MATH 2415
Calculus III

Western Texas College

  1. Basic Course Information
    1. Course Description:  Advanced topics in calculus, including vectors and vector-valued functions, partial differentiation, Lagrange multipliers, multiple integrals, and Jacobians; application of the line integral, including Greeen’s Theorem, the Divergence Theorem, and Stoke’s Stokes’ Theorem.
    2. Any required prerequisites:  Students must make a C or better in MATH 2414 Calculus II.
    3. Online course content is administered through the college’s learning management system (LMS), Moodle, also called eCampus.  A link to eCampus can be found on and to Moodle (the big M with a graduation cap) on the college’s home page,
  2. Student Learning Outcomes. Upon successful completion of the course the student will:
    1. Perform calculus operations on vector‐valued functions, including derivatives, integrals, curvature, displacement, velocity, acceleration, and torsion.
    2. Perform calculus operations on functions of several variables, including partial derivatives, directional derivatives, and multiple integrals.
    3. Find extrema and tangent planes.
    4. Solve problems using the Fundamental Theorem of Line Integrals, Green's Theorem, the Divergence Theorem, and Stokes' Theorem.
    5. Apply the computational and conceptual principles of calculus to the solutions of real-world problems.
  3. Testing Requirements
    1. The Midterm exam and the Final exam must be proctored by an approved testing organization.  (Ask you instructor for more details.)
    2. Students are NOT allowed to use their book or notes of any kind while taking their proctored Midterm and Final exams.
    3. All quizzes and exams are timed.
    4. Students are allowed to use a calculator.  However, the TI-89, TI-Inspire with CAS or any other calculator with CAS capability are not permitted.
  4. Major Course Requirements
    1. There will be a Midterm and a comprehensive final exam.
    2. There will be homework for every section covered.
    3. There will be lab activity for each chapter
    4. There will be a cumulative chapter quiz for each chapter.
  5. Information on Books and Other Course Materials
    1. Book:  Calculus (Early Transcendentals) 2nd Edition by Briggs, Cochran and Gillett. Textbook alone ISBN: 80321954428. 
    2. Required Access Code:  Online Students must purchase a MyMathLab Access Code.  This code can be purchased stand alone or bundled with the textbook. MyMathLab stand alone (provides e-book) ISBN:  0321653998. A la carte version w/MML ISBN: 9780321965165.
    3.  Calculators:  A TI-84 or its equivalent is strongly recommended.  A Graphing Calculator is required.
    1. Grading system:
      Midterm ………….………….…………30%
      Final Comprehensive Exam…………..35%
    2. Final Grade:  A = 90 - 100,  B = 80- 89,  C = 70 -79,  D = 60 - 69,  F = 59 and below.
  6. Other Policies, Procedures and important dates.  Please refer to the WTC Catalog for the following:
    1. Campus Calendar
    2. Final exam schedule
    3. How to drop a class.
    4. Withdrawal information
    5. Student Conduct/Academic Integrity
    6. Classroom Attendance
    7. Students with disabilities
  7. Course Content



Chapter 11

11.1  Vectors in the Plane
11.2  Vectors in Three Dimensions
11.3  Dot Products
11.4  Cross Products
11.5  Lines and Curves in Space
11.6  Calculus of Vector-Valued Functions
11.7  Motion in Space
11.8  Length of Curves
11.9  Curvature and Normal Vectors

Chapter 12

12.1  Planes and Surfaces
12.2  Graphs and Level Curves
12.3  Limits and Continuity
12.4  Partial Derivatives
12.5  The Chain Rule
12.6  Directional Derivatives and the Gradient
12.7  Tangent Planes and Linear Approximation
12.8  Maximum and Minimum Problems
12.9  Lagrange Multiplier

Chapter 13

13.1  Double Integrals over Rectangular Regions
13.2  Double Integrals over General Regions
13.3  Double Integrals in Polar Coordinates
13.4  Triple Integrals
13.5  Triple Integrals in Cylindrical and Spherical Coordinates
13.6  Integrals for Mass Calculations
13.7  Change of Variables in Multiple Integrals

Chapter 14

14.1  Vector Fields
14.2 Line Integrals
14.3  Conservative Fields
14.4  Green’s Theorem
14.5  Divergence and Curl
14.6  Surface Integrals
14.7  Stokes’  Theorem
14.8  Divergence Theorem


Last Modified: August 31, 2017