# SRJC Course Outlines

 4/23/2024 10:21:51 AM MATH 16 Course Outline as of Summer 2017 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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Presents techniques of calculus with emphasis placed on the application of these concepts to business and management related problems. The applications of derivatives and integrals of functions including polynomials, rational, exponential and logarithmic functions are studied.

Prerequisites/Corequisites:
Course Completion of MATH 154 or Course Completion of MATH 155 or higher; or Qualifying Placement from Math Assessment. See Student Success & Assessment Services (assessment.santarosa.edu) for more information about the assessment process.

Recommended Preparation:

Limits on Enrollment:

Schedule of Classes Information
Description: Untitled document
Presents techniques of calculus with emphasis placed on the application of these concepts to business and management related problems. The applications of derivatives and integrals of functions including polynomials, rational, exponential and logarithmic functions are studied.

Prerequisites:Course Completion of MATH 154 or Course Completion of MATH 155 or higher; or Qualifying Placement from Math Assessment. See Student Success & Assessment Services (assessment.santarosa.edu) for more information about the assessment process.
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. Find the derivatives of polynomial, rational, exponential, and logarithmic functions;
2. Find the derivatives of functions involving constants, sums, differences, products,
quotients, and the chain rule;
3. Sketch the graph of functions using horizontal and vertical asymptotes, intercepts,
and first and second derivatives to determine intervals where the function is increasing
and decreasing, maximum and minimum values, intervals of concavity and points of
inflection;
4. Analyze the marginal cost, profit and revenue when given the appropriate function;
5. Determine maxima and minima in optimization problems using the derivative;
6. Use derivatives to find rates of change and tangent lines;
7. Use calculus to analyze revenue, cost, and profit;
8. Find definite and indefinite integrals by using the general integral formulas, integration by
substitution, and other integration techniques;
9.  Use integration in business and economics applications; and
10. Use concepts in multivariable calculus to solve application problems.

Topics and Scope
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I.  Functions and their graphs
A. Definition and characteristics
B. Symbolic, graphical, and numerical representations
C. Operations and composition
D. Modeling with functions
E. Graphical and algebraic solutions of equations
F. Graphs of polynomial, rational, algebraic, exponential and logarithmic
functions
II.  Limits and intuitive limit definition of derivative
III. Increments, tangent lines, and rate of change
IV. Rules of differentiation
A.  Sum, product, and quotient
B.  Chain rule
V.  Implicit differentiation
VI. Applications of derivatives
A.  Marginal analysis
B. Optimization
C. Curve sketching
D. Relative rate of change
E.  Elasticity of Demand
VII.  Antiderivatives, indefinite and definite integrals
VIII. Multiple techniques of integration
A.  Rules of integration including sum and difference, power, and
exponential (base e)
B.   Substitution
IX.  Area between curves
X.   Approximating definite integral as a sum
XI.  Applications of integration in business and economics, including
consumers' surplus
XII.  Multivariable Calculus
A.  Introduction to functions of two or more variables
B.  Partial differentiation
C.  Applications

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)