Download Calculus II - Chabot College

Chabot College
Fall 2004
Replaced Fall 2010
Course Outline for Mathematics 2
CALCULUS II
Catalog Description:
2 – Calculus II
5 units
Continuation of differential and integral calculus, including transcendental, inverse, and hyperbolic functions.
Techniques of integration, parametric equations, polar coordinates, sequences, power series and Taylor
series. Introduction to three-dimensional coordinate system and operations with vectors. Primarily for
mathematics, physical science, and engineering majors. Prerequisite: Mathematics 1 (completed with a
grade of “C” or higher). 5 hours lecture, 0 – 1 hours laboratory.
[Typical contact hours: lecture 87.5, laboratory 0 - 17.5]
Prerequisite Skills:
Before entering the course, the student should be able to:
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use delta notation;
explain limits and continuity;
use Newton’s method;
apply the definition of the derivative of a function;
define velocity and acceleration in terms of mathematics;
differentiate algebraic and trigonometric functions;
apply the chain rule;
find all maxim, minima and points of inflection on an interval;
sketch the graph of a different function;
apply implicit differentiation to solve related rate problems;
apply the Mean Value Theorem;
demonstrate an understanding of the definite integral as the limit of a Riemann sum;
demonstrate an understanding of the Fundamental Theorem of Integral Calculus;
demonstrate an understanding of differentials and their applications;
integrate using the substitution method;
find the volume of a solid of revolution using the shell, disc, washer methods;
find the volume of a solid by slicing;
find the work done by a force;
find the hydrostatic force on a vertical plate;
find the center of mass of a plane region;
approximate a definite integral using Simpson’s Rule and the Trapezoidal Rule.
Expected Outcomes for Students:
Upon completion of the course, the student should be able to:
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define natural logarithmic function in terms of a Riemann integral;
integrate and differentiate logarithmic functions;
define and differentiate inverse functions;
define an exponential function;
differentiate and integrate exponential functions;
differentiate and integrate inverse trigonometric functions;
differentiate and integrate hyperbolic functions and their inverses;
solve application problems involving logarithmic, exponential, inverse trigonometric, and hyperbolic
functions;
solve differential equations using separation of variables;
Chabot College
Course Outline for Math 2, page 2
Fall 2004
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use standard techniques of integration such as integration by parts, trigonometric integrals,
trigonometric substitution, partial fractions, rational functions of sine and cosine;
graph polar equations and find area of regions enclosed by the graphs of polar equations;
evaluate limits using L’Hopital’s Rule;
evaluate improper integrals;
use parametric representations of plane curves;
perform basic vector algebra in R2 and R3 and interpret the results geometrically;
find equations of lines and planes in R3;
construct polynomial approximations (Taylor polynomials) for various functions and estimate their
accuracy using an appropriate form of the remainder term in Taylor’s formula;
determine convergence of sequences:
determine whether a series converges absolutely, converges conditionally or diverges;
construct (directly or indirectly) power series representations (Taylor series) for various functions,
determine their radii of convergence, and use them to approximate function values.
Course Content:
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Definition of the natural logarithmic function in terms of a Riemann integral
Inverse functions
a. Definition
b. Differentiation Rule
Application of inverse function theory to define and derive properties of the exponential function from
the natural logarithm
Differentiation, integration and applications of transcendental functions
a. Logarithmic
b. Exponential
c. Inverse trigonometric
d. Hyperbolic functions
e. Inverse hyperbolic
Introduction to separable differential equations
Indeterminate forms and L’Hopital’s Rule
Techniques of integration
a. By parts
b. Trigonometric substitutionial equations
c. Trigonometric integrals
d. Partial fractions
e. Rational functions of sine and cosine
Improper integrals
Sequences and series, power series
Polynomial approximations: Taylor Polynomial
Parametric equation
Polar coordinates
Vectors
a. Vectors in two or three dimensions
b. The dot product
c. The cross product
d. Lines and planes
Methods of Presentation:
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Lecture/discussion
Audio-visual materials
Chabot College
Course Outline for Math 2, page 3
Fall 2004
Assignments and Methods of Evaluating Student Progress:
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Typical Assignments
a. A ladder 10 feet long leans against a vertical wall. If the bottom of the ladder slides away from
the base of the wall at a speed of 2 feet per second, how fast is the angle between the ladder
and the wall changing when the bottom of the ladder is 6 feet from the base of the wall?
b. Describe the motion of a particle with position (x,y) as t varies in the given interval
x = 4 – 4t,
y = 2t +5,
0<t<2
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Methods of Evaluating Student Progress
a. Homework assignments
b. Quizzes
c. Exams and final exams
Textbook(s) (typical):
Calculus, James Stewark, Brooks/Cole, 2003
Special Student Materials:
A graphing calculator may be required.
CB:al
Revised: 10/03/03