	Effective Term: Fall 2006

PALOMAR COLLEGE
COURSE OUTLINE FOR CREDIT COURSE

Courses numbered 1 - 49 are remedial or college preparatory courses which do not apply toward an A. A. Degree and are not intended for transfer.
Courses numbered 50-99 apply toward an AA Degree, but are not intended for transfer.
Courses numbered 100 and higher apply toward an AA Degree and/or are intended for transfer to a four-year college or university.

Course Number and Title: MATH 140 Calculus with Analytic Geometry, First Course

Unit Value: 5

Lecture Hours Per Week: 5

Lab Hours Per Week:

Lecture/Lab Hours Per Week:

Grading Basis: Grade/Pass/No Pass

Basic Skills Requirements: Appropriate Language and/or Computational Skills.

Requisite(s)
To satisfy a prerequisite, the student must have earned a letter grade of A, B, C or P(Pass) in the prerequisite course, unless otherwise stated.: Prerequisite:
A minimum grade of 'C' in MATH 135 , or MATH 110 and MATH 115 , or eligibility determined through the math placement process; Corequisite:
None; Prerequisite: Completion of, or concurrent enrollment in
None; Recommended Preparation:
None; Limitation on Enrollment:
None

Catalog Description:
An introduction to analytic geometry, differentiation and integration of algebraic and transcendental functions of a single variable, and applications of differentiation.

Specific Course Objectives:
Upon successful completion of the course the student will be able to:

Compute limits of elementary algebraic and transcendental functions analytically, graphically, and numerically.
Differentiate elementary algebraic and transcendental functions of a single variable.
Integrate selected elementary and transcendental functions of a single variable.
Analyze the behavior of functions using the tools of calculus.
Formulate and solve optimization and related rate application problems using graphical, numerical, and analytical methods.
Apply critical thinking skills and tools from this course to analyze problems arise in engineering, sciences and mathematics, and formulate appropriate solutions.
Apply critical thinking skills by explaining and presenting their problem-solving results and conclusions in a coherent written mathematical format.

Methods of Instruction:
Methods of Instruction may include, but are not limited to, the following:

Lecture

Content in Terms of Specific Body of Knowledge:

At least the following topics will be covered:

I. Limits and Their Properties

A. Concept and Definition of Limits

B. Finding Limits Graphically and Numerically

C. Evaluating Limits Analytically

D. Continuity and One-Sided Limits

E. Infinite Limits

II. Differentiation

A. The Derivative and the Tangent Line Problem

B. Basic Differentiation Rules and Rates of Change

C. The Product and Quotient Rules and Higher-Order Derivatives

D. The Chain Rule

E. Implicit Differentiation

F. Related Rates

III. Applications of Differentiation

A. Extrema on an Interval and the Extreme Value Theorem

B. Rolle's Theorem and the Mean Value Theorem

C. Increasing and Decreasing Functions and the First Derivative Test

D. Concavity and the Second Derivative Test

E. Limits at Infinity

F. Curve Sketching

G. Optimization Problems

H. Newton's Method

I. Differentials and Applications

IV. Integration

A. Antiderivatives and Indefinite Integration

B. Concept of Area using limits

C. Riemann Sums and Definite Integrals

D. The Fundamental Theorems of Calculus

E. Integration by Substitution

F. Numerical Integration

G. Area of a Region Between Two Curves

V. Logarithmic, Exponential, and Other Transcendental Functions

A. The Natural Logarithmic Function: Differentiation

B. The Natural Logarithmic Function: Integration

C. Inverse Functions

D. Exponential Functions: Differentiation and Integration

E. Exponential and Logarithmic functions with bases other than e and Applications

F. Inverse Trigonometric Functions: Differentiation

G. Inverse Trigonometric Functions: Integration

H. Hyperbolic Functions and Inverse Hyperbolic Functions

VI. Differential Equations

A. Differential Equations: Growth and Decay

B. Separation of Variables and the Logistic Equation

Additional topics may be included at instructor's discretion.

Textbooks/Resources:
May Include Textbooks, Manuals, Periodicals, Software, and Other Resources

Larson, Roland E., Robert P. Hostetler, and Bruce H, Edwards. Calculus with Analytic Geometry. 8th ed. Lexington: Houghton Mifflin and Company, 2006.
Stewart, James. Single Variable Calculus, Volume I. 5th ed. Pacific Grove: Brooks/Cole, 2005.

Required Reading:

Suggested Reading:

Critical Thinking:
Students are expected to use critical thinking skills along with skills learned in this course to analyze problem situations arising in mathematics, engineering and sciences, and formulate appropriate solutions.

Required Writing:
Problem-solving exercises on homework assignments and written tests are more appropriate. In addition, students may be required to write reports from one paragraph to several pages explaining concepts or explaining and interpreting solutions to non-routine or applied problems.

Outside Assignments:
Students are expected to spend a minimum of three hours per unit per week in class and on outside assignments, prorated for short-term classes.

Students are expected to read the text, study lecture notes, and complete daily homework assignments. Homework assignments may include practice solving routine problems, explaining concepts, and solving application or non-routine problems. Other assignments at instructor's discretion.

Methods of Assessment:
Methods of Assessment may include, but are not limited to, the following:

Exams/Tests
Homework
Quizzes

Open Entry/Open Exit:
No, course is not offered as open entry/open exit.

Is Course Repeatable for Reason(s) Other Than Deficient Grade? No

Contact Person: Mathews T. Chakkanakuzhi