HILL COLLEGE
112 Lamar Dr.
Hillsboro, Texas 76645
COURSE SYLLABUS
Course Prefix and Number
MATH 2414
Course Title
CALCULUS II
Prepared by: T. Calhoun
Approved by:
Date: August 2013
Date:
Academic Dean Chair
Approved by:
Date:
Vice President of Instruction
Disabilities/ADA
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 2414 Calculus 2
Differentiation and integration of transcendental functions; parametric equations and
polar coordinates; techniques of integration; sequences and series; improper integrals.
Lecture Hours:
3
Lab. Hours:
3
Semester Credit Hours:
4
Prerequisites:
MATH 2413 or equivalent, 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 (at least a TI-83).
Objectives:
At the completion of this course the student should be able to:
1. Use the concepts of definite integrals to solve problems involving area, volume, work,
and other physical applications.
2. Use substitution, integration by parts, trigonometric substitution, partial fractions, and
tables of anti-derivatives to evaluate definite and indefinite integrals.
3. Define an improper integral.
4. Apply the concepts of limits, convergence, and divergence to evaluate some classes
of improper integrals.
5. Determine convergence or divergence of sequences and series.
6. Use Taylor and MacLaurin series to represent functions.
7. Use Taylor or MacLaurin series to integrate functions not integrable by conventional
methods.
8. Use the concept of polar coordinates to find areas, lengths of curves, and
representations of conic sections.
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; they 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:
TECHNIQUES OF INTEGRATION.
7.1 Integration by Parts.
7.2 Trigonometric Integrals.
7.3 Trigonometric Substitution.
7.4 Partial Fractions.
7.5 Other Integration Strategies.
7.6 Numerical Integration.
7.7 Improper Integrals.
7.8 Introduction to Differential Equations.
II. Sequences and Infinite Series
8.1
8.2
8.3
8.4
8.5
8.6
An Overview.
Sequences.
Infinite Series.
The Divergence and Integral Tests.
The Ratio and Comparison Tests.
Alternating Series.
III. Power Series
9.1 Approximating Functions with Polynomials.
9.2 Power Series.
9.3 Taylor Series.
9.4 Working with Taylor Series.
IV. PARAMETRIC AND POLAR CURVES
10.1
10.2
10.3
10.4
Parametric Equations.
Polar Coordinates.
Calculus with Polar Coordinates.
Conic Sections.
V. VECTORS AND VECTOR-VALUED FUNCTIONS
11.1 Vectors in the Plane.
11.2 Vectors in Three Dimensions.
11.3 Dot Products.
11.4 Cross Products.
11.5 Lines and Curves in Space.
11.6 Calculus of Vector-Valued Functions.
11.7 Motions in Space.
11.8 Length of Curves.
11.9 Curvature and Normal Vectors.
BIBLIOGRAPHY:
Briggs, Cochran; Calculus, Early Transcendentals. Pearson 1st edition 2011