MATH 141
1.
Calculus I
Catalog Description
MATH 141 Calculus I (4)
(Also listed as HNRS 141)
GE B1
Limits, continuity, differentiation. Introduction to integration. 4 lectures. Prerequisite: Completion
of ELM requirement and passing score on appropriate Mathematics Placement Examination, or
MATH 118 and high school trigonometry, or MATH 119.
2.
Required Background or Experience
Math 118 and Math 119 or equivalent.
3.
Learning Objectives
The student should:
a. Understand the meanings of functions, and be able to represent them by means of graphs.
b. Understand fundamental concepts of limits and continuity.
c. Understand the meaning of a derivative and be able to compute derivatives of algebraic
functions and trigonometric functions.
d. Be able to use derivatives to solve problems involving maxima, minima, and related rates.
e. Begin to understand integration.
4.
Text and References
Weir, Maurice, et al., Thomas’ Calculus, 12th edition, Addison-Wesley, 2010.
5.
Minimum Student Materials
Paper, pencils and notebook.
6.
Minimum University Facilities
Classroom with ample chalkboard space for class use.
7.
Content and Method
The sections listed below are considered to be the core of the course, and it is estimated that about
31 lectures will be needed to cover them. Quarters vary from 38 to 41 lectures. Possible uses for
any remaining lecture time include:
1.
2.
3.
4.
covering more sections
covering some sections in more depth
computer labs
group projects/class presentations
It is also possible to free up more class time by assigning some sections as reading assignments.
Comments accompanying some of the sections are intended to give some guidance to new
instructors, as well as to suggest possible ways in which class time might be saved without losing
important content.
12/6/2013
Modified 12/6/2013
Content
No. of Lectures
CHAPTER 1 –
FUNCTIONS
1
CHAPTER 2 –
2.1
2.2
2.4
2.5
2.6
LIMITS AND CONTINUITY
Rates of Change and Tangents to Curves
Limit of a Function and Limit Laws
One-Sided Limits
Continuity
Limits Involving Infinity; Asymptotes of Graphs
6
CHAPTER 3 –
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
DIFFERENTIATION
Tangents and the Derivative at a Point
The Derivative as a Function
Differentiation Rules
The Derivative as a Rate of Change
Derivatives of Trigonometric Functions
The Chain Rule
Implicit Differentiation
Related Rates (may be covered lightly)
Linearization and Differentials (the application of differentials may be
skipped)
9
CHAPTER 4 –
4.1
4.2
4.3
4.4
4.5
4.7
APPLICATIONS OF DERIVATIVES
Extreme Values of Functions
The Mean Value Theorem
Monotonic Functions and the First Derivative Test
Concavity and Curve Sketching
Applied Optimization
Antiderivatives
9
CHAPTER 5 –
5.1
5.2
INTEGRATION
Area and Estimating with Finite Sums
Sigma Notation and Limits of Finite Sums (calculations involving sigma
notation may be covered lightly)
The Definite Integral
The Fundamental Theorem of Calculus
Indefinite Integrals and the Substitution Method
Substitution and Area Between Curves (focus on substitution over
area between curves)
6
5.3
5.4
5.5
5.6
Total
Method
Largely lecture with blackboard illustration of the discussion along with supervised work and
individual conferences.
8.
Methods of Assessment
The primary methods of assessment are examinations, quizzes and homework. A comprehensive
final examination is required. Students are expected to show their work, and are graded on the
correctness of their answers as well as their understanding of the concepts and techniques.
____
31