# MATH 161: Calculus I

Credit Hours

4

Prerequisites

Math Placement Test or MATH 118

Description

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.)

James Stewart. Calculus, Early Transcendentals (packaged with WebAssign) 8th ed. Cengage Learning

Chapter 1: Functions and Models [1 week]
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 [2.5 weeks]
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 weeks]
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 [3 weeks]
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 [2.5 weeks]
5.1 Areas and Distances
5.2 The Definite Integral
5.3 The Fundamental Theory of Calculus
5.4 Indefinite Integrals and the Net Change Theorem
5.5 The Substitution Rule