MATH-2415 Calculus III


Cynthia Vega-Hernandez

Credit Spring 2024


Section(s)

MATH-2415-002 (76825)
LEC TuTh 6:30pm - 8:15pm DIL DLS DIL

MATH-2415-005 (76827)
LEC MW 9:00am - 10:45am HYS HYS1 01212.00

Course Requirements

Grades

 

Grade Components

Major Proctored: 85% (exams will be in class)

Major Unproctored: 7.5% ( tech/exploration projects/ch13, 14, & ch15 hw quizzes/take-home test portions)

Minor assessments: 7.5% (quick checks & ch16, ch17 hw quizzes) (MLM can be a replacement grade)

Grading Scale

A: 90 - 100

B: 80 – 89

C: 70 – 79

D: 60 – 69

F: < 60

What will we do in this class?

Tests: Unit tests will be given during class time. (85% category)

Homework: Practices are available in MyLabMath.  The unit average of MLM practice may be used to replace 2 quick checks per corresponding (exam) unit OR one of the quiz grades in the major unproctored grade category (if not quick checks are missing)

Quick Checks/HW Quiz: Quick checks are like “mini-quizzes”- they are intended as short problem sets and are assigned for most sections.  These are due according to the calendar- the dates have been chosen to allow weekend time to hopefully avoid late submissions.   These are intended to be short regularly completed assignments to check for understanding and help keep you caught up.  They are (hopefully) not considered too lengthy, in an effort to give you manageable practice on a regular basis for grading and feedback.  (7.5% minor unproctored category)

Group work: group work will be encouraged to discuss problems, quick checks, warm-ups, and projects

Projects/Explorations: Expect at least 2 projects that will involve technology and/or exploration activities related to our topics. ( 7.5% major unproctored category)

Take-Home Test: At times, some topics may be on a take-home test portion that will count in the 7.5% major unproctored category.   (these may or may not occur- depends on time, topics and test length)

What happens if I miss something?

Dropped Grade Policy: There will be 2 dropped grades in the minor category (quick checks)

Late Work Policy:  Late work may be awarded up to 50% credit.  Usually, once a key is posted, no late work is graded.  Keys will be posted quite efficiently, usually within 24 hours of when the work was due. 

Missed Exam Policy: There is no retest exam policy.  With notice, it may be possible to test at the testing center, in the event you miss the test day.  In the event of an emergency, notice must be given by before class ends on testing day or advance notice if you are aware of a conflict. 

Attendance/Class Participation: Regular and punctual class and group attendance is expected of all students.  If attendance or compliance with other course policies is unsatisfactory, the instructor may withdraw students from the class. Please be an active participant-

In the event the college or campus closes due to unforeseen circumstances (for example, severe weather or other emergency), the student is responsible for communicating with their professor during the closure and completing any assignments or other activities designated by their professor as a result of class sessions being missed.


Readings

Required Materials 

This is a First Day™ class. The cost of required course materials, including an online version of the textbook and software access, has been added to your tuition and fees bill.    

Textbook: Calculus: Early Transcendentals, 3rd Edition by Briggs, Cochran, Gillette, & Schulz. Pearson Publishing (MyLab software) ISBN: 9780134763644

Online Component:MyLab Homework will not be required for our course.  Watching assigned videos or use of MLM for projects will be included.  Access to the software is included with the First Day version of the text.  There are optional assignments- they are not graded and are provided for your own practice.

Calculator: You must have access to technology that enables you to (1) Graph a function, (2) Find the zeroes of a function. (3) Do numerical integration. Most ACC faculty are familiar with the TI family of graphing calculators. Hence, TI calculators are highly recommended for student use. Other calculator brands can also be used. Your instructor will determine the extent of calculator use in your class section.  If you use Desmos, please be aware that the lock-down browser for testing will not allow you to simultaneously access Desmos during tests.

Other Technology: Access to a webcam and microphone are required for this course. Various websites will be used for plotting/other 3D models.  Eligible students can check out required technology at https://www.austincc.edu/students/student-technology-services.


Course Subjects

Course Calendar

https://docs.google.com/spreadsheets/d/1pOTFZe82YKh_t2sH5-f8ee9klIjHJKp3ikQ-BWBOgMc/edit?usp=sharing

Note: Schedule changes may occur during the semester. Any changes will be announced in class, usually  posted as a Blackboard Announcement and updated in the google sheet calendar (link above)

 

Week

Sections

Material

1

13.1, 13.2

Vectors in the Plane, Vectors in Three Dimensions

 

13.3

Dot Products

2

13.4

 Cross Products

 

13.5

 Lines and Planes in Space

3

13.6

 Cylinders and Quadric Surfaces

 

14.1, 14.2

 Vector-Valued Functions,  Calculus of Vector-Valued Functions

4

14.3

 Motion in Space

 

 

 Test 1

5

14.4

 Length of Curves

 

14.5

 Curvature and Normal Vectors

6

15.1, 15.2

 Graphs and Level Curves, Limits and Continuity

 

15.3, 15.4

 Partial Derivatives, The Chain Rule

7

15.5

 Directional Derivatives and the Gradient

 

15.6

 Tangent Planes and Linear Approximation

8

15.7

 Maximum/Minimum Problems

 

 

 Test 2

9

15.8

 Lagrange Multipliers

 

16.1

 Double Integrals over Rectangular Regions

10

16.2

 Double Integrals over General Regions

 

16.3

 Double Integrals in Polar Coordinates

11

16.4

 Triple Integrals

 

16.5

 Triple Integrals in Cylindrical and Spherical Coordinates

12

16.7

 Change of Variables in Multiple Integrals

 

 

 Test 3

13

17.1

 Vector Fields

 

17.2

 Line Integrals

14

17.3

 Conservative Vector Fields

 

17.4, 17.5

 Green’s Theorem, Divergence and Curl

15

17.6

 Surface Integrals

 

17.7

 Stokes’ Theorem

16

17.8

 Divergence Theorem

 

 

 Final Exam


Student Learning Outcomes/Learning Objectives

Course Rationale

The first two semesters of the calculus sequence dealt with material in two-dimensional rectangular Cartesian coordinates. A primary goal of Calculus III is to extend these ideas to three dimensions and to other coordinate systems. Therefore, in this course we introduce:

(i) several methods for interpreting graphs of multivariable functions

(ii) properties of vectors

(iii) differentiation and integration of multivariable functions

(iv) parametric equations of curves in two and three dimensions

(v) a mathematical description of motion in space

Student Learning Outcomes

Upon successful completion of the course, a student should be able to:

  1. Demonstrate the ability to analyze and visualize curves, surfaces, and regions in 2 and 3 dimensions, in Cartesian, polar, cylindrical, and spherical coordinate systems.
  2. Perform calculus operations on vector‐valued functions including limits, derivatives, integrals, curvature, and the description of motion in space.
  3. Perform calculus operations on functions of several variables including limits, partial derivatives, directional derivatives, and multiple integrals.
  4. Find and classify extrema and tangent planes of functions of two variables.
  5. Apply some of the theorems of vector calculus, such as the Fundamental Theorem of Line Integrals, Green’s Theorem, the Divergence Theorem, and Stokes' Theorem, to simplify integration problems.
  6. Apply the computational and conceptual principles of calculus to the solutions of various scientific and business applications.

 

General Education Competencies

  1. Critical Thinking: gathering, analyzing, synthesizing, evaluating and applying information is covered in every SLO. 
  2. Quantitative and Empirical Reasoning: applying mathematical, logical, and scientific principles and methods is covered in every SLO. 
  3. Technology Skills: using appropriate technology to retrieve, manage, analyze, and present information is covered in SLOs # 1, 2, 3, 5, and 7. 
  4. Written, Oral and Visual Communication: communicating effectively adapting to purpose, structure, audience and medium is covered in every SLO.

Office Hours

M W 1:45 PM - 2:30 PM SAC 1134

NOTE Also: HYS MW 10:45 AM - 11:25 AM; Adjunct office/classroom SAC TTh 4pm-4:30 pm rm 1134 Online: BB Zoom Link TTh 1:20-1:50pm (in 1351 class) Online: BB Zoom Link TTh 8:15pm-8:45pm ( in 2415 class)

Published: 01/04/2024 18:59:18