Chabot College
Fall 2010
Course Outline for Mathematics 2
CALCULUS II
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Catalog Description:
MTH 2 - Calculus II
5.00 units
• Continuation of differential and integral calculus, including transcendental, inverse, and hyperbolic functions.
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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: MTH 1 (completed with a grade of "C" or higher)
Units
Contact Hours
Week
Term
5.00
Lecture
Laboratory
Clinical
Total
•
5.00
5.00
0
0.00
5.00
87.50
0
0.00
87.50
Prerequisite Skills:
Before entry into this course, the student should be able to:
1. use delta notation;
2. explain limits and continuity;
3. use Newton’s method;
4. apply the definition of the derivative of a function;
5. define velocity and acceleration in terms of mathematics;
6. differentiate algebraic and trigonometric functions;
7. apply the chain rule;
8. find all maxima, minima and points of inflection on an interval;
9. sketch the graph of a differentiable function;
10. apply implicit differentiation to solve related rate problems;
11. apply the Mean Value Theorem;
12. find the value of a definite integral as the limit of a Riemann sum;
13. integrate a definite integral using the Fundamental Theorem of Integral Calculus;
14. differentiate appropriate functions using the Fundamental Theorem of Integral Calculus;
15. find differentials and use differentials to solve applications;
16. integrate using the substitution method;
17. find the volume of a solid of revolution using the shell, disc, washer methods;
18. find the volume of a solid by slicing;
19. find the work done by a force;
20. find the hydrostatic force on a vertical plate;
21. find the center of mass of a plane region;
22. approximate a definite integral using Simpson’s Rule and the Trapezoidal Rule.
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Expected Outcomes for Students:
Upon completion of this course, the student should be able to:
1. define natural logarithmic function in terms of a Riemann integral;
2.
3.
4.
5.
6.
7.
8.
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;
9. solve differential equations using separation of variables;
10. use standard techniques of integration such as integration by parts, trigonometric integrals,
trigonometric substitution, partial fractions, rational functions of sine and cosine;
11. graph polar equations and find area of regions enclosed by the graphs of polar equations;
12. evaluate limits using L’Hopital’s Rule;
13. evaluate improper integrals;
14. use parametric representations of plane curves;
15. perform basic vector algebra in R^2 and R^3 and interpret the results geometrically;
16. find equations of lines and planes in R^3;
17. construct polynomial approximations (Taylor polynomials) for various functions and estimate their
accuracy using an appropriate form of the remainder term in Taylor’s formula;
18. determine convergence of sequences:
19. determine whether a series converges absolutely, converges conditionally or diverges;
20. construct (directly or indirectly) power series representations (Taylor series) for various functions,
determine their radii of convergence, and use them to approximate function values.
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Course Content:
1. Definition of the natural logarithmic function in terms of a Riemann integral
2. Inverse functions
A. Definition
B. Differentiation Rule
3. Application of inverse function theory to define and derive properties of the exponential function
from the natural logarithm
4. Differentiation, integration and applications of transcendental functions
A. Logarithmic
B. Exponential
C. Inverse trigonometric
D. Hyperbolic functions
E. Inverse hyperbolic
5. Introduction to separable differential equations
6. Indeterminate forms and L’Hopital’s Rule
7. Techniques of integration
A. By parts
B. Trigonometric substitutionial equations
C. Trigonometric integrals
D. Partial fractions
E. Rational functions of sine and cosine
8. Improper integrals
9. Sequences and series, power series
10. Polynomial approximations: Taylor Polynomial
11. Parametric equation
12. Polar coordinates
13. Vectors
A. Vectors in two or three dimensions
B. The dot product
C. The cross product
D. Lines and planes
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Methods of Presentation
1. Lecture/Discussion
2. Audio-visual materials
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Assignments and Methods of Evaluating Student Progress
1. 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
2. Methods of Evaluating Student Progress
A. Exams/Tests
B. Quizzes
C. Home Work
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Textbook (Typical):
1. Haas (2010). University Calculus Pearson/Addison Wesley.
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Special Student Materials
1. A graphing calculator may be required.