Chabot College
Fall 2013
Course Outline for Mathematics 16
APPLIED CALCULUS II
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Catalog Description:
MTH 16 - Applied Calculus II
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3.00 units
Techniques of integration; multivariable calculus; calculus of trigonometric functions; differential equations;
Taylor polynomials. Applications in business, economics and the life and social sciences.
Prerequisite: MTH 15 (completed with a grade of "C" or higher) or an appropriate skill level demonstrated
through the Mathematics Assessment process.
Strongly Recommended: MTH 36 or , MTH 37
Units
Contact Hours
Week
Term
3.00
Lecture
Laboratory
Clinical
Total
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3.00
3.00
0
0.00
3.00
52.50
0
0.00
52.50
Prerequisite Skills:
Before entry into this course, the student should be able to:
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graph polynomial, rational, exponential and logarithmic functions;
find limits numerically, graphically, and using limit properties;
determine intervals of continuity graphically and using continuity properties;
differentiate using the definition of the derivative;
differentiate using the rules of differentiation including the chain rule;
find equations of tangent lines;
find marginal cost, marginal revenue and marginal profit;
find all maxima, minima and points of inflection;
solve applied optimization problems;
differentiate implicitly;
solve related rate problems;
find antiderivatives using basic rules of integration and substitution;
evaluate definite integrals using the Fundamental Theorem of Calculus;
find total change given rate of change.
Expected Outcomes for Students:
Upon completion of this course, the student should be able to:
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find antiderivatives using integration by parts and tables of integrals;
evaluate improper integrals;
find partial derivatives;
solve optimization and constrained optimization problems involving functions of two variables;
evaluate double integrals;
find derivatives and integrals of trigonometric functions;
solve applied problems involving differentiation or integration of trigonometric functions;
solve simple differential equations;
solve problems involving exponential growth/decay, limited growth, and logistic growth;
10. approximate functions with Taylor Polynomials;
11. find event probabilities by integrating probability density functions;
12. find expected value, variance, and standard deviation of continuous random variables.
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Course Content:
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Methods of Presentation
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Integration Techniques
A. Integration by parts
B. Integration using tables
C. Applications
D. Improper integrals
Multivariable Calculus
A. Functions of several variables
B. Partial derivatives
C. Optimization and constrained optimization
D. Double integrals
E. Applications
Trigonometric Functions
A. Review definitions of trigonometric functions
B. Derivatives of trigonometric functions
C. Integrals of trigonometric functions
D. Applications
Differential Equations
A. Solutions of differential equations
B. Separation of variables
C. Applications
Taylor Polynomials
Probability and Calculus
A. Probability distributions
B. Expected value and variance
Lecture/Discussion
Problem Solving
Assignments and Methods of Evaluating Student Progress
1. Typical Assignments
A.
The concentration (in mg/mL) of a certain drug in a patient’s bloodstream t hours after it
has been administered is given by
B. Find the average concentration of the drug in the patient’s bloodstream over the first 12
hours after administration.
C. A company produces two types of desks, x finished desks and y unfinished desks per
week. The total weekly profit (in dollars) is given by the profit function
D. If the company’s management decides to restrict the production of these desks to a total
of 200 desks per week, how many finished desks and how many unfinished desks should
be produced each week to maximize the company’s weekly profit?
E. The life span of a certain plant species (in days) is described by the probability density
function
F. Find the probability that a plant of this species will live for 100 days or less.
G. The weekly closing price (in dollars per share) of XYZ Corporation stock in week t is
approximated by
H. Find the average closing price of the stock over the 15-week period.
2. Methods of Evaluating Student Progress
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Exams/Tests
Quizzes
Home Work
Final Examination
Textbook (Typical):
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Tan, Soo (2008). Applied Calculus Brooks Cole.
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Special Student Materials
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Scientific or graphing calculator