Math 270
Calculus I
Text: Calculus Early Transcendentals, 10th edition, Anton, Bivens, and Davis, Wiley, 2012
Prerequisites: Minimum ACT math score of 28, MATH 109 and MATH 110 with a grade of C or better,
MATH 143 with a grade of C or better, or permission of department.
WILEY PLUS is required. A TI-83 or TI-84 Graphing Calculator is required.
Calculus is a branch of mathematics which for over three centuries has served as the basis for the analysis
of continuous change. Applying calculus to real-life problems in science, engineering, or other fields requires
both an understanding of how the mathematics can be used to model problems and the capability of performing the calculations and computations necessary to obtain solutions. The textbook concentrates on the
most important topics of calculus (limits, derivatives, integrals, etc.), but with emphasis on the graphical and
numerical representation of functions and other relations as well as the traditional use of symbolic formulas.
The materials in our text are meant to be read thoroughly and carefully.
Week
Sections and Topics
1
Basic Review
1.1 Limits
1.2 Computing Limits
1.3 Limits at Infinity; End Behavior of a Function
2
1.5 Continuity
1.6 Continuity of Trigonometric, Exponential, and Inverse Functions
2.1 Tangent Lines and Rates of Change
3
2.2 The Derivative Function
Review
4
2.3 Introduction to Techniques of Differentiation
2.4 The Product and Quotient Rules
5
2.5 Derivatives of Trigonometric Functions
Test 1 (1.1, 1.2, 1.3, 1.5, 1.6, 2.1, 2.2)
2.6 The Chain Rule
3.1 Implicit Differentiation
6
3.2 Derivatives of Logarithmic Functions
Review
Test 2 (2.3, 2.4, 2.5, 2.6, 3.1, 3.2)
3.3 Derivatives of Exponential and Inverse Trigonometric Functions
7
3.3 Derivatives of Exponential and Inverse Trigonometric Functions
8
3.5 Local Linear Approximation; Differentials
3.4 Related Rates
3.6 L’Hopital’s Rule; Indeterminate Forms
Review
Test 3 (3.3, 3.4, 3.5, 3.6)
9
4.1 Analysis of Functions I: Increase, Decrease, and Concavity
4.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials
10
4.3 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents
4.4 Absolute Maxima and Minima
4.5 Applied Maximum and Minimum Problems
1
Week
Sections and Topics
11
4.6 Rectilinear Motion
4.8 Rolle’s Theorem; Mean-Value Theorem
Review
Test 4 (4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.8)
12
5.1 An Overview of the Area Problem
5.2 The Indefinite Integral
5.4 The Definition of Area as a Limit
5.5 The Definite Integral
13
5.6 The Fundamental Theorem of Calculus (Part I only)
Review
Test 5 (5.1, 5.2, 5.4, 5.5, 5.6)
Last updated 12 August 2015.
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