Functions of several variables, multiple integrals and applications, partial differentiation and applications, calculus of vector functions, Green's Theorem, Stokes's Theorem and Divergence Theorem.
64.000-72.000 Total Hours
Total Hours
128.000-144.000 Total Hours
64.000-72.000 Total Hours
Prerequisite: MATH 160 Prerequisite or Corequisite: None Concurrent Corequisite: None Course Advisories: None Limitation on Enrollment: None
Course Objectives:
Determine Equations of lines and planes.
Perform vector operations.
Use vector-valued functions to describe curvilinear motion and compute arc length.
Find the limit of a function at a point.
Determine if a function is differentiable at a point.
Write the equation of the tangent plane at a point.
Compute extrema and test for saddle points using the second partials test and Lagrange multipliers.
Compute double and triple integrals in different coordinate systems.
Compute line and surface integrals.
Apply Green's Theorem, Stokes' Theorem, the Divergence Theorem, and the Fundamental Theorem of Calculus for Line Integrals.
Compute and analyze the divergence and curl of a vector field.
Student Learning Outcomes
MATH200 SLO1 - Parameterize curves and surfaces in space.
MATH200 SLO2 - Determine extreme values of functions of several variables.
MATH200 SLO3 - Set up and evaluate double and triple integrals that represent areas and volumes.
MATH200 SLO4 - Set up and evaluate line and surface integrals that represent work and flux.
MATH200 SLO5 - Apply an appropriate Fundamental Theorem of Calculus to evaluate line and surface integrals.
MATH200 SLO6 - Solve problems from the sciences using vector calculus.
Vectors, Lines, Planes, and Surfaces in Three Dimensions
Vector Operations in Two and Three dimensions
Dot product, Cross Product, Triple Product
Projections
Work and Flux
Vector and Parameteric Equations of Lines and Planes
Rectangular Equation of a Plane
Surfaces
Vector valued functions
Limits and Continuity
Derivatives and Integrals
Arc length and Curvature
Tangent, Normal, and Binormal Vectors
Velocity and Acceleration
Real-Valued Functions of Several Variables
Graphs and Level Curves
Limits and Continuity
Differentiability and Tangent Planes
Differentials and the Linearization
Partial derivatives and Higher Order Derivatives
Chain rule
Directional Derivatives
Gradient and its Properties
Extreme Values and Saddle Points
Lagrange multipliers
Multiple Integration
Double integrals
Triple integrals
Integrals in polar, cylindrical and spherical co-ordinates
Change of Variables and the Jacobian Determinant
Applications of Multiple Integrals
Calculus of Vector Fields
Line integrals
The Gradient Field and Conservative Vector Fields
Green's theorem
Surface Integrals
Surface Area and Parametrically Defined Surfaces
Curl and divergence
Stokes's theorem
Divergence theorem
Methods of Instruction
Lecture
Lecture, problem solving and the use of mathematical software are the central instructional techniques. Students are expected to work outside of class on reading the text, on assigned exercises, and on computer assignments using mathematical software.
-Find the center of mass of the lamina that lies inside the unit circle and above the line y = - x if its density is |x| + |y|.
1. Appropriate Readings: Students are required to read assigned chapters in texts.
2. Writing Assignments: Students must work assigned mathematical problems requiring the understanding of abstract ideas.
3. Appropriate Outside Assignments: Students will be expected to spend a sufficient amount of time outside of class to practice techniques taught during class time, read assigned materials, and complete frequent homework and computer assignments.
4. Appropriate Assignments that Demonstrate Critical Thinking: Students must demonstrate mathematical skills which involve analyzing information, recognizing concepts in new contexts, and analysis of logical arguments. Students will learn to apply their abstract knowledge to solve problems in the sciences and will learn to use computer software in solving problems from multivariable calculus.
A student's grade will be based on multiple measures of performance in the solving of problems, designing mathematical models, preparations and analysis of graphs, and analysis of logical arguments. Such measures will typically include four hours of exams and a comprehensive final examination requiring demonstrations of problem solving skills. In addition, instructors may make use of quizzes, written homework assignments, computer assignments, or other appropriate means to judge a student's dexterity with arithmetic skills and familiarity with mathematical vocabulary and methods of proof.
Calculus with Early TranscendentalsRogawski, Freeman Publishing, 2019
TI-84 Graphing Calculator, Maple, or equivalent computer algebra system