HILL COLLEGE
112 Lamar Dr.
Hillsboro, Texas 76645
COURSE SYLLABUS
Course Prefix and Number
Course Title
MATH 2413
CALCULUS I
Prepared by: T. Calhoun
Date: August 2013
Approved by:
Date:
Dean of Math & Science
Approved by:
Date:
Vice President of Instruction
Di sabi l i ti es/ AD A
In accordance with the requirements of the Americans with Disabilities
Act (ADA) and the regulations published by the United States Department of
Justice 28 C.F.R. 35.107(a), Hill College’s designated ADA coordinator, Melanie
Betz, Director of Academic Advising & Student Success, shall be responsible for
coordinating the College’s efforts to comply with and carry out its
responsibilities under ADA. Students with disabilities requiring physical,
classroom, or testing accommodations should contact the Director of Academic
Advising & Student Success, Melanie Betz, at (254) 659-7651.
Course Description: MATH 2413 Calculus 1
Limits and continuity; the Fundamental Theorem of Calculus; definition of the
derivative of a function and techniques of differentiation; applications of the
derivative to maximizing or minimizing a function; the chain rule, mean value
theorem, and rate of change problems; curve sketching; definite and indefinite
integration of algebraic, trigonometric, and transcendental functions, with an
application to calculation of areas.
Lecture Hours:
3
Lab. Hours:
3
Semester Credit Hours:
4
Prerequisites:
High school algebra, trigonometry, and geometry or approval of instructor.
Introduction and Purpose:
This course is meant both as a terminal math course and to prepare students for
more advanced topics in mathematics.
Instructional Materials:
Textbooks: Calculus: Early Transcendentals with MyMathLab. Brigss
Cochran. 1st edit. Pearson, 2011.
Supplies:
Pencils, paper, and graphing calculator.
Objectives:
At the completion of this course the student should be able to:
1. Develop solutions for tangent and area problems using the concepts of limits,
derivatives, and integrals.
2. Draw graphs of algebraic and transcendental functions considering limits,
continuity, and differentiability at a point.
3. Determine whether a function is continuous and/or differentiable at a point
using limits.
4. Use differentiation rules to differentiate algebraic and transcendental functions.
5. Identify appropriate calculus concepts and techniques to provide mathematical
models of real-world situations and determine solutions to applied problems.
6. Evaluate definite integrals using the Fundamental Theorem of Calculus.
7. Articulate the relationship between derivatives and integrals using the
Fundamental Theorem of Calculus.
The students' success in completing these objectives will be measured using
a set of examinations and assignments described in detail under the section of
this syllabus headed Method of Evaluation.
Methods of Instruction:
This course will be taught face-to-face and by various distance learning
delivery methods.
Audio-visual materials and computer-based technology will be used when
appropriate. Students will be shown how to use a calculator where appropriate.
Methods of Evaluation:
A series of three or more major exams and homework assignments will be given
during the semester; these will make up 75% of the student's final grade. The
comprehensive final will count 25%.
Letter grades for the course will be based on the following percentages:
90 - 100%
A
80 - 89%
B
70 - 79%
C
60 - 69%
D
Below 60%
F
Class policies:
Regular attendance at all class meetings is expected. Disruptions in class will
not be tolerated.
Topic Outline:
FUNCTIONS
1.1 Review of Functions
1.2 Representing Functions
1.3 Inverse, Exponential, and Logarithmic Functions
1.4 Trigonometric Functions and Their Inverses
LIMITS
2.1 The Idea of Limits
2.2 Definitions of Limits
2.3 Techniques for Computing Limits
2.4 Infinite Limits
2.5 Limits at Infinity
2.6 Continuity
2.7 Precise Definitions of Limits
DERIVATIVES
3.1 Introducing the Derivative
3.2 Rules of Differentiation
3.3 The Product and Quotient
Rules 3.4 Derivatives of
Trigonometric
3.5 Functions Derivatives as Rates of Change
3.6 The Chain Rule
3.7 Implicit Differentiation
3.8 Derivatives of Logarithmic and Exponential Functions
3.9 Derivatives of Inverse Trigonometric
Functions 3.10 Related Rates
APPLICATIONS OF THE DERIVATIVE
4.1 Maxima and Minima
4.2 What Derivatives Tell Us
4.3 Graphing Functions
4.4 Optimization Problems
4.5 Linear Approximation and Differentials
4.6 Mean Value Theorem
4.7 L’Hôpital’s Rule
4.8 Antiderivatives
ITEGRATION
5.1 Approximating Areas under Curves
5.2 Definite Integrals
5.3 Fundamental Theorem of Calculus
5.4 Working with Integrals
5.5 Substitution Rule
APPLICATIONS OF INTEGRATION
6.1 Velocity and Net Change
6.2 Regions between Curves
6.3 Volume by Slicing
6.4 Volume by Shells
6.5 Length of Curves
6.6 Physical Applications
6.7 Logarithmic and exponential functions revisited
6.8 Exponential models
BIBLIOGRAPHY
Briggs, Cochran; Calculus, Early Transcendentals. Pearson 1st edition 2011