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MATH 1172

Calculus II

0.5 credits · Undergraduate

Spring 2026 · Calculus II / Calculus II for Engineers

Topics

  • Integration by Substitution
  • Applications of Integration (areas of regions between curves, volumes
  • of solids of revolution, arc length of a curve, surface area of a surface
  • of revolution, center of mass, work, average value of a function)
  • Techniques of Integration (integration by parts, trigonometric integrals
  • trigonometric substitution, partial fractions)
  • Indeterminate Forms and L’Hospital’s Rule
  • Improper Integrals
  • Infinite Sequences and Series (sequences, limits of sequences, series
  • tests for convergence, power series, representation of functions as power
  • series, Maclauring and Taylor Series)

Readings

  • Recommended: Any edition of the following: ˆ Calculus: Early Transcendentals, by Ron Larson and Bruce Edwards, (8th Edition Hardcopy early-transcendental-functions-8e-larson-edwards/9780357759325), (Chancellor Paterson Library, Paterson Books - 4th floor; QA 303 L3274 2003).
  • Recommended: ˆ Calculus: Early Transcendentals, by James Stewart, (9th Edition Hardcopy early-transcendentals-9e-stewart-clegg-watson/9781337613927), (Chancellor Paterson Library, Paterson Books - 4th floor; QA 303 L3274 2003).
  • Recommended: Free Online Textbooks: ˆ Calculus Volume 2 by Edwin Herman, Gilbert Strang (
  • Recommended: ˆ Apex Calculus, Version 3 by Gregory Hartman (
Winter 2026

Topics

  • Applications of Integration (area between curves, volumes, center of mass
  • Pappus’s Theorem on Volumes, work, average value of a function)
  • Inverse Functions (one-to-one functions and inverses, exponential, logarithmic
  • power and inverse trigonometric functions, hyperbolic functions)
  • The Natural Exponential and Logarithmic Functions (properties, derivatives
  • and integrals, logarithmic differentiation, exponential growth and decay)
  • Indeterminate forms and l’Hospital’s Rule
  • Techniques of Integration (Integration by Parts, Trigonometric integrals
  • Trigonometric Substitution, Partial Fractions, Improper Integrals)
  • Infinite Sequences and Series (sequences, limits of sequences, infinite series
  • tests for convergence, Power Series, Representation of Functions as Power Series
  • Taylor Series)
  • mass, average values, and work in physical and engineering contexts
  • Analyze and construct inverse functions, including exponential, logarithmic, power
  • and inverse trigonometric and use their properties to solve contextual problems
  • Differentiate and integrate natural exponential and logarithmic functions, using
  • logarithmic differentiation and exponential growth and decay models to interpret real
  • situations
  • and interpret function behavior
  • Use advanced techniques of integration (such as integration by parts, trigonometric
  • solve non‑elementary integrals

Readings

Winter 2026

Readings

  • Calculus, one and several variables, Tenth edition, by Salas, Hille, Etgen
Winter 2025

Topics

  • Hyperbolic Functions and Inverse Hyperbolic Functions Lecture Notes
  • Differentiating and Integrating Hyperbolic Functions
  • Integration By Parts
  • Integrating Trigonometric Products
  • Partial Fractions
  • Volumes of Revolution 3.4
  • Arc Length
  • Improper Integrals
  • Sequences
  • Infinite Series
  • The Divergence and Integral Tests
  • Comparison Tests
  • Alternating Series
  • Ratio and Root Tests
  • Taylor and Maclaurin Series

Readings

Winter 2017

Topics

  • Applications of Integration (areas between curves, volumes, work, average
  • value of a function)
  • Inverse Functions (one-‐to-‐one functions and inverses, exponential, logarithmic
  • power and inverse trigonometric functions, hyperbolic functions)
  • The Natural Exponential and Logarithmic Functions (properties, derivatives
  • and integrals, logarithmic differentiation, exponential growth and decay)
  • Indeterminate forms and l’Hospital’s Rule
  • Techniques of Integration (Integration by Parts, Trigonometric integrals
  • Trigonometric Substitution, Partial Fractions, Improper Integrals)
  • Infinite Sequences and Series (sequences, limits of sequences, infinite series
  • tests for convergence, Power Series, Representation of Functions as Power Series
  • Taylor Series)
  • The material for the course
  • added, if time permits

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 the opportunity to enhance your understanding. If you purchased the multi-‐term Enhanced WebAssign last semester, you DO NOT have to purchase anything for this semester. Otherwise, here is the link for a single-‐term use:
  • To sign in to WebAssign for MATH 1172
Sources