MATH 261 - Multivariate Calculus

1. Perform basic vector operations including the dot and cross product
2. Identify space curves and surfaces including lines, planes, and quadric surfaces
3. Analyze vector-valued functions and use them to solve problems
   1. Solve problems involving displacement, velocity and acceleration
   2. Evaluate limits
   3. Differentiate and integrate
   4. Evaluate arc length
   5. Evaluate curvature
   6. Identify tangent and normal vectors
4. Analyze functions of several variables
   1. Compute partial derivatives
   2. Compute gradient vectors and directional derivatives
   3. Find local linearizations and evaluate differentials
   4. Find planes tangent to function surfaces
   5. Identify extreme values and saddle points
   6. Use the chain rule to differentiate functions of several variables
5. Evaluate double integrals in Cartesian and polar coordinates
6. Evaluate triple integrals in Cartesian, cylindrical, and spherical coordinates
7. Evaluate line integrals and surface integrals of vector fields
8. Use Green’s Theorem, Stokes’ Theorem, and Gauss’ Divergence theorem

1. Vectors and three-dimensional objects
   1. Algebraic operations
   2. Dot (scalar) and cross (vector) products
   3. Lines in space
   4. Vector-valued functions and space curves
   5. Planes
   6. Quadric surfaces
   7. Parametric surfaces
2. Calculus of vector-valued functions
   1. Limits
   2. Derivatives
   3. Integrals
   4. Curvature
   5. Arc Length
   6. Applications to motion
3. Multivariate functions and their derivatives
   1. Contour diagrams
   2. Graphs
   3. Limits and continuity
   4. Partial derivatives
   5. Gradients and directional derivatives
   6. Local linearization and differentials
   7. Chain rule
   8. Optimization, including the method of Lagrange multipliers
4. Integration
   1. Double integrals: rectangular coordinates
   2. Double integrals: polar coordinates
   3. Change in variables in double integrals
   4. Triple integrals: rectangular coordinates
   5. Triple integrals: cylindrical and spherical coordinates
   6. Volume applications of double and triple integrals
   7. Surface area and surface integrals
5. Calculus of vectors
   1. Vector fields
   2. Line integrals
   3. Divergence and curl
   4. Green’s Theorem and Stokes’ Theorem
   5. Divergence Theorem

 
Course Addendum - Syllabus (Click to expand)