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MATH 1171

Calculus I

0.5 credits · Undergraduate

Winter 2026

Topics

  • study limits, continuity, differentiation, and integration, with a focus on theory, applications
  • and problem solving. A detailed outline of course topics is provided below
  • Functions (definition, domain and range, representation of functions, piecewise
  • functions, catalog of essential functions, symmetry, new functions from old ones
  • combining functions, composition of functions)
  • Limits (intuitive definition, one-sided limits, infinite limits, limits laws
  • trigonometric limits, vertical and horizontal asymptotes, squeeze theorem, precise
  • definition)
  • Continuity (definition, types of continuous functions, types of discontinuities
  • intermediate value theorem)
  • continuity, power rule, product rule, quotient rule, chain rule, implicit differentiation
  • higher derivatives, derivative formulas)
  • Applications of Derivatives (extreme value theorem, mean value theorem
  • monotonicity and concavity, extrema, inflection points, first derivative test, second
  • derivative test, optimization problems, rate of change, related rates, curve sketching)
  • Integrals (definite integral, The Fundamental Theorem of Calculus, indefinite
  • integrals, u-substitution)
  • Analyze and describe functions (including piecewise functions)
  • identify symmetries
  • create new functions through transformations, algebraic operations and composition
  • Prove limits of functions using the epsilon-delta definition and calculate limits graphically

Readings

Winter 2026 · Calculus I / Calculus I for Engineers

Topics

  • Functions
  • limits and continuity
  • differentiation rules
  • optimization and related rates
  • definite and indefinite integration
  • Fundamental Theorem of Calculus
  • substitution.

Readings

  • No textbook purchase required. Suggested: Stewart, Calculus; Salas, Hille and Etgen, Calculus; Thomas, Weir and Hass, Calculus. Free supplements: Herman and Strang, Calculus Volume 1 (OpenStax); Gregory Hartman, Apex Calculus, version 4. Free WeBWorK is required for homework.
  • https://openstax.org/details/books/calculus-volume-1 ↗
    Source-linked resource
Fall 2025

Topics

  • ˆ Review of Real Numbers and Functions
  • – Be able to solve equalities and inequalities involving absolute values, and to express your
  • answer in interval notation
  • – Be familiar with the essential functions (linear, polynomial, piecewise, rational, trigono
  • metric, exponential, and logarithmic) and be able to compute their domains
  • – Understand how to compute the composition of two functions and find its domain
  • ˆ Limits and Continuity
  • – Be able to compute the limit of a function algebraically and from a graph when it exists
  • – Identify when the limit of a function does not exist
  • – Understand the definition of continuity in terms of limits
  • – Be able to use limits to demonstrate when a function is continuous
  • ˆ Derivatives and Differentiation Formulas
  • – Interpret the derivative as the instantaneous rate of change of a function at a given point
  • and as the slope of the corresponding tangent line
  • – Be able to compute the derivative of a function using both the limit definition and differ
  • entiation formulas

Readings

Fall 2024

Topics

  • Introduction and review
  • Exponential, trigonometric, and inverse functions
  • Limits and continuity
  • Limits at infinity, derivatives
  • Differentiation rules
  • Implicit differentiation, derivatives
  • Related rates, maximum and minimum values, relation
  • Optimization problems, L’hospital’s rules
  • The definite integral, Fundamental Theorem of Calculus
  • Substitution, areas between curves

Readings

Fall 2016

Topics

  • system
  • limits and continuity of functions
  • derivatives and differentiation formulas
  • applications of derivatives
  • anti-‐derivatives, definite integrals, indefinite integrals
  • Fundamental Theorem of Calculus
  • u-‐substitution

Readings

  • WebAssign Access will be required to complete the assignments. It contains the eBook, Calculus 8th Edition by Stewart, along with a wealth of resources that will give you opportunity to enhance your understanding. Use the following link and class key to enroll.
Fall 2014

Topics

  • Basic properties of real number system (
  • Limits and continuity of functions (
  • Derivatives and differentiation formulas (
  • Applications of derivatives (
  • Anti-derivatives, definite integrals, indefinite integrals (
  • Fundamental Theorem of Calculus (
  • u-substitutions (

Readings

  • Required: Calculus: one and several variables by Salas, Hille and Etgen, 10th edition. (We will cover Chapters 1-5.)
Fall 2011

Topics

  • Basic properties of the real number system
  • limits and continuity of functions
  • derivatives and differentiation formulas
  • applications of derivatives
  • anti
  • derivatives, definite integrals, indefinite integrals
  • Calculus
  • u-substitution

Readings

  • Book 1 Calculus: One and several variables, 10th Edition by S. Salas, G. Etgen, E. Hille MATH-1171 will cover Chapters 1-5.
  • Monday, Wednesday, and Friday 11:30 a.m. – 12:30 p.m. in UC0050 for MATH-1171-FB Pre-reading related sections in the textbook is expected.
Sources