Loyola University Chicago

Mathematics and Statistics

MATH 161

Textbook for MATH 162 and MATH 162: Dwyer and Gruenward. Calculus Resequenced for Students in STEM, preliminary edition. Wiley. ISBN: 978-1119321590.


Note: MATH 162A uses a different textbook. Namely, James Stewart. Calculus, Early Transcendentals (WebAssign eBook) 8th ed. Cengage Learning. Be sure you are reading the correct information.

Chapter 1: Functions and Models
  1.1 Four Ways to Represent a Function
  1.2 Mathematical Models: A Catalog of Essential Functions
  1.3 New Functions from Old Functions
  1.4 Exponential Functions and Logarithms
  1.5 Inverse Functions and Logarithms 
    Optional: Graphing with calculators, Mathematica, Wolfram Alpha (pp. xxiv-xxv)

Chapter 2: Limits and Derivatives
  2.1 The Tangent and Velocity Problems
  2.2 The Limit of a Function
  2.3 Calculating Limits Using the Limit Laws
  2.4 The Precise Definition of a Limit
  2.5 Continuity
  2.6 Limits at Infinity; Horizontal Asymptotes
  2.7 Derivatives and Rates of Change
  2.8 The Derivative as a Function

Chapter 3: Differentiation Rules
  3.1 Derivatives of Polynomials and Exponential Functions
  3.2  The Product and Quotient Rules
  3.3 Derivatives of Trigonometric Functions
  3.4 The Chain Rule
  3.5 Implicit Differentiation
  3.6 Derivatives of Logarithmic Functions
  3.7 Rates of Change in Natural and Social Sciences
  3.8 Exponential Growth and Decay
  3.9 Related Rates
  3.10 Linear Approximations and Differentials 
  3.11 Optional: Hyperbolic Functions

Chapter 4: Applications of Derivatives
  4.1 Maximum and Minimum Values
  4.2 The Mean Value Theorem
  4.3 How Derivatives Affect the Shape of a Graph
  4.4 Indeterminate Forms and l'Hospital's Rule
  4.5 Summary of Curve Sketching
  4.6 Optional: Graphing with Calculus and Calculators 
  4.7 Optimization Problems
  4.8 Optional: Newton's Method
  4.9 Antiderivatives

Chapter 5: Integrals
  5.1 Areas and Distances
  5.2 The Definite Integral
  5.3 The Fundamental Theorem of Calculus
  5.4 Indefinite Integrals and the Net Change Theorem
  5.5 The Substitution Rule

Should you choose Math 161/162 or Math 131/132?

Any questions about placement in calculus or other 100-level courses that remain after reading that section should be directed to John Houlihan, Mathematics Placement Director. Please e-mail him to set up an appointment.

Math 161/162 (Calculus I, Calculus II) is a traditional calculus sequence covering all the basic topics of one-variable calculus. This sequence is a prerequisite for Multivariable Calculus (Math 263) as well as for almost all higher-level math courses. It is required for all students majoring in Chemistry, Engineering Science, Mathematics, Physics and Statistics. It is highly recommended, although not required, for students majoring in Biology, Computer Science and Economics.

Math 131/132 (Applied Calculus I, Applied Calculus II) is more of a survey sequence covering many of the basic topics in one-variable calculus as well as some topics in multivariable calculus and differential equations. It is a terminal sequence in that it does not satisfy the prerequisites of upper-level mathematics and statistics courses. Students who enjoyed mathematics in high school and earned ACT math scores of 28 and higher or SAT math scores of 660 and higher are encouraged to choose the Math 161/162 sequence.

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Loyola Math Club Tutoring

The Loyola Math Club offers free tutoring to students in 100-level MATH courses (and others). 

Click here to see when it is offered this semester.