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 line integrals and interpret the result 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

• Differentiation of trigonmetric, inverse trigonometric, exponential and logarithmic functions, techniques of integration (direct and inverse substitution, integration by parts, trigonometric integrals and partial fractions)

• Vector operations
• Calculus of several variables, including use of gradients, partial differentiation and multiple integrals, curl and divergence and Green’s Theorem