This course is an introduction to multivariable calculus. It includes the study of three dimensional space curves, vector-valued functions, partial derivatives, differentials, directional derivatives, multiple integration, vector fields, line integrals, Greens and Stokes theorems, surface integrals, and the divergence theorem.
Prerequisites
MATH& 153 or permission of instructor.
Upon successful completion of the course, students should be able to demonstrate the following knowledge or skills:
- Visualize three dimensional mathematical objects.
- Find the limits of multidimensional functions.
- Differentiate and integrate multidimensional functions.
- Find extreme of multidimensional functions.
- Find the surface area and volume of multidimensional objects.
- Solve applied problems in physics and engineering using the calculus of several dimensions.
IO2 Quantitative Reasoning: Students will be able to reason mathematically.
Introduction to functions of several variables
Limits and continuity
Partial derivatives
Differentials
Chain rule for functions of several variables
Directions derivatives and gradients
Tangent planes and normal lines
Extrema of functions of two variables
Multiple Integration
Terated integrals and area in the deplane
Double integrals and volume
Change of variables: Polar Coordinates
Center of mass and moments of inertia
Surface area
Triple integrals and applications
Triple integrals in cylindrical and spherical coordinates
Change of variables: Jacobians
Vector Analysis
Vector Fields
Line integrals
Conservative vector fields and independence of path
Green’s theorem
Surface integrals
Divergence theorem
Stoke’s theorem