MA 3501 - Engineering Mathematics I

• Perform vector operations and their applications to area and volume
• Determine the length of parametrically defined curves
• Find tangent lines to parametrically defined curves
• Find gradients and directional derivatives
• Find tangent planes and normal lines to surfaces
• Find extrema of functions of two variables
• Evaluate the integrals and interpret the results as Work
• Evaluate curl and divergence of a vector field
• Evaluate iterated integrals, including the interchange of order in rectangular and polar coordinates
• Evaluate moments and centroids
• Apply Green’s Theorem to evaluate line integrals around simple closed curves

• MA 226   or equivalent: differentiation of trigonometric, inverse trigonometric, exponential and logarithmic functions, techniques of integration (direct and inverse substitution, integration by parts, trigonometric integrals and partial fractions)

• Parametric Equations
• Arc-length (in R2)
• Arc-Length (in R2 & R3)
• Vectors and vector operations (scalar (dot) product)
• Vectors and vector operations ( vector (cross) product)
• Applications of Vectors
• The geometry of R3
• Spheres, Lines and planes in R3
• Lines and Planes in R3 (parametric interpretation)
• Partial Derivatives
• Gradients and Total Differentials
• Directional Derivatives and Tangents
• Tangents and Normals
• Tangents and Normals (level surface interpretation)
• Maxima and Minima of Functions of Two Variables
• Line Integrals
• Line Integrals as Work
• Independence of Path
• Curl and Divergence
• Double Integrals (Rectangular Regions)
• Iterated Integrals
• Iterated Integrals, Interchange of Order
• Centroids and Moments (in R2)
• Green’s Theorem
• Polar Coordinates
• Double Integrals in Polar Coordinates