Loyola University Chicago

Mathematics and Statistics

MATH 161: Calculus I

Credit Hours



Math Placement Test or MATH 118


A traditional introduction to differential and integral calculus. Functions, limits, continuity, differentiation, intermediate and mean-value theorems, curve sketching, optimization problems, related rates, definite and indefinite integrals, fundamental theorem of calculus, log and exponential functions. Applications to physics and other disciplines.

(Students may not receive credit for both MATH 161 and MATH 131 without permission of the departmental chair.)


G.B. Thomas, et al. Thomas' Calculus: Early Transcendentals (Single Variable) (packaged with MyMathLab), 13th ed. Pearson (2014). I 0-32-195287-1  978-0321-95287-5.

Common Syllabus for MATH 161

Chapter 1. Functions [1 week]
    Functions and their graphs: identifying functions, mathematical models. 
    Combining functions; shifting and scaling graphs. 
    Graphing with calculators and computers (introduction to Mathematica). 
    Exponential functions.
    Inverse functions and logarithms. 
    Optional: Hyperbolic functions.

Chapter 2. Limits and Continuity [1.5 weeks] 
    Rates of change and tangents to curves. 
    Calculating limits using the limit laws. 
    The precise definition of a limit. 
    One-sided limits, continuity. 
    Limits involving infinity: limits at infinity, infinite limits; asymptotes of graphs.

Chapter 3. Differentiation [4 weeks] 
    Tangents and the derivative at a point.
    The derivative as a function. 
    Differentiation rules: for polynomials and exponentials; for products and quotients. 
    The derivative as a rate of change. 
    Derivatives of trigonometric functions. 
    The chain rule.
    Implicit Differentiation. 
    Derivatives of inverse functions and logarithms. 
    Inverse trigonometric functions. 
    Related Rates. 
    Linearization and differentials. 
    Additional material (§§11.1, 11.2): parametric equations and their derivatives.
    Derivatives of Hyperbolic Functions.

Chapter 4. Applications of Derivatives [3 weeks] 
    Extreme values of functions. 
    Rolle’s theorem and the mean value theorem. 
    Monotonic functions and the first derivative test. 
    Concavity and curve sketching. 
    Applied optimization problems. 
    Indeterminate forms and l’Hopital’s rule. 
    Newton’s Method. 

Chapter 5. Integration [4 weeks] 
    Area estimates with finite sums. 
    Sigma notation and limits of finite sums. 
    The definite integral. 
    The fundamental theorem of calculus. 
    Indefinite integrals and the substitution method.
    Substitution and area between curves.