Math 2415 Calculus III Information

LSC-CyFair Math Department

Catalog Description

Advanced topics in calculus, including three dimensional coordinate systems, limits and continuity of multivariable functions, partial derivatives, directional derivatives, the gradient, extreme values, multiple integration, the calculus of vector valued functions and line and surface integrals.    

Course Learning Outcomes

The student will:

  • Perform calculus operations on vector-valued functions, including derivatives, integrals, curvature, displacement, velocity, acceleration, and torsion.
  •  Perform calculus operations on functions of several variables, including partial derivatives, directional derivatives, and multiple integrals.
  •  Find extrema and tangent planes.
  • Solve problems using the Fundamental Theorem of Line Integrals, Green's Theorem, the Divergence Theorem, and Stokes' Theorem.
  • Apply the computational and conceptual principles of calculus to the solutions of real-world problems.
  • Explore selected topics of solid analytic geometry pertaining to lines and planes.
  • Use the cylindrical and spherical coordinate systems.
  • Use three space vector operations.
  • Acquire a graphic and algebraic understanding of quadratic surfaces.
  • Analyze and apply the concepts of limits and continuity to multivariable functions.    

Contact Hour Information

Credit Hours:  4
Lecture Hours:  4
Lab Hours:  1
External Hours:  0
Total Contact Hours:  80    

Prerequisites

MATH 2414;
College level readiness in reading and writing

Required Materials

Textbook:

Willliam Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz; Calculus, Early Transcendentals, 3rd ed.; Pearson
Required: Students must buy an access code to MyMathLab, an online course management system which includes a complete eBook; students will first need a Course ID provided by the instructor in order to register; online purchase of MyMathLab access at www.mymathlab.com;
ISBN for hard copies of access codes: 9780134856926
Hardbound text (optional), ISBN: 9780134995991
Loose Leaf text + free MyMathLab access, ISBN: 9780134996684

Calculator:

Calculators may be required for some assignments/assessments at the discrection of the Instructor.  Refer to class syllabus for details.
Neither cell phones nor PDA’s can be used as calculators.  Calculators may be cleared before tests.

Textbook Sections

Chapter 13.  Vectors and the Geometry of Space

13.1  Vectors in the Plane

13.2  Vectors in Three Dimensions

13.3  Dot Products

13.4  Cross Products

13.5  Lines and Planes in Space

13.6  Cylinders and Quadric Surfaces
 

Chapter 14.  Vector-Valued Functions

14.1  Vector-Valued Functions

14.2  Calculus for Vector-Valued Functions

14.3  Motion in Space

14.4  Length of Curves

14.5  Curvature and Normal Vectors
 

Chapter 15.  Functions of Several Variables

15.1  Graphs and Level Curves

15.2  Limits and Continuity

15.3  Partial Derivatives

15.4  The Chain Rule

15.5  Directional Derivatives and the Gradient

15.6  Tangent Planes and Linear Approximation

15.7  Maximum / Minimum Problems


Chapter 16.  Multiple Integration

16.1  Double Integrals Over Rectangular Regions

16.2  Double Integrals Over General Regions

16.3  Double Integrals in Polar Coordinates

16.4  Triple Integrals

16.5  Triple Integrals in Cylindrical and Spherical Coordinates

16.6  Integrals for Mass Calculations
 

Chapter 17.  Vector Calculus

17.1  Vector Fields

17.2  Line Integrals

17.3  Conservative Vector Fields

17.4  Green’s Theorem

17.5  Divergence and Curl

17.6  Surface Integrals

17.7  Stoke's Theorem

17.8  Divergence Theorem

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