# SRJC Course Outlines

 9/14/2024 7:26:43 AM MATH 16 Course Outline as of Fall 1999 Changed Course CATALOG INFORMATION Discipline and Nbr:  MATH 16 Title:  INTRO 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 17.5 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 function, limits, differential and integral calculus in one variable with applications, partial derivatives.  Emphasis on applications in business and economics.

Prerequisites/Corequisites:
MATH 155.

Recommended Preparation:

Limits on Enrollment:

Schedule of Classes Information
Description: Untitled document
Exponential and logarithmic functions, limits, differential and integral calculus in one variable with applications, partial derivatives. Emphasis on application in business and economics.

Prerequisites:MATH 155.
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: Not Certificate/Major Applicable

COURSE CONTENT

Outcomes and Objectives:
At the conclusion of this course, the student should be able to:
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To be successful, students should 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.  Define and apply characteristics functions in graphing polynomial,
rational, algebraic, exponential, and logarthmic 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.  Apply derivatives to graphing, optimization, 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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FUNCTIONS
Symbolic, graphical, and numerical representations, Operations and
composition, Inverse functions, Modeling.
GRAPHS OF FUNCTIONS
Definition and characteristics, Graphical solutions and numerical
solutions of equations, Graphs of polynomial rational, algebraic,
exponential and logarithmic functions, Graphs of Inverse functions.
DIFFERENTIAL CALCULUS
Limit of function. Derivatives(including exponential and logarithmic
functions). Techniques of differentiation, (including product,
quotient, and chain rules), Applications of the derivatives
including max/min). Antiderivatives.
INTEGRAL CALCULUS
The Fundamental Theorem of Calculus, Integration by substitution,
Tables of integrals, Applications of integration.
MULTIVARIABLE CALCULUS
Multrivariable functions and limits, Partial differentiation.
Relative max/min in two variables and Lagrange multipliers.

Assignments:
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1.  The student will have daily outside reading, problem set assignments
from required text(s), or instructor chosen supplementary materials.
2.  Instructional methodology may include, but not limited to: lecture,
demonstrations, oral recitation, discussion, supervised practice,
independent study, outside project or other assignments.