Math 161

Calculus I

Text: George Thomas, et al, Thomas’ Calculus: Early Transcendentals (Part 1), 12th edition, Addison-Wesley (2010), packaged with MyMathLab or MyMathLab stand-alone. Alternatively, a student may purchase only MyMathLab since the entire book is online. ISBN Volume 1 ET + MML:  0-321-705408, Make sure any online purchase includes MML.

Notes:

1. The TI-84 Plus graphing calculator or equivalent is required.
2. Depending upon your section, you may be required to use either the Mathematica or Maple software package. Both are available in the Mathematics computer labs, Crown Center 103 and 105, as well as on the Loyola network. Students may wish to purchase (at a student discount) a copy for home use as well.

Prerequisite: Math 118 (Precalculus) with a grade of "C-" or better, or appropriate score on the math placement test..

Catalog Description: This course provides a standard introduction to differential and integral calculus and covers topics ranging from functions and limits to derivatives and their applications to definite and indefinite integrals and the fundamental theorem of calculus and their applications.

Syllabus:

• Chapter 1:   Functions  (1 week)   (This chapter is essentially a review of topics covered in precalculus and algebra.)

            Functions and Their Graphs

            Identifying Functions; Mathematical Models

            Combining Functions:  Shifting and Scaling Graphs

            Graphing with Calculators and Computers  (Introduction to Maple or Mathematica)

            Exponential Functions

            Inverse Functions and Logarithms

            Optional:  Hyperbolic functions may be introduced here.

• Chapter 2:  Limits and Continuity (1.5 weeks)

            Rates of Change and Limits

            Calculating Limits Using the Limit Laws

            The Precise Definition of a Limit

            One-Sided Limits and Limits at Infinity

            Infinite Limits and Vertical Asymptotes

            Tangents and Derivatives

• Chapter 3:  Differentiation (4 weeks)

            The Derivative as a Function

            Differentiation Rules for Polynomials and Exponentials, Products and Quotients

            The Derivative as a Rate of Change

            Derivatives of Trigonometric Functions

            The Chain Rule and Parametric Equations

            Implicit Differentiation

            Derivatives of Inverse Functions and Logarithms

            Inverse Trigonometric Functions

            Related Rates

            Linearization and Differentials

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

            Antiderivatives

• Chapter 5:  Integration (4 weeks)

Estimating with Finite Sums

Sigma Notation and Limits of Finite Sums

The Definite Integral

The Fundamental Theorem of Calculus

Indefinite Integrals and the Substitution Rule

Substitution and Area between Curves