SRJC Course Outlines

 9/20/2024 1:15:00 AM MATH 16 Course Outline as of Spring 2011 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
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.

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: BMC Communication and Analytical ThinkingMath 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:
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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, describe and utilize in graphing the characteristics of
polynomial, rational, algebraic, exponential and logarithmic
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. Calculate limits and use limit notation with multivariable
functions.
12. 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 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. Derivatives (including exponential and logarithmic functions)
C. Techniques of differentiation (including product, quotient, and
chain rules)
D. Applications of the derivatives (including optimization)
E. Antiderivatives
IV.   Integral calculus
A. The fundamental theorem of calculus
B. Integration by substitution
C. Tables of integrals
D. Applications of integration
V.    Multivariable calculus
A. Multivariable functions and limits
B. Partial differentiation
C. Relative max/min in two variables
D. LaGrange multipliers

Assignments:
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1. Reading outside of class (approximately 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)