SRJC Course Outlines

5/28/2024 1:14:23 AMMATH 16 Course Outline as of Fall 2014

Changed Course
CATALOG INFORMATION

Discipline and Nbr:  MATH 16Title:  INTRO TO MATH ANALYSIS  
Full Title:  Introduction to Mathematical Analysis
Last Reviewed:1/9/2024

UnitsCourse Hours per Week Nbr of WeeksCourse Hours Total
Maximum4.00Lecture Scheduled4.0017.5 max.Lecture Scheduled70.00
Minimum4.00Lab Scheduled06 min.Lab Scheduled0
 Contact DHR0 Contact DHR0
 Contact Total4.00 Contact Total70.00
 
 Non-contact DHR0 Non-contact DHR Total0

 Total Out of Class Hours:  140.00Total 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:
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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: Untitled document
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:
 B4Math/Quantitative ReasoningFall 1981
 
IGETC:Transfer Area Effective:Inactive:
 2AMathematical Concepts & Quantitative ReasoningFall 1981
 
CSU Transfer:TransferableEffective:Fall 1981Inactive:
 
UC Transfer:TransferableEffective:Fall 1981Inactive:
 
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:
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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
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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:
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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:
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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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