Active Outline

General Information

Course ID (CB01A and CB01B)
MATHD001C
Course Title (CB02)
Calculus III
Course Credit Status
Credit - Degree Applicable
Effective Term
Fall 2024
Course Description
Students in this course will learn about infinite series, lines, and planes in three dimensions, vectors in two and three dimensions, parametric equations of curves, derivatives, and integrals of vector functions.
Faculty Requirements
Course Family
Not Applicable

Course Justification

This course satisfies the CSU GE/Breadth requirement Area B4 Mathematics and Quantitative Reasoning. This course satisfies the IGETC requirement Area 2 Mathematical Concepts and Quantitative Reasoning. This course is CSU and UC transferable. This course is a required core course for the A.S.-T degree in Mathematics. This is the third course in a sequence of four courses in calculus. This course emphasizes calculus in polar coordinates and for parametric functions, sequences and series, introduces vectors, lines, planes, and vector functions in three dimensions.

Foothill Equivalency

Does the course have a Foothill equivalent?
No
Foothill Course ID

Course Philosophy

Course Philosophy
Building on the ideas and techniques of calculus in MATH 1A and MATH 1B, this course introduces students to the application of derivatives and integrals to studying infinite series. Of particular interest is the way in which calculating definite integrals, not possible using elementary techniques, can be approximated using infinite series. Students are then introduced to lines, planes and vectors in three dimensions as well as alternate coordinate systems for representing them. At this juncture, students learn to compare and contrast the strengths and weaknesses of the various coordinate systems, and to develop ideas regarding their appropriate usage. Finally, students are introduced to derivatives and integrals of vector functions, and apply these ideas to arc length, curvature, and motion in space. Students are also introduced to parametric equations of curves. Here, students experience for the first time that the ideas of differentiation and integration are not limited to two dimensions, but can be generalized and studied in multi-dimensional format.



This outline contains historical notes relevant to the material covered in the sections they appear. They are not part of the actual course outline. These historical notes are to be used at the discretion of the instructor.

Formerly Statement

Course Development Options

Basic Skill Status (CB08)
Course is not a basic skills course.
Grade Options
  • Letter Grade
  • Pass/No Pass
Repeat Limit
0

Transferability & Gen. Ed. Options

Transferability
Transferable to both UC and CSU
CSU GEArea(s)StatusDetails
CGB4CSU GE Area B4 - Mathematics/Quantitative ReasoningApproved
IGETCArea(s)StatusDetails
IG2XIGETC Area 2 - Mathematical Concepts and Quantitative ReasoningApproved
C-IDArea(s)StatusDetails
MATHMathematicsApprovedMATH D001A & MATH D001B & MATH D001C required for C-ID MATH 900 S MATH D001B & MATH D001C required for C-ID MATH 220 MATH D001C & MATH D001D required for C-ID MATH 230

Units and Hours

Summary

Minimum Credit Units
5.0
Maximum Credit Units
5.0

Weekly Student Hours

TypeIn ClassOut of Class
Lecture Hours5.010.0
Laboratory Hours0.00.0

Course Student Hours

Course Duration (Weeks)
12.0
Hours per unit divisor
36.0
Course In-Class (Contact) Hours
Lecture
60.0
Laboratory
0.0
Total
60.0
Course Out-of-Class Hours
Lecture
120.0
Laboratory
0.0
NA
0.0
Total
120.0

Prerequisite(s)

MATH D001B or MATH D01BH (with a grade of C or better) or equivalent

Corequisite(s)

Advisory(ies)

ESL D272. and ESL D273., or ESL D472. and ESL D473., or eligibility for EWRT D001A or EWRT D01AH or ESL D005.

Limitation(s) on Enrollment

(Not open to students with credit in the Honors Program related course.)

Entrance Skill(s)

General Course Statement(s)

(See general education pages for the requirements this course meets.)

Methods of Instruction

Lecture and visual aids

Discussion of assigned reading

Discussion and problem-solving performed in class

In-class exploration of internet sites

Quiz and examination review performed in class

Homework and extended projects

Guest speakers

Collaborative learning and small group exercises

Collaborative projects

Problem solving and exploration activities using applications software

Problem solving and exploration activities using courseware

Assignments

  1. Required readings from text
  2. Problem solving exercises
  3. A selection of homework/quizzes, group projects, exploratory worksheets.
  4. Optional project synthesizing various concepts and skills from course content

Methods of Evaluation

  1. Periodic quizzes and/or assignments from sources related to the topics listed in the curriculum are evaluated for completion and accuracy in order to assess student’s comprehension and ability to communicate the course content as well as to provide timely feedback to students on their progress.
  2. At least three one-hour exams without projects, or at least two one-hour exams with projects are required. In these evaluations the student is expected to provide complete and accurate solutions to problems that include both theory and applications by integrating methods and techniques studied in the course. The student shall receive timely feed back on their progress.
  3. One two-hour, comprehensive, final examinations is required, in which students are expected to display comprehension of course content and be able to choose methods and techniques appropriate to the various types of problems that cover course content.
  4. Projects (optional)

    Projects may be used to enhance the student's understanding of topics studied in the course in group or individual formats where communicating their understanding orally through classroom presentation or in writing. The evaluation to be based on completion and comprehension of course content and the students shall receive timely feed back on their progress.

Essential Student Materials/Essential College Facilities

Essential Student Materials: 
  • Students will use technology (computers or graphing calculators) to examine mathematical concepts graphically and numerically
Essential College Facilities:
  • None.

Examples of Primary Texts and References

AuthorTitlePublisherDate/EditionISBN
James Stewart, Daniel Clegg & Saleem Watson "Calculus: Early Transcendentals", 9th Ed. Cengage 2021.

Examples of Supporting Texts and References

AuthorTitlePublisher
Hass, Weir, and Thomas, "University Calculus, Early Transcendentals", 4th Ed. Pearson 2020.
Anton, Bivens, and Davis, "Calculus: Early Transcendentals", 10th Ed. Wiley 2011.
Hughes-Hallett, et al., "Calculus, Single and Multivariable", 7th Ed. Wiley 2017.
Mathematics Multicultural Bibliography, available on the De Anza Math department resources website.

Learning Outcomes and Objectives

Course Objectives

  • Examine sequences and series
  • Examine and apply the various convergence tests for infinite sequences and series.
  • Use power series to represent functions, and use polynomials to approximate them.
  • Examine the polar coordinate system, and graph, differentiate and integrate polar functions.
  • Investigate vectors in two and three dimensions and perform vector operations.
  • Examine vector functions and parametric curves, and graph, differentiate and integrate curves in parametric form; compute arc length.
  • Determine the equations of lines and planes.

CSLOs

  • Analyze infinite sequences and series from the perspective of convergence, using correct notation and mathematical precision.

  • Apply infinite sequences and series in approximating functions.

  • Synthesize and apply vectors, polar coordinate system and parametric representations in solving problems in analytic geometry, including motion in space.

Outline

  1. Examine sequences and series
    1. Examine the properties of infinite sequences.
    2. Examine series as limits of partial sums.
    3. Examine geometric series.
    4. Examine the harmonic series.
    5. Historical Note: Leonhard Euler (1707-1783).
  2. Examine and apply the various convergence tests for infinite sequences and series.
    1. Examine the ratios, root, integral and comparison tests.
    2. Examine the alternating series and convergence tests related to these series.
    3. Establish the idea of absolute convergence.
  3. Use power series to represent functions, and use polynomials to approximate them.
    1. Examine power series
    2. Approximate functions locally using Taylor , polynomials, Taylor series, and power series.
    3. Determine the radius and interval of convergence of power series.
    4. Differentiate and integrate power series.
    5. Historical note:
      1. Brook Taylor (1685-1731)
      2. Colin Maclaurin (1698-1746)
  4. Examine the polar coordinate system, and graph, differentiate and integrate polar functions.
    1. Introduce the polar coordinate system.
    2. Graph polar equations.
    3. Find areas of regions defined by polar functions
    4. Find arc lengths of graphs of polar functions
  5. Investigate vectors in two and three dimensions and perform vector operations.
    1. Define vector quantities such as magnitude and direction.
    2. Define vector operations.
    3. Resolve a vector into its components.
    4. Introduce theorems from geometry regarding vectors (optional)

      (helps students appreciate the ease in certain geometric ideas from a vector point of view).
    5. Apply vectors to physical attributes such as velocity, acceleration, force, distance, displacement, position, work, torque, etc.
    6. Define the dot, cross and triple product
    7. Define projections.
  6. Examine vector functions and parametric curves, and graph, differentiate and integrate curves in parametric form; compute arc length.
    1. Establish the geometric idea of representing a curve parametrically.
    2. Find derivatives and integrals of vector-valued functions.
    3. Calculate arc length and curvature.
    4. Find the tangent, normal, and binormal unit vectors.
    5. Investigate motion in space
      1. Use parametric representations and vector-valued functions to find velocity and acceleration.
      2. Use Kepler's Law to examine motion in space. (optional)
    6. Historical note:
      1. Johannes Kepler (1571-1630)
      2. Zeno's paradoxes on motion.
  7. Determine the equations of lines and planes.
    1. Find the symmetric, parametric and vector equations of a line.
    2. Find the rectangular, parametric and vector equations of a plane.
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