II.  Academic Credit:  Four semester hours

 

III. Course Description:  Plane and 3-space vectors, vector valued functions, Lagrange multipliers, multiple integrals and vector calculus.  Prerequisite:  Math 142

 

IV.  Place of the Course in the Curriculum:  This course is required in the mathematics major, minor, and engineering program

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V.  Course Objectives:  This course

      A.  Extends the skills and concepts mastered and developed in the first two calculus courses to the three dimensional world in which we live, enabling the student, more realistically, to understand and appreciate the beauty and structure of God's creation.

     B.  Reviews algorithms and skills developed in the first two calculus courses, in terms of more than one dependent variable, introduces the concept of multidimensional vectors and provides practice in using these tools to solve and analyze problems.

      C.  Provides practice for the student in developing skills to analyze the components of real world problems and rewriting them in terms of differential and integral calculus notation, or as vectors.

      D.  Provides opportunity for the student to review and understand new mathematical terms and symbols, using them in the correct form and with the proper definition as understood by the international mathematical community.

      E.  Stresses the relationship to other areas of  mathematics such as real analysis, linear algebra, differential equations, statistics, as well as to the other disciplines by providing application problems in physics, biology, business, medicine, engineering, chemistry, and history. 

  

 VI.  Student Outcomes:  Upon successful completion of this course a student should be able to

      A.  Plot points and sketch curves using rectangular, cylindrical, and spherical coordinates.

      B.  Translate between rectangular, cylindrical, and spherical equations.

      C.  Sketch two and three dimensional vectors given their components; or  given the sketch of two and three dimensional vectors, write the equations of the vectors.

      D.  Calculate the dot and cross product of vectors and apply these skills to problem solving.

      E.  Sketch equations of lines and planes in space, using rectangular, cylindrical, or spherical coordinates; or, given the sketch of a line or surface, write its equation.

      F.  Calculate the derivatives and integrals of vector functions.

      G.  Use the derivatives and integrals of vectors functions to:

            1.  find the gradient of a vector

            2.  calculate velocity and acceleration vectors in space

            3.  determine the length of a curve and the amount of its curvature

            4.  calculate the equation of an osculating circle

      H.  Find the limits and continuity of multivariate functions.

       I.  Calculate the partial derivatives of multivariate functions, extending through the use of the chain rule for more than two independent variables.

       J.  Use the method of Lagrange multipliers to solve problems involving extremes in more than one independent variable.

      K.  Use first and second partial derivatives to determine the extremes of a surface.

      L.  Use multiple-integration to find the volumes and areas of three dimensional surfaces.

      M.  Write the equation of a simple vector field, given its plot; or sketch a vector field given its vector equation.

       N.  Calculate the line integrals of functions and vectors.

       O.  Use Green's theorem to evaluate line integrals.

       P.  Use surface integrals to calculate the area of a surface, given its boundaries.

       Q.  Use Stoke's theorem to evaluate surface integrals.

 

 VII.  Learning Resources:  You will need the text:  Calculus Early Transcendentals, 5th edition by James Stewart and a standard scientific calculator.

 

 VIII.  Evaluation:  Learning will be measured using textbook assignments and exams.  Textbook assignments will be due on Friday for assignments given on Monday and Tuesday of that week and on Tuesday for assignments given on Wednesday and Friday of the previous week. I will pick up and grade your problems but not necessarily every one.  Show and organize your work.  Exams will be given on Fridays.  All exams will be schievement exams and written as such.  Including the final, there will be four exams which will coung for 80% of your gradae.  Textbook assignments will count for the other 20%.Occasionally, I will present challenge problems which I will ask that you work on your own and hand in  at test time for bonus points.  Otherwise, study together, but hand in your own work.

 

 IX.  Grading:  Grading will be on a percent scale with A's in the 90% range, B's in the 80% range, C's in the 70% range, D's in the 60% range and failing below 60%.

 

 X.  Attendance Policy:  You are expected to be in class.  Absences make it very difficult to do well in class.  Four unexcused absences will drop you from the class.  Notify the instructor prior to the class if you must be absent.

 

XI.  The instructor reserves the right to modify, amend or change the syllabus as the curriculum and/or program require(s).

 

Instructor:  Larry Matthews                              Office:  Meyer Hall 314

Email:  lmatthews@blc.edu                               Phone: 344-7587

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