Math 3 Multivariable Calculus (4 credits) & Linear Algebra (1 credits)
Course Outline for Meetings 5 Days Per Week for 14 Weeks + Final Week |
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Topics |
Thomas' Calculus 10th ed. |
Days |
Project/Lab |
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Overview of Calculus Topics (1 week) |
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Basic Concepts & Important Theorems (MVTs & FTIC) |
3.2, 4.5 |
1 |
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L’Hôpital’s Rule and Important Limits |
7.6 |
1 |
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Improper Integrals and Monte Carlo Numerical Integration |
7.5, 7.7 |
1.5 |
Lab on improper integrals and Monte Carlo integration |
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Conic Sections and Polar Coordinates |
9.5, 9.6, 10.8 |
1.5 |
Students research and report on satellite or planet orbits |
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Vector Functions of a Scalar Variable (3 weeks) |
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Vectors in the Plane |
9.1, 9.2 |
1 |
Lab on the dot product and using vectors to represent lines and find distances |
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Linear Regression Using Vectors |
Worksheet |
1 |
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Modeling Projectile Motion with Parametric Equations |
9.3, 9.4 |
2 |
Lab on motion of a figure skater |
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EXAM |
1 |
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Vectors in Space and the Algebra of Vectors |
10.1 |
1 |
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Angles, Orthogonality, and Projections |
10.2 |
2 |
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Equations of Lines and Planes in 3-Space |
10.3 |
1 |
Lab on using vector definitions to graph lines and planes |
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Linear Transformations |
10.3 |
1 |
Lab on mappings and x-ray projections |
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Lines and Curves in Parametric Form |
10.5 |
2 |
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Vector-Valued Functions and the TNB Frame |
10.5-10.7 |
2 |
Lab on moving in 3-D |
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EXAM |
1 |
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Scalar Functions of Vector Variables (6 weeks) |
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Cylinders and Quadric Surfaces |
10.4 |
2 |
Lab on plotting cylinders and quadric surfaces |
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Cylindrical and Spherical Coordinates |
12.6 |
2 |
Lab on plotting surfaces and contours and plotting in different coordinate systems |
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Surfaces and Level Curves |
11.1,11.2 |
3 |
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Partial Derivatives |
11.3 |
1 |
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Gradient and Directional Derivative |
11.5 |
3 |
Lab on the directional derivative |
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Tangent Planes and Linearization |
11.6 |
2 |
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EXAM |
1 |
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Unconstrained Optimization |
11.7 |
2 |
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Constrained Optimization |
11.8 |
2 |
Lab on Lagrange skateboarding |
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Partial Differential Equations |
End of 11 |
1 |
Lab on the heat equation |
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Multiple Integrals (Double and Triple) |
12.1,12.4 |
3 |
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Multiple Integrals in Different Coordinate Systems |
12.3,12.6 |
2 |
Lab on setting up and computing volume integrals |
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Applications of Multiple Integrals |
12.2,12.5 |
3 |
Lab on applications of means and moments |
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Jacobian Matrix for Transformations |
12.7 |
1 |
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Monte Carlo Methods for Double Integrals |
7.5 in 3D |
1 |
Lab on applying Monte Carlo method in 3-D and analyzing the error |
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EXAM |
1 |
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Vector Functions of Vector Variables (2.5 weeks) |
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Line Integrals, Work, and Flux |
13.1-13.3 |
5 |
Lab exploring work integrals with conservative and nonconservative forces |
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Green's Theorem and Conservative Force Fields |
13.4 |
4 |
Lab verifying Green’s Theorem in circulation and flux forms |
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Surface Integrals (Stokes' and Divergence) |
13.5-13.8 |
3 |
Lab exploring surface integrals and applying the Divergence Theorem |
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EXAM |
1 |
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Series (1 week) |
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Taylor Series and Linearizations |
8.7,11.10 |
2 |
Lab demonstrating Taylor series expansions |
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Euler's Formula |
8.7, A-4 |
.5 |
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Fourier Series |
8.9, 8.10 |
2 |
Lab computing the coefficients of the Fourier series and applying the results |
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Final Student Presentations and Wrap-up (.5 week) |
2.5 |
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FINAL COMPREHENSIVE EXAM |
Week 15 |
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