SRJC Course Outlines

10/22/2020 1:31:05 AMMATH 1A Course Outline as of Fall 2021

Changed Course
CATALOG INFORMATION

Discipline and Nbr:  MATH 1ATitle:  CALCULUS 1  
Full Title:  Calculus, First Course
Last Reviewed:9/14/2020

UnitsCourse Hours per Week Nbr of WeeksCourse Hours Total
Maximum5.00Lecture Scheduled5.0017.5 max.Lecture Scheduled87.50
Minimum5.00Lab Scheduled08 min.Lab Scheduled0
 Contact DHR0 Contact DHR0
 Contact Total5.00 Contact Total87.50
 
 Non-contact DHR0 Non-contact DHR Total0

 Total Out of Class Hours:  175.00Total Student Learning Hours: 262.50 

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

Catalog Description:
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Limits and continuity, differentiation, applications of the derivative, integration, applications of the integral.

Prerequisites/Corequisites:
Completion of MATH 27 or higher (MATH); OR Course Completion of MATH 25 and MATH 58; OR appropriate placement based on AB 705 mandates


Recommended Preparation:

Limits on Enrollment:

Schedule of Classes Information
Description: Untitled document
Limits and continuity, differentiation, applications of the derivative, integration, applications of the integral.
(Grade Only)

Prerequisites:Completion of MATH 27 or higher (MATH); OR Course Completion of MATH 25 and MATH 58; OR appropriate placement based on AB 705 mandates
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 900S Single Variable Calculus Sequence SRJC Equivalent Course(s): MATH1A AND MATH1B

Certificate/Major Applicable: Major Applicable Course



COURSE CONTENT

Student Learning Outcomes:
Upon completion of the course, students will be able to:
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1. State and apply basic definitions, properties, and theorems of first semester calculus.
2. Calculate limits, derivatives, definite integrals, and indefinite integrals of algebraic and transcendental functions.
3. Model and solve application problems using derivatives and integrals of algebraic and transcendental functions.
 

Objectives: Untitled document
Students will be able to:
1.   Calculate limits and use limit notation.
2.   Determine continuity of a function at a real value.
3.   Determine derivatives of polynomial, rational, algebraic, exponential, logarithmic, and trigonometric functions.
4.   Use techniques of differentiation, including product, quotient, and chain rules; determine derivatives implicitly and determine derivatives of inverse functions.
5.   Apply derivatives to graphing, optimization, and science problems.
6.   Determine antiderivatives of polynomial, rational, algebraic, exponential, logarithmic, and trigonometric functions.
7.   Use limits of Riemann sums to evaluate definite integrals to find areas.
8.   Evaluate definite integrals using the fundamental theorem of calculus.
9.   Use Trapezoidal and Simpson's Rules to approximate definite integrals.
10. Apply definite integration to compute area, volumes, and arc length, and to solve problems in science and related fields.
11. Evaluate integrals with the use of tables or a computer algebra system.

Topics and Scope
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I. Limits
    A. Definition
     B. Limits from graphs
    C. Limits evaluated analytically
         1. Limit laws
         2. Limits at infinity
         3. Infinite limits
         4. Indeterminate forms
 
II. Continuity
    A. Definition
    B. Determining continuity from definition
    C. Continuity from graphs
 
III. The Derivative
    A. Difference quotient
         1. Slope of the secant line
         2. Average rate of change
    B. Limit definition and evaluating the derivative from the definition
    C. Interpreting the derivative
         1. Slope of the tangent line
         2. Instantaneous rate of change, velocity, acceleration
    D. Rules of differentiation
    E. Product, quotient, and chain rules
    F. Basic differentiation formulas
         1. Algebraic
         2. Trigonometric
         3. Exponential
         4. Logarithmic
         5. Hyperbolic
         6. Inverses of functions
    G. Antiderivatives
 
IV. Applications of the Derivative
    A. Implicit differentiation
    B. Mean value theorem
    C. Graphing curves
    D. Linearization and differentials
    E. Related rates
    F. Optimization
    G. Other applications and modeling
    H. L'Hospital's rule
 
V. The Integral
    A. Definite integrals as limits of Riemann sums
    B. Definite and indefinite integrals
    C. Fundamental theorem of calculus
    D. Integration of polynomial, logarithmic, exponential, and trigonometric functions
    E. Integration by substitution
    F. Numerical integration using Trapezoidal and Simpson's Rules
    G. Evaluation by tables or computer algebra systems
 
VI. Applications of the Integral
    A. Area
    B. Volumes
    C. Arc length
    D. Separable differential equations
    E. Other applications and modeling

Assignments:
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1. Daily reading outside of class (20-50 pages per week)
2. Problem set assignments from required text or supplementary materials chosen by the instructor (1-6 assignment sets per week)
3. Quizzes (0-4 per week)
4. Exams (2-7 per term)
5. Final Exam
6. Projects, for example, computer explorations or modeling activities (0-10 per term)

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%
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%
Quizzes, exams, final exam
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: Early Transcendentals. 8th ed. Stewart, James. Cengage Learning. 2016 (classic)

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