Download Calculus I - Chabot College

Chabot College
Fall 2003
Replaced Fall 2010
Course Outline for Mathematics 1
CALCULUS I
Catalog Description:
1 – Calculus I
units
Elements of analytic geometry, derivatives, limits and continuity, differentiation of algebraic and
trigonometric functions, the definite integral. Prerequisite: Mathematics 20 (completed with a grade of “C” or
higher) or an appropriate skill level demonstrated through the mathematics assessment process. 5 hours
lecture, 0 – 1-hour laboratory.
[Typical contact hours: lecture 87.5, laboratory 0 - 17.5]
Prerequisite Skills:
Before entering the course the student should be able to:
1. apply the methods of the Theory of Equations (synthetic division, Rational Roots Theorem, etc.) to
factor polynomials and to solve algebraic equations;
2. graph algebraic functions and relations;
3. solve equations involving logarithmic, exponential and trigonometric functions;
4. prepare detailed graphs of conic sections;
5. create mathematical models using algebraic or transcendental functions;
6. use sign graphs to solve non-linear inequalities;
7. construct a proof using mathematical induction;
8. graph using translations, reflections and distortions;
9. identify and use the trigonometric functions in problem solving;
10. prove trigonometric identities;
11. develop and use exponential, logarithmic and trigonometric formulas;
12. graph exponential and trigonometric functions and their inverses;
13. graph polar equations.
Expected Outcomes for Students:
Upon completion of 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 maxima, minima and points of inflection on an interval;
sketch the graph of a differentiable 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.
Course Content:
1. Review relations, functions and graphs
2. Review lines, equations and slopes
Chabot College
Course Outline for Mathematics 1
Fall 2003
Page 2
Course Content: continued
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Limits and continuity
Mean Value Theorem
Differentials and their applications
Differentiation of algebraic functions
Differentiation of trigonometric functions
Chain rule
Related rate problems
Maxima, minima and points of inflection
Curve sketching
Applications of differentiation
Newton’s Method
Riemann sum
Definite integral and the Fundamental Theorem of Integral Calculus
Mean Value Theorem for Definite Integrals
Average value of a function
Integration by substitution
Simpson’s and Trapezoidal Rule
Areas of plane regions
Volume and surface area of solids of revolutions
Volume of solid by slicing
Arc length of plane curves
Center of mass for a plane region
Theorem of Pappus
Application of integral calculus to work and hydrostatic pressure problems
Methods of Presentations:
1. Informal lectures
2. Class discussion of problems, solutions and student’s questions
3. Audio-visual materials
Assignments and Methods of Evaluating Student Progress:
1. Typical Assignments
a. Exercises from the textbook such as the following: Show, using implicit differentiation, that any
tangent line at a point P to a circle with center O is perpendicular to the radius OP.
b. Collaborative: Given a variety of functions, to differentiate the functions.
2. Methods of Evaluating Student Progress
a. Homework
b. Quizzes
c. Class participation
d. Exams
e. Final exam
Textbook(s) (Typical):
Calculus, James Stewart, Brooks/Cole Publishing Company, 1999
Special Student Materials:
A calculator may be required.
hps 989Curriculum Math/1/9820.07 CSS Math 1 Course Outline Fall 2003 Revised: 08-23-02 Revised: 03-10-03