MAT 281 - Calculus III
Triple integrals with cylindrical and spherical coordinates. Vector geometry and vector calculus in two and three dimensions. Calculus of multivariable functions: gradient, extrema and optimization (with and without constraints). Line and surface integrals. Green's theorem and Stokes' theorem.
Prerequisite: MAT 182 Calculus II
4 Class Hours
Learning Outcomes of the Course:
Upon successful completion of this course the student will be able to:
1. Graph surfaces in three space.
2. Find the domain and determine continuity of a function of two or more variables.
3. Compute limits of functions of two variables.
4. Compute partial derivatives.
5. Find directional derivatives and gradients.
6. Find maxima and minima of functions of several variables.
7. Find derivatives using the multivariable chain rule.
8. Compute iterated integrals.
9. Find volume by using double integrals.
10. Find area and volume by using iterated integrals.
11. Compute triple integrals using rectangular, cylindrical and spherical coordinates.
12. Use triple integrals to solve application problems.
13. Compute line and surface integrals.
14. Use Green's Theorem and Stokes' Theorem.
15. Use LaGrange Multipliers.
16. Use graphing calculators to aid in problem solving.
17. Find scalar and vector products.
18. Use vector-valued functions.
19. Find unit tangents and normal vectors.
20. Find equations of lines and planes in three spaces.
21. Evaluate curvature.
22. Describe the motion of a projectile using vectors.
In the context of the course objectives listed above, upon successful completion of this course the student will be able to:
1. Interpret and draw inferences from mathematical models such as formulas, graphs, tables and schematics.
2. Represent mathematical information symbolically, visually, numerically and verbally.
3. Employ quantitative methods such as arithmetic, algebra, geometry, or statistics to solve problems.
4. Estimate and check mathematical results for reasonableness.
5. Recognize the limitations of mathematical and statistical methods.
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