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Course Syllabus

MATH2415 - Calculus III with Analytic Geometry

Catalog Description: Vector functions and motion, surfaces, cylindrical and spherical coordinate systems, and curve sketching. Limits and continuity of functions of two variable, partial derivatives, directional derivatives, gradient, surfaces, tangent planes, differential a

Semester Credit Hours: 4
Lecture Hours per Week:
Contact Hours per Semester: 64
State Approval Code: 2701015900

Course Subject/Catalog Number: MATH 2415
Course Title: Calculus III With Analytical Geometry

Instructional Goals and Purposes:

Lee College's instructional goals include 1) creating an academic atmosphere in which students may develop their intellects and skills and 2) providing courses so students may receive a certificate/an associate degree or transfer to a senior institution that offers baccalaureate degrees.  

General Course Objectives:

Successful completion of this course will promote the general student learning outcomes listed below. The student will be able

  1. To apply problem-solving skills through solving application problems.
  2. To demonstrate arithmetic and algebraic manipulation skills.
  3. To read and understand scientific and mathematical literature by utilizing proper vocabulary and methodology.
  4. To construct appropriate mathematical models to solve applications.
  5. To interpret and apply mathematical concepts.
  6. To use multiple approaches – physical, symbolic, graphical, and verbal – to solve application problems.

Specific Course Objectives:

Upon successful completion of the course, the student will be able

  1. To apply calculus to vectors and vector-valued functions.
  2. To describe and use partial differentiation.
  3. To apply Lagrange multipliers to solve problems.
  4. To solve multiple integrals.
  5. To find the Jacobian using determinant notation.
  6. To apply Green’s Theorem to evaluate line integrals around a bounded area.
  7. To apply the Divergence Theorem and Stokes’ Theorem to specific problems.

Course Content:

Students will be required to do the following:

  1. Find the component form of a vector.
  2. Use the properties of vector operations.
  3. Identify the direction cosines and angles for a vector.
  4. Calculate the projection of one vector onto another.
  5. Solve application problems using the dot and cross products.
  6. Determine the standard, parametric, and symmetric equations for a line in space. 7. Determine the distance between a point and a line in space.
  7. Identify and sketching quadric surfaces.
  8. Convert equations and points between rectangular, cylindrical, and spherical coordinate forms.
  9. Determine derivatives and integrals of vector-valued functions.
  10. Solve application problems involving velocity and acceleration using vector-valued functions.
  11. Solve application problems involving arc length and curvature using vector-valued functions.
  12. Determine tangent and normal vectors to a surface in space.
  13. Calculate limits and continuity for functions of several variables.
  14. Determine partial derivative and differentials.
  15. Use the chain rule for functions of several variables.
  16. Calculate directional derivatives and gradients.
  17. Determine tangent planes and normal lines.
  18. Determine extrema and saddle point for functions of several variables.
  19. Determine Lagrange multipliers.
  20. Solve application problems involving area and volume using iterated integrals.
  21. Solve application problems involving center of mass, moments of inertia, and surface area.
  22. Solve application problems using triple integrals.
  23. Determine triple integral using cylindrical and spherical coordinates.
  24. Determine double integrals using a change of variables and the Jacobian.
  25. Use the properties of vector fields.
  26. Determine the curl.
  27. Determine line integrals.
  28. Solve application problems using independence of path.
  29. Determine surface integrals.
  30. Apply Green’s theorem and Stokes’ theorem to certain line and surface integrals.

Methods of Instruction/Course Format/Delivery:

Faculty may choose from but are not limited to the following methods of instruction:   lecture, discussion, Internet, video, television, demonstrations, field trips, collaboration, readings.

Assessment:

Faculty may assign both in- and out-of-class activities to evaluate students' knowledge and abilities.   Faculty may choose from the following methods:  

  • Attendance
  • Book reviews
  • Class preparedness and participation
  • Collaborative learning projects
  • Compositions
  • Exams/tests/quizzes
  • Homework
  • Internet  
  • Journals
  • Library assignments
  • Readings
  • Research papers
  • Scientific observations
  • Student-teacher conferences
  • Written assignments

Course Grade:

Students' final grades are determined by:
100-90 A
89-80 B
79-70 C
69-60 D
59 or below F

Texts, Materials, and Supplies:

For current texts and materials, use the following link to access bookstore listings:   http://www.leecollegebooks.com

Other: