12/26/2024 11:10:37 PM	MATH 16 Course Outline as of Fall 2014	Changed Course
CATALOG INFORMATION
Discipline and Nbr:  MATH 16	Title:  INTRO TO MATH ANALYSIS
Full Title:  Introduction to Mathematical Analysis
Last Reviewed:1/9/2024

Units		Course Hours per Week			Nbr of Weeks	Course Hours Total
Maximum	4.00	Lecture Scheduled	4.00		17.5 max.	Lecture Scheduled	70.00
Minimum	4.00	Lab Scheduled	0		6 min.	Lab Scheduled	0
		Contact DHR	0			Contact DHR	0
		Contact Total	4.00			Contact Total	70.00
		Non-contact DHR	0			Non-contact DHR Total	0

Total Out of Class Hours:  140.00

Total Student Learning Hours: 210.00

Title 5 Category:  AA Degree Applicable
Grading:  Grade or P/NP
Repeatability:  00 - Two Repeats if Grade was D, F, NC, or NP
Also Listed As: 
Formerly: 

Catalog Description:

Exponential and logarithmic functions, limits, differential and integral calculus with applications, partial derivatives, and calculator techniques.  Emphasis on applications in business and economics.

Prerequisites/Corequisites:
Completion of MATH 154 or higher (VE)

Recommended Preparation:

Limits on Enrollment:

Schedule of Classes Information
Description:

Exponential and logarithmic functions, limits, differential and integral calculus with applications, partial derivatives, and calculator techniques.  Emphasis on applications in business and economics.

(Grade or P/NP)
Prerequisites:Completion of MATH 154 or higher (VE)
Recommended:
Limits on Enrollment:
Transfer Credit:CSU;UC.
Repeatability:00 - Two Repeats if Grade was D, F, NC, or NP

ARTICULATION, MAJOR, and CERTIFICATION INFORMATION

Associate Degree:		Effective:	Fall 1981	Inactive:
Area:	B MC	Communication and Analytical Thinking Math Competency
CSU GE:	Transfer Area			Effective:	Inactive:
	B4	Math/Quantitative Reasoning		Fall 1981
IGETC:	Transfer Area			Effective:	Inactive:
	2A	Mathematical Concepts & Quantitative Reasoning		Fall 1981
CSU Transfer:	Transferable	Effective:	Fall 1981	Inactive:
UC Transfer:	Transferable	Effective:	Fall 1981	Inactive:
C-ID:
CID Descriptor: MATH 140	Business Calculus	SRJC Equivalent Course(s): MATH16

Certificate/Major Applicable: Major Applicable Course

COURSE CONTENT

Outcomes and Objectives:
At the conclusion of this course, the student should be able to:

Upon successful completion of the course, students will be able to:

1.  Perform advanced operations with functions (using symbolic, graphical, and numerical representations) and apply knowledge to modeling problems.

2.  Define and graph inverse functions.

3.  Recognize and describe the characteristics of polynomial, rational, algebraic, exponential and logarithmic functions, and utilize these in graphing the functions.

4.  Solve equations graphically and algebraically.

5.  Calculate limits and use limit notation.

6.  Define the derivative and calculate derivatives of polynomial, rational, algebraic, exponential, and logarithmic functions.

7.  Use techniques of differentiation, including product, quotient and chain rules.

8.  Use derivatives as an aid to graphing, in optimization problems, and to analyze business and economic applications.

9.  Calculate antiderivatives.

10. Evaluate definite integrals using the fundamental theorem of calculus.

11. Use partial differentiation and the method of LaGrange multipliers in optimization problems.

Topics and Scope

I.    Functions

     A. Symbolic, graphical, and numerical representations

     B. Operations and composition

     C. Inverse functions

     D. Modeling with functions

II.   Graphs of functions

     A. Definition and characteristics

     B. Graphical and algebraic solutions and numerical solutions of equations

     C. Graphs of polynomial, rational, algebraic, exponential and logarithmic functions

     D. Graphs of inverse functions

III.  Differential calculus

     A. Limits of functions

     B. Increments, tangent lines, and rate of change

     C. Derivatives (including exponential and logarithmic functions)

     D. Techniques of differentiation (including sum, product, quotient, and chain rules, and implicit differentiation.)

     E. Applications of the derivatives (including marginal analysis, optimization, and curve sketching)

     F. Antiderivatives

IV.  Integral calculus

     A.  Definite and indefinite integrals and the fundamental theorem of calculus

     B. Integration by substitution

     C. Tables of integrals

     D. Applications of integration (area between curves, and applications to business and economics)

     E. Approximations to the definite integral

V.   Multivariable calculus

     A. Multivariable functions

     B. Partial differentiation

     C. Relative max/min in two variables

     D. LaGrange multipliers

Assignments:

1. Reading outside of class (0-50 pages per week)

2. Homework problem sets  (10-30)

3. Exams (3-7) and quizzes (0-30)

4. Projects (e.g. computer exploration or game analysis)  (0-2)

Methods of Evaluation/Basis of Grade.

Writing: Assessment tools that demonstrate writing skill and/or require students to select, organize and explain ideas in writing.		Writing 0 - 0%
None
This is a degree applicable course but assessment tools based on writing are not included because problem solving assessments are more appropriate for this course.
Problem solving: Assessment tools, other than exams, that demonstrate competence in computational or non-computational problem solving skills.		Problem Solving 5 - 20%
Homework problem sets
Skill Demonstrations: All skill-based and physical demonstrations used for assessment purposes including skill performance exams.		Skill Demonstrations 0 - 0%
None
Exams: All forms of formal testing, other than skill performance exams.		Exams 70 - 95%
Objective exams and quizzes
Other: Includes any assessment tools that do not logically fit into the above categories.		Other Category 0 - 10%
Projects

Representative Textbooks and Materials:

Calculus With Applications (10th ed.).  Lial, Margaret; Greenwell, Raymond; Ritchey, Nathan.  Pearson  2011.

Calculus And Its Applications (13th ed). Goldstein, Larry; Lay, David; Schneider, David.  Pearson 2013.

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