to compute the area between two functions.

Optional Topics

• Newton's Method: Iterative root-finding using derivatives.
• L'Hopital's Rule: Limits of indeterminate forms (introduced here at some institutions; deferred to MAC2312 at others).
• Volumes of Solids of Revolution: Disk and washer methods (most institutions cover in MAC2312).
• Separable Differential Equations: Brief introduction with applications (growth, decay).
• Average Value of a Function: Application of definite integrals.
• Hyperbolic Functions: Introduction (often deferred to MAC2312).

Resources & Tools

• Standard Textbooks: Calculus: Early Transcendentals by Stewart (most widely adopted in Florida); Calculus by Larson and Edwards; Calculus: Single Variable by Hughes-Hallett, McCallum, et al.; OpenStax Calculus Volume 1 (free, openstax.org)
• Online Homework Platforms: WebAssign (Stewart); Pearson MyLab Math; Cengage MindTap; UF Xronos (developed at UF, used in MAC2311 and beyond)
• Required Calculator: Texas Instruments TI-84 Plus or TI-84 Plus CE graphing calculator; some institutions allow TI-89 or TI-Nspire CX CAS but prohibit CAS calculators on exams; some institutions prohibit graphing calculators entirely on exams (e.g., UF restricts certain models).
• Free Online Tools: Desmos graphing calculator (desmos.com) — exceptional for visualization; GeoGebra; Wolfram Alpha for verification; Symbolab for step-by-step solutions
• Tutoring Resources: Free college tutoring centers at every Florida public college; Khan Academy Calculus (free); Paul's Online Math Notes (tutorial.math.lamar.edu); Professor Leonard, 3Blue1Brown, and Krista King video channels on YouTube
• UF Resources: UF MAC2311 syllabus archive (syllabus.math.ufl.edu); Department of Mathematics tutoring

Career Pathways

MAC2311 is the gateway course for STEM pathways across Florida higher education and is required across many engineering, science, and quantitative disciplines:

• Engineering Pathways – Required for transfer to all Florida public engineering programs (UF, USF, UCF, FAU, FIU, FAMU-FSU College of Engineering, FGCU, Florida Polytechnic, UNF, ERAU); part of the engineering A.A. transfer pathway.
• Mathematics and Statistics Majors – Foundation for the entire calculus sequence (MAC2311, MAC2312, MAC2313), differential equations (MAP2302), linear algebra (MAS3114), and upper-division mathematics.
• Physical Sciences – Required for physics (PHY2048/2049), chemistry (CHM 2210/2211), and astronomy majors.
• Computer Science – Required at all Florida public universities for the Computer Science B.S.; foundation for algorithms, machine learning, and theoretical CS.
• Biological and Health Sciences (some programs) – Required for some biology B.S. tracks, biomedical engineering, and competitive medical/dental school admission.
• Florida Industry Application – Calculus literacy underpins Florida's aerospace and defense (Lockheed Martin, L3Harris, Boeing, Northrop Grumman, SpaceX, Blue Origin), advanced manufacturing, semiconductor (growing in central Florida), data science, and fintech sectors.

Special Information

Gen-Ed Core Designation

MAC2311 is part of Florida's General Education Core Course Options in Mathematics, established by the Florida Department of Education and codified in Florida Statute 1007.25. All Florida public colleges and universities accept MAC2311 as fulfilling the Gen-Ed Mathematics core requirement. Students must earn a grade of C or better ("C-" is generally not accepted) for the course to satisfy degree requirements. A minimum grade of C in MAC2311 typically satisfies the four credits of general-education mathematics requirement and the Florida Statute 1007.25 "computational portion" of the State Core Mathematics requirement.

Prerequisite and Placement

Students must demonstrate readiness for college calculus through one of the following: minimum acceptable score on an institutional placement exam (e.g., UF requires ALEKS PPL ≥ 76); minimum grade of C in MAC1147 (Pre-Calculus Algebra and Trigonometry combined) or in both MAC1140 (Pre-Calculus Algebra) and MAC1114 (Trigonometry); AP Calculus AB or BC credit at the institution's required score; IB credit. Direct placement from MAC1105 (College Algebra) is generally not allowed.

Course Equivalence and Variations

MAC2311 is offered as both MAC2311 (lecture-only, 4 credits) and MAC2311C (with integrated supplemental instruction, 4-5 credits). The two forms are equivalent for transfer and Gen-Ed credit. UF and several other institutions offer an honors version (MAC3472 - Honors Calculus 1) for highly prepared students.

Workload and Time Expectations

Calculus I is widely recognized as one of the most demanding courses in the engineering/science transfer pathway. Most institutions expect 9-12 hours of weekly out-of-class work, including 4-6 hours on online homework, 2-3 hours studying notes and worked examples, and 2-3 hours in tutoring or study groups. The DFW (D, F, withdraw) rate is historically elevated; success requires consistent daily practice rather than cramming.

Foundation for Upper-Division Coursework

MAC2311 is the prerequisite for Calculus II (MAC2312), and indirectly for Calculus III (MAC2313), Differential Equations (MAP2302), Linear Algebra (MAS3114), and a wide range of upper-division engineering, physics, and computer science courses. Strong preparation in this course is essential for success in STEM majors.