SPRINGFIELD TECHNICAL COMMUNITY COLLEGE
School of Mathematics, Sciences, and Engineering Transfer
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Calculus II
Math 255
4
A. Course Description
Topics include antiderivatives, indefinite and definite integration, the Fundamental
Theorem of Calculus, integration techniques, differential equations, infinite series and
Taylor Polynomials. Computer based labs are an integral part of the course.
B. Required Texts
WebAssign access code, Cengage Publishing. The text we will be using is Calculus with
Early Transcendentals, 5th ed., Larson/ Edwards WebAssign will include an e-book as
well as the online homework material.
C. Instructional Objectives
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Write the general solution of a differential equations
Use basic integration rule to find the antiderivatives.
Find particular solutions of differential equations.
Use Sigma notation to write and evaluate a sum.
Approximate the area of a plane region.
Evaluate a definite integral using limits.
Evaluate a definite integral using properties of definite integrals.
Evaluate a definite integral using the Fundamental Theorem of Calculus.
Understand and use the Mean Value Theorem.
Find the average value of a function over a closed interval.
Use a change of variables to evaluate a definite integral.
Integrate generalized trigonometric forms.
Integrate inverse trigonometric forms.
Define the hyperbolic trig functions.
Differentiate and integrate basic hyperbolic trig forms.
Find a particular solution of a differential equations
Solve growth and decay functions.
Find the area bounded by the graphs of two functions.
Find the volume of a solid of revolution
by disc method
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a. by washer method
b. by cylindrical shells
Find the arc length and area of a surface of revolution.
Find the work by a constant and variable force
Find the center of mass.
Find fluid pressure and fluid force.
Use integration by parts.
Solve trigonometric integrals.
Use trigonometric substitutions to integrate expressions.
Use partial fractions to integrate rational expressions.
Solve Apply L'Hopital's Rule to appropriate limits.
Use special substitutions where ƒ appropriate.
Identify and evaluate improper integrals.
Define sequences and infinite series.
Determine the convergence or divergence of an infinite series by the
appropriate convergence test.
Expand a function with a MacLaurin's or Taylor's power series.
Determine the radius of convergence of a power series.
D. Teaching Procedures
This course will involve both traditional learning (explanations and examples given at the
blackboard) as well as individual work on problem sets. There will be homework
assigned online, a test on each chapter, labs and a final exam.
E. Course Topics
Chapter 5
Integration
5.1
Antiderviatives and Indefinite Integration
5.2
Area
5.3
Riemann Sums and Definite Integrals
5.4
Fundamental Theorem of Calculus
5.5
Integration by Substitution
5.7
The Natural Logarithmic Function: Integration
5.8
Inverse Trigonometric Functions: Integration
5.9
Hyperbolic Functions
Chapter 6
Differential Equations
6.2
Differential Equations: Growth and Decay
6.3
Differential Equations: Separation of Variables
Chapter 7:
Applications of Integration
7.1
Area of a Region Between Two Curves
7.2
Volume: The Disk Method
7.3
Volume: The Shell Method
7.4
Arc Length and Surfaces of Revolution
7.5
7.6
7.7
Work
Moments, Centers of Mass and Centroids
Fluid Pressure and Fluid Force
Chapter 8:
Integration Techniques, L’Hôpital’s Rule, and Improper Integrals
8.1
Basic Integration Rules
8.2
Integration by Parts
8.3
Trigonometric Integration
8.4
Trigonometric Substitution
8.5
Partial Fractions
8.6
Integration by Tables and Other Techniques
8.7
Indeterminate Forms and L’Hôpital’s Rule
8.8
Improper Integrals
Chapter 9:
Infinite Series
9.1
Sequences
9.2
Series and Convergence
9.3
The Integral Test and p-series
9.4
Comparisons of Series
9.5
Alternating Series
9.6
Ratio and Root Tests
9.7
Taylor polynomials and Approximations
9.8
Power Series
9.9
Representation of Functions by Power Series
9.10 Taylor and MacLaurin Series
F.
Grading
Your average will be based on the following: Homework is 30% of your grade. The
average of your labs counts as 1 test and the final counts as 2 tests. I will drop the lowest
exam (not the final or the lab average) 70% is your test grade
G. Attendance and Classroom Conduct Policy
Late arrival to class, early departure, listening to music, and talking on the on the phone
in class constitute disruptive behavior. Students who wish to leave early should request
permission. Cell phones, pagers, portable music players, headphones and other
communications devices are not allowed in class.
H.
Academic Dishonesty:
If at any time during the semester there is any evidence of academic dishonesty by a
student on an examination, then the exam will be taken from the student and a zero will be
given and the student may be taken to the Dean Students for further action and possible
removal from the course with an F.