Loyola University Chicago

Mathematics and Statistics

MATH 161: Calculus I

Course Details
Credit Hours: 4
Prerequisites: MATH 118 with a grade of C- or higher, or Math Placement Assessment
Description: A traditional introduction to differential and integral calculus. Functions, limits, continuity, differentiation, the Intermediate Value and Mean Value Theorems, curve sketching, optimization problems, related rates, definite and indefinite integrals, the Fundamental Theorem of Calculus, logarithm and exponential functions, applications to the natural and social sciences. (Students may not receive credit for both MATH 161 and MATH 131 without permission of the departmental chair.)

Textbook for MATH 162 and MATH 162: Dwyer and Grunwald, “Calculus: Resequenced for Students in STEM”, Preliminary Edition, Wiley.


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
1.1 Functions and Their Graphs
1.2 Library of Functions
1.3 Implicit Functions and Conic Sections
1.4 Polar Functions
1.5 Parametric Functions


Chapter 2: Limits
2.1 Limits in Calculus
2.2 Limits: Numerical & Graphical Approaches
2.3 Calculating Limits Using Limit Laws
2.4 Limits at Infinity & Horizontal Asymptotes
2.5 Continuity & the Intermediate Value Theorem
2.6 Formal Definition of Limit


Chapter 3: The Derivative
3.1 Tangents, Velocities, Other Rates of Change
3.2 Derivatives
3.3 Rules for Differentiation
3.4 Product and Quotient Rules
3.5 Trigonometric Fn’s and Their Derivatives
3.6 Chain Rule
3.7 Tangents to Parametric and Polar Curves
3.8 Implicit Differentiation
3.9 Inverse Functions and Their Derivatives
3.10 Logarithmic Functions & Their Derivatives


Chapter 4: Applications of the Derivative
4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem
4.3 Derivatives and Graphs
4.4 Optimization
4.5 Applications to Rates of Change
4.6 Indeterminate Limits and L’Hopital’s Rule
4.7 Polynomial Approximations
4.8 Tangent Line Approximations: Differentials and Newton’s Method


Chapter 5: The Integral
5.1 Antiderivatives and Indefinite Integrals
5.2 Area Under a Curve and Total Change
5.3 The Definite Integral
5.4 The Fundamental Theorem of Calculus
5.5 Integration by Substitution

See Course Page for additional resources.