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MATH 161: Calculus I

Course Description

Course Catalog

Textbook Information

Stewart/Clegg/Watson’s Calculus: Early Transcendentals 9th edition, Multi-Term
Instant Access ISBN: 9780357128930 

Common Syllabus

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
1.5 Inverse Functions and Logarithms

Chapter 2: Limits
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: The Derivative
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 and Inverse Trigonometric Functions
10.1 Curves Defined by Parametric Equations
10.2 Calculus with Parametric Curves
10.3 Polar Coordinates
10.4 Calculus in Polar Coordinates
3.7 Rates of Change in the Natural and Social Sciences
3.8 Exponential Growth and Decay
3.9 Related Rates
3.10 Linear Approximations and Differentials

Chapter 4: Applications of the Derivative
4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem
4.3 What Derivatives Tell Us about the Shape of a Graph
4.4 Indeterminate Forms and l’Hospital’s Rule
4.5 Summary of Curve Sketching
4.7 Optimization Problems
4.9 Antiderivatives

Chapter 5: The Integral
5.1 The Area and Distance Problems
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